• JOHNS HOPKINS UNIVERSITY CIRCULARS

Published wit/i the approbation ofthe Board of Trustees

VOL. 11.—No. 25.11 BAlTIMORE, AUGUST, 1883. [PRIcE 10 CENTS.

CALENDAR, 1883-84. Tuesday, September 18. Next Term Begins. Tuesday, Sept. 18—Saturday, Sept. 22. Examinations for Matriculation. Tuesday, September 25. Instructions Resumed. Friday, June 7. Next Term Closes.

CONTENTS. PACE PAGE Scientific Notes: ~. M. ARMSTRONG, Taxation in Maryland.—T. WILLIAMS, Phzlology. The Revised Tariff in its Relation to the Economic History B. L. GILDI~RSLEEVI~, Symmetry in. Pindar.—A. H. TOLMAN, of the United States, 140—148 Lawsof Tone-Color in the English Language.—J. R. HARRIs, Notes on the Euthalian Stichometry—A. M. ELLIOTT, Pane- Biology. tional Differences of the Pa4 Participle in the Periphrastic E Ml. HAUTWELL, On the Relation of Bilateral Symmetry to Perfects of the Latin, etc—Mi. WARRRN On a Plautine Pun..— Function.—A. H. TUTTLE, Ciliated Epithelium in the Human M. BLOOM FIELD, Etymologyof~iAog.—H. C. G. V. .JAGEMANN, Kidney 149 Relation of the Norman Dialect to English Pronunciation.— Correspondence: C. W. E. MILLER, Lyricand Non-lyric in Aristophanes.— B. L. GILDERSLERVE, Note on the last named paper, . 138-142 ~ braryHAMMOND.—A.Building CAYLEY.—N. H. MORIsON, The Peabody 160—161Li MetIsemetics. J. J. SYLVESTER, On F’arey Series.—W. E. STORY, On the Num- Effects of Temperature on the Mammalian Heart, by H. N. ber of Intersections of Curves traced on aScroll of any Order.— MARTIN, ...... 151 F. FRANKLIN, On an Expression fir Euler’s Constant—A. S. The Eclipse of the Sun on May 6, 1883, . . . . 162 HATHAWAY, A Proof of a Theorem of Jacobi.—O. H. MITCHRLL, Note on Conic Sections.—E W. DAvis, Note on List of Works in the Peabody Library Relating to Assyrian, Bi,~odal Quartics.—E. BARNES, Note on the Strophoids.— etc., Texts, and Inscriptions 168 G. S. ELY, Some Notes on the Numbers of Bernoullli and Euler 143—146 List of Models of Mathematical Surfaces 154 Physics. Synopsis of Recent Journals: C. H. KOYL, On Professor Langley’s “Selective Absorption,” . 145 American Jotirnal of Philology 164 History and Political Science. Degrees Conferred, 1883 166 C. H. SHINN, Spanish Plots in the Southwest; Immigration.— Appointments, 1883-84, 155 F. J. GooDNGW, The Office of Public Prosecut~r.—H. W. CAL DWELL, The Income Tax in the United States. — Proceedings of Societies, 166

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University Circular, No. 24, containing announcements of the courses offered for the next academic year, and a Special Circular relating to College Courses will be sent on application~ 138 JOHNS HOPKINS [No. 25.

SCIENTIFIC NOTES On the work of Members of this University in Mathematics, Physics, Chemistry, Biology, Ancient and Modern Languages, History, Political Science, Psychology, Ethics, and Logic. NOTES IN PHILOLOGY. that Delphic expressioa, it ought to have an m~qoPa2u6t’ also. But there is Symmetry in Pindar, by B. L. GILDE1I~LEEVE. danger of carrying the analogy too far. The trunk of man, for instance, [Abstract of a paper read at the meeting of the University Philological Association, is beautifully symmetrical on the outside, but within the vital organs are April 6, 1883]. packed away with scant regard to symmetry. Beart, lungs, liver, with- It is impossible for any one that studies Greek literary art not to out which the skin would be a dead hide, are not remarkable for the count on symmetry. The tendency to balance, to parallelism is univer- balance of their forms. So it may be said that the inner organism of a sal. In Greek the tendency is a law. Pindaric ode need not correspond to the outer form, and that the five It is needless to enlarge on this. The law of correspondence—measure triads of the Third Pythian may be chopped up into seven Terpandrian answering to measure—is fundamental and has been applied to every parts—chopped up, for the knife does not come down on the rhythmical sphere of Greek art, pictorial, plastic, literary, not without overstraining, joints. But where shall we find anything like this in Greek literature? yet not without great profit. In music as in architecture it is unques- The further we penetrate into Greek poetry, the greater reason have we tioned. Even frivolous Offenbach has said: “Music is an algebra.” to acknowledge the reign of symmetry. Violation of symmetry, of cor- Poetry like music is made up of equations. respondence, may be referred in every instance either to defective tradi- In Pindar the symmetry of form is evident. The odes are composed tion or to designed disturbance. As in Greek architecture, so in Greek either of corresponding strophes or of corresponding triads (strophe, anti- poetry, departures from symmetry are not only suffered but enjoined strophe, and epode). But this is not enough. There must be within each for the sake of a higher symmetrical effect, for the maintenance of the strophe, each epode, another balance, another correspondence, another feeling of life. The straight line of mechanics becomes the curved line symmetry. Westphal first distinctly postulated this correspondence and of art. The entasis of the Doria column, the flexure of the Doria stylobate opened the way for the establishment of it, but like other bold and bril- are familiar illustrations of the law of visual effect. The Greek artist liant originators, he wearied of his own work, renounced his own princi- had regard to the position that his work was to occupy, to the angle in ples. Perhaps he did not like his following. Heinrich Schmidt began which it would present itself to the eye of the beholder. So in Greek his metrical and rhythmical studies as a worker on the lines laid down by poetry we must consider the law of higher symmetry, the principle of Westphal, although he differs from his forerunner at every turn, and in artistic unity, the calculated effect on the hearer—and we must remember the last few weeks Moriz Schmidt, well known as a Pindaric scholar, far that we have to do with the hearer, not with the reader. ~2rtxoiivOiais from being satisfied with the results of his predecessors, has set up his well, but when passionate utterance gives two verses the time of one, we schemes in opposition to Westphal’s and Heinrich Schmidt’s. must not heedle-sly apply the knife because the passage looks out of bal- A sample of the divergencies may be given. In the epode of 0. 6 Ross- ance. But these interferences apart, we expect a symmetry in contents bach-Westphal saw three mesodic periods with an epodikon: corresponding to symmetry in form, and we cannot admit a logical divis- ion which shall ruthlessly run across all the lines of the artistic structure. 1.3,2,3. II. 442,44. III. 43,33,33,4. 4Epod. We must seek the symmetry of thought, where the symmetry of the form is revealed, in strophe, in triad. Each strophe has its office, each triad Heinrich Schmidt marks five: its function, and as it is important that nothing should tempt the eye I. 323. II. 442. Ill. 44,4. 3br. IV. 3333. V. 44. from its work, an edition of Pindar, with a triad on each page, is almost a necessity to the student who wishes to approach the poet directly. The Moriz Schmidt pronounces both wrong and constructs a different only concessions that must be made to logical distribution are those that scheme: must be made in the same department of art. We must simply allow.the A 6 44 6=20. B 44444= 16. A’ 66 44=20. strophe and the triad the same play that we allow foot and series in the It will be observed that the number of bars in Rossbach-Westphal end verse.* in H. Schmidt is the same. In Moriz Schmidt, owing to the great range Reduce the Terpandrian v6,io~ to a more simple expression, see in it he allows himself in the use of rov4 and ?uc ia—the power of prolonging nothing more than a somewhat bizarre statement of the general principles and the power of resting—the number is slightly increased. He has that manifest themselves in an oration of Isokrates or a dialogue of Plato fifty-six against flftythree. But the other differences are graver. Still as well as in an ode of Pindar, and I should not object to become a Ter- whether we accept the short periods or the long, the recognition of some pandrian myself. Certainly I should prefer that result to the acceptance principle of symmetry cannot be withheld. These choral structures were of Dissen’s elaborate systematization. ln his chapter “De dispositione made not only to balance each other, but also to balance themselves. partium,” Dissen has treated at length the arrangement of the elements So niuch for symmetry of form. Is there any corresponding symmetry of the epinikion—the preparatory office of the prooemium and the inter- of contents? We find it elsewhere in Greek poetry. We find response weaving of the parts. “With the exception of the very short pieces,” he of antistrophe to strophe in the drama, not only in form but to a certain says, “all Pindar’s odes have at least two parts besides the prooemium,” degree in sense. Are we to renounce this in Pindar? If we are to listen and Dissen has interested himself in showing how the poet prepares his to the oracles of to-day, yes I Westphal found in Pollux a notice of the theme, interposes a myth, and then returns to his theme, and how from Terpandrian v6~ao~, emended it, applied it. What is true in it amounts the simple arrangement which he represents by a b a, the poet advances to simply to the old principle of beginning, middle, end. To be sure abaca, abcba, abcbda, and the crowning glory, abededa. ~irap~d,[tcrapxd, aararpowd, b~la2~6g, ficra ararpow6s, albpayi~, t~66tov have a ~ ~=-~ mystic sound, but the seven parts (iMlezger gives eight) are not all found in each ode, and, so far as I can see, the discovery amounts to nothing * See Croiset’s chapter on this subject, in his “Pindare.” The views I amhere present- more than the rednnouncement of a requirement as old as art itself. Plato ing I have long entertained, but in this, as in all other matters, I am more desirous of demands of every 2u6yoi’ that it shall be a ~5ov. A ~5ov ought to have thinking a right thought than a new one. As I have not gone into the question of the 5 cannot be content without head and foot, and if the b~opa2~6iPvxot of to-day relation of strophe to antistrophe and epo~e, I would add here that J. H. H. Schmidt, in his Metrik (S. 350), has shown that Pindar has paused shout twice as often at the end * ‘O~uI,aX611IvXeL dicti primum Bogomili; deinde ila appellati per indibriurn a Barlamo of the strophe as at the end of the antistrophe. The object of this, as Schmidt thinks, Calabro monachi aetatis istins qul Sc ievxsor6e vocahant, a modo qno preces fondehant, isto breakup themechanical balance ofstrophe and antistrophe, or, as heputs it, e+ (a -I- b) KLVSVVIE5 nempe rbv aLe.fh is more common than a -j- a + (8). Thisis, ofcourse, a reinforcement ofthe position taken in this paper, 6v,etc. 1r~v ~iaA~bv ai’in’ iAp v&~ ~;‘ IS~e,~) i-ac KOLALSC ~yevvDL’CANGE.KaTa rev ~,.c4~a;\ AUGUST, 1883.] UNIVERSITY CIRC ULAI?S. 139

There is of course an element of truth in these recurrences. There is a offended by the excurrence there nor the mind by the excurrence here. cyclical movement in many of the Pindaric odes. The myth is usually Making this allowance then and suffering the sense to bind strophes and belted by the praise of the victor and the victor’s home, but it is impos- triads together while the dominant themes of strophes and triads are sible to accept an elaborately systematic arrangement of the subject within distinct, we shall find no insuperable difficulty in establishing simple the symmetrical structure of the rhythm and independent of it. Dyads and easy proportions for most of the Pindaric poems. Problems there and triads there are in Pindar, but they’ do not disturb the rhythmi- will always be, and bold would be the man who should maintain that he cal working of the odes; and Dissen often elevates to the rank of an had said the last word on such a theme. organic part what has been brought in simply as a foil. Everything in Of the forty-four ]?indaric odes, seven only are composed in single Pindar must have a deep significance, an independent value, a special strophes. allusion, whereas much is put there for the sake of heightening the effect Of these, 0. 14 has two, P. 12, four, N. 2, five, P. 6, six, I. 7, seven, N. by contrast. 9, eleven, N. 4, twelve. 7 Dissen has gone through all the odes and reduced them to schemes, for Most of them are in triads: which he claims great simplicity and beauty. Furtwdngler has selected a few, and expended on them a great wealth of fancy. It cannot be said of Onetriad: 0. 4, 11(10), 12; P.2 4 him that he is indifferent to the claims of symmetry. To him the Pin- Three triads: 0.3,5; N. 5,6,8,11; 1.2,4,5,6, . . . 10 daric odes are so many temples, and he sees ground-plans and elevations, Four triads: 0. 1,8,9, P.2,5,10, 11; N. 1,3,1. 1,. . . 10 and rows of columns, and groups of figures in the rhythmical structures Five triads: 0. 2, 6, 7, 10(11), 13 P. 1, 3, 8, 9, N. 7,10, I. 3, . 12 of Pindar. Most persons will consider Furtwdngler’s book a waste of fancy Thirteen triads~ P 4 1 and ingenuity, and yet it has not been written all in vain. Temple and 44 ode are both built on a plan, both obey the laws of symmetry, and so one may serve to illustrate the other. But the manifestations are dif- It is evident that the single strophe poems will admit of greater free- ferent. The temple is to be developed from the cell, the ode from the dom of handling, and I shall take those up after discussing the triadic rhyjhm. Regard the ode as a great verse and much of the difficulty poems. in finding symmetry in the Pindaric poems will disappear. One triad is evidently too short for any except slight occasional poems. Is it a mere fancy to regard the odes as a great verse? Certainly not. In 0. 4, an exceptional poem, the strophe has chiefly to do with God, the There are trochees and trochees, the ordinary trochee (tribrach) antistrophe chiefly with man, the epode is an illustrative myth. In 0. 11 (111) and the rpo~a~o~ a avr6 (444). The strong part is to the (10) the antithetical structure runs through strophe, antistrophe, and weak part as 2: 1 in both cases. And so, ifthe analysis proved it, I should epode, but each member revolves about a separate element of the iwcviiaov. not objectto calling Pindars triads trochees or chorees, his tetrads dactyls, 0. 12 rocks even more than 0. 11 (10). Each element is distinct. P. 7 has and his pentads cretics, only that system does not seem to work. But we bee,s considered a fragment, but whether it is a fragment or not, each do notice and shall hope to consider more carefully hereafter a manner of member has its special office. limitation to the length of the Pindaric odes. Take out the Fourth Two-triad poems do not occur.* The only two-strophe poem 0. 14 is Pythian and no ode made up ofstrophe, antistrophe, and epode goes beyond suspicious, and cannot be cited to prove that two triads would give ample a pentad. This has its analogy in the law of limit to the length of series. room. If we are to have introduction, myth, and conclusion, it would be The iambus and the trochee are limited to eighteen morae (2 x 3 x 3), the hard to distribute them properly through two triads. Three triads give dactyl to sixteen (4 x 4) the cretic to twenty-five (5 X 5). That is to a natural division, and so we find that it is used nearly as often as five, say, each typical foot gives the norm for combination according to its own though the number five suggests a better proportion logically. Each triad proportion. A dactylic verse when reproducing.cretic movement cannot has its dominant theme. 0. 5 occupies an exceptional position among the go beyond the square of the cretic. The dactylic pentapody Pindaric poems, but the distribution forms no exception. There is no overlapping in it. 5 4 5 Four triads are used as often as three. There is no mechanical uni- formity, but, as we should expect, the introduction would dominate one is a cretic on a large scale, and the 20 rnorae which compose it fall within triad, the myth two, the conclusion one, in most of the odes. This is the the 5 >K 5. In like manner, the limitation of the number of Pindar’s sys- type, 1 . .2. 1. Overlapping is the rule. It is remarkable that in Pindar’s tems inevits~bly suggests the principle of a rhythmical proportion in the earliest piece, P. 10, there is no overlapping, and the student of English whole piece, which proportion is dependent on the relation of strophe to versiflcation will be reminded of the early timidity of blank verse. P. 10 epode. But it would be premature to discuss this point now, and, besides, then would present us with 1 . 2. 1, pure and simple. Under 1 . 2. 1, I the problem of immediate interest is the distribution of the matter of the ode among the strophes or the trinds, as the case may be, and here the would put 0. 1, 0. 9, N. 8. Under 1 . 2. 1, I would put 0. 11. analogue of the verse as a rhythmical structure and the verse as a logical unit will aid us. The verse, as a rhythmical structure, is made up of 0. 8, I. 1, might be represented by 1. 1 . 2, N. 1 by 1. 1 . 2, P. 2 by 1. 1 verse-feet; the verse, as a logical unit, is made up of word-feet. The 1+1. I. 3isopentodiscussion. P. Sis 1+1.1.1. coincidence and the discrepancy of verse-foot and word-foot constitute respectively diceresis and caesura, if, indeed, one may be allowed to use Five triads might be expected to distribute themselves thus: Introduc- this nomenclature, which certainly has its convenience. tion = 1, Myth = 3, Conclusion = 1, and this is the arrangement in 0. 2, Now a verse in which verse-foot and word-foot should coincide through- 0.6, 0.7, 0.10 (11), P.8, N.10. On the other hand 0. 13(1+1.2.1) out as in the famous sparsis j hasiis I longis campus splendet et lsorret and P. 1 (2. 2. 1) have a quasi epodic structure, two triads representing of Ennius would lack unity, and a succession of them would be intoler- strophe, two antistrophe and one the epode. But P. 3 and P. 9 throw ably monotonous. Hence the office of caesura to effect unity by dividing the weight of the poem on the myth, which leads, (3 . 1. 1), while the a word between two feet and so to force a more energetic recitation. structure of N. 7 is far from being transparent on any theory. Diaeresis serves to distribute the masses, caesura to unite them. In the Fourth Pythian we have no less than thirteen triads, and it might Of course where the masses are so large as in the Pindaric odes there is seem at first as if the epic mass had crushed the lyric proportion. But not the same danger of monotony. Each triad might present a complete when we examine the structure more closely we find that the first three whole. In fact each strophe, each antistrophe, each epode might be triads form the overture, if I may say so. It is a prelude which gives the rounded off as a separate element without much offence. But the Greek motif of the piece. These three triads are followed by seven triads with sense of unity demanded a less mechanical distribution, and the parts of the story of the Argonauts in detail, while the conclusion is prepared and each ode often fit into each other as the parts of an hexameter or a tri- consummated in the last three triads. meter. The preparation, as Dissen would call it, does not count, nor Of the strophic poems I have already considered 0. 14. In P. 12 we does the connexion. The body of the thought falls within the limits; recognize the familiar distribution 1. 2. 1. P. 6 is represented by 2. 2 .2. that is enough. In studying the Pindaric odes I have often thought of the lines of color used in maps to designate boundaries. The eye is not * See J. H. H. Schmidt, Metrik, s. 349. 140 JOHNS HOPKINS [No. 25.

[Notes in Philology Continued]. Introductory Note on the Eutlialian Stichometry, by J. IREN-. In N. 2 there.is a curious iteration of the name of the victor and his fam- DEL HARRIS. ily 1. 1 + 1 + 1. 1. The twelve strophes of N. 4 divide into 3. 6. 8, the [Abstractof a paper read at a meeting of the University Philological Association, April 6, 1883]. eleven of N. 9 into 2 . 7 . 2. The difficult I. 7 with its seven strophes is The object of this paper was to clear away certain fundamental miscon- reserved. ceptions as to the connexion between the arixom, which are so often reck- To those who must have sharp figures at any cost, these statements will oned in MSS. of the New Testament, and a certain Euthalius, a deacon be disappointing, hut the exact symmetry is cared for in the rhythm, the of the Church of Alexandria somewhere about A. D., 458. It was metre. We should he offended by an irregular wall. For the figures shown that in no sense was Euthalius the author of stichometric divisions, that surmount the wall we only claim a general balance. nor did these in the New Testament correspond to sentences. The importance of the work of Euthalius consists in the fact that he professes to have made accurate measurements upon superior MSS. viz., those preserved at Cie~area in the Library of Pamphilus. The Laws of Tone.Color in the English Language, by A. The principal authority for Euthalius is Zacagni, Colleclanea monumen- H. TOLMAN. torum veterum ecciesice Grcecce, Rome, 1698, from which a full idea may be gained of the prefaces and pi~ologues introduced by Euthalius and the [Abstract ofa paperread at a meeting of the University Philological Association, May 4, 1883]. passages measured. The primary requirements of artistic language are clearness, concise- As an example of the work of Euthalius we may take the Acts of the ness, rhythm, and suggestiveness. Tone color is usually secondary and Apostles which is divided into 16 lections, to each of which the stichome- subordinate. Tone-color is the difference between sounds of the same tric subscription is appended. lt becomes, therefore, interesting to ex- pitch and intensity. For convenience we speak of the consonant and amine whether these lections correspond to the appended number of verses, upon the supposition ofa fixed hexameter cri~o~. vowel colors. The proposition is that• certain colors naturally express M. Graux (Revue de Philologie: April, 1878) seems to have attempted certain allied ideas and emotions. Other colors may express them accord- ing to the accepted meanings of the words, but they will lack the force this comparison, but was perplexed to find that the numbers given by Zecagni, from the Vatican MS. Regius Alexandrinus, did not correspond which comes from an inner fitness between the coloring and the idea. Tone-color has been neglected for two reasons: 1st. It has given rise with those supplied by a Madrid MS. Codex Escorial, ~— 111-6 and apparently dropped the subject. to unpopular or indefinite theories as to the origin of language, such as Onomatopmia and Laut-metaphor. But Onomatopmia and Laut-metaphor Comparison is now given, for the Acts of the Apostles, in the following as facts in artistic language may be true, irrespective of the use which table between the data supplied by Zacagni’, and the Madrid MS., and the actual measurement of the text of Westcott and Hort’s New Testa- Wedgwood, Heyse, and others make~of them. 2d. Investigators have ment into 16-syllabled hexameters. not recognized the subordinate character of tone-color. Vowel Colors. The accented vowel colors form a natural scale. The Lection. Chapter&Verse. Cod. Esc. R.Al. Syllabic. colors at one end naturally express certain ideas and emotions, and those 1 i.1 40 — 40 at the other end the contrasted ideas. The order of the vowels in natural 2 i.15 80 80 30 pitch, their physiological order, and the law of onomatopeia, as given by 3 ii.1 109 109 111 Koch and Wedgwood, all confirm the scale which was given. The laws 4 iii.l 136 136 143 of correct elocution are such that differences in natural pitch, &c., must S iv.32 100 100 121 give a difference in the natural expressional power of each vowel. 6 vi. 1 88 220 188 Quotations from Shakapeare and others were given, illustrating the .7 vii.1 (iyivrro) 92 120 94 general scale and important specializations. A table was given, showing 8 viii.1 75 95 77 by per centages the use of the different colors in Poe’s poem, The Bells. 9 ix.32 216 250 210 (Jonsonant Colors. The natural expressional power of each consonant 10 xi.27 283 300 271 color, and class of colors, was discussed and illustrated by quotations. 11 xv.1 193 200 201 Anastomosis, the joining of words. This must be smooth, unless 12 xvii.1 164 180 164 struggle or difficulty is to be expressed. 13 xix.1 239 240 239 Variety of Coloring. The most complete variety possible is rarely 14 xxi. 15 293 293 307 called for in artistic language. 15 xxiv.27 168 268 158 Repetition and Similarity of Coloring. Poetry regularly repeats the 16 xxvii.1 198 192 coloring in some form, as it repeats ideas and the verse-foot. Every color repetition is expressive or non-expressive; that is, it either makes use of Some corrections are then made, and the total stichometry of the Acts the full expressional value of the color, or it is pleasant simply because it of the Apostles discussed. The remerkable agreement between the is a repetition, and gives a merely sensuous pleasure. columns is a sufficient proof that Euthalius measured by the sixteen syl- English verse began with alliteration. It has developed also rime, termi- labled hexameter or something very nearly equal to it. The subscrip- nal and internal; syzygy; assonance; the repetition of a word in the same tions, however, in R. Al. are frequently corrupt. connection; the repetition of a word within the line; the repetition of Similar results will shortly be exhibited for.the whole New Testament phrases, lines (refrains), and stanzas (choruse~). By syzygy and asson- and applied to its textual criticism. ance is meant, respectively, the general prevalence in a passage of some consonant or vowel color, or class of colors. Mr. Lanier ridicules asson- ance; but it is used by the best poets in proper moderation. 7.22 per cent. of the pentameter lines in Love’s Labor Lost, repeat an important word within the line; 2.21 per cent., in the Tempest. The Additional Note on the Ettthalian Stichometry, by J. REN- other comedies of Shakspeare come between these. DEL HARRIS. Rime was discussed. Contiguous nines should have contrasted colors, [Abstractof a paper read at a meeting of the University Philological Association, May which interferes with expressive riming where there is a fixed rime- 4,1883]. scheme. The measurements already tabulated for Westcott and Hort’s text show Repetitions of colors, and cases of a general similarity of coloring, are a remarkable agreement with the traditional numbers, but there is almost less prominent in prose, but are frequent and important. always an excess on thesideof the measured verses,and since it can hardly be maintained that the text of Westcott and Hort is open to the charge of too great expansion from primitive copies, it follows that the difference AUGUST, 1883] UNIVERSITY 011WULARS. 141 must be due to abbreviations on the part of Euthalius. Allowing a deduc- the participle idea were discussed, and their theories shown to be untena- 6~, and of two syl- tion of one syllable for the abbreviation of 6r6~, xpIar ble for certain phenomena, while they are insufficient to account for the lables for b~uoi~, ,ci3ptog, and correcting our previous results, we have varied growth of others under similar or identical influences. Traditional. Measured. James. 242 287 1 Peter. 286 289 2 Peter. 164 167 On a Plautine Pun, by M. WARREN. 1 John. 274 261 [Abstract of a paper read at a meeting of the University Philological Association, 2 John. 80 80 May 4, 1883.] 8 John. 82 81 In Aulularia, v, 49, it was proposed to keep the reading of the manu- Jude. 68 68 scripts Romans. 920 918 Tesiddineum i8turn tibi ego gradib6 gradum 1 Corinthians. 870 872 instead of changing it with the editors to grandibo. Plautus is fond of 2 Corinthians. 690 698 puns where there is a difference of quantity in the vowels of the words Galatians. 293 298 played upon, as ex6ssalum t~s, crilcietum cr~2sa1um, liido Islto, mitlis mitis, Ephesians. 812 818 indlis indium, heel infelicet. The tendency of n to disappear not only Philippians. 208 208 before s, but also before gutturals and dentals, was noticed and examples Colossians. 208 208 cited, e. g. before d in facieda, Kaledas, Secudus, cladestinus, quado, cf. 1 Thessalonians. 193 189~ Corssen Vocalismus I, p. 267 The epithet of Mars, Gradivus, cannot be 2 Thessalonians. 106 106 derived from grddios- on account of the difference in quantity, Grddivus Hebrews. 708 708 occurring only four times at the close of an hexameter, while Grddivus is 1 Timothy. 280 288 found at least fifty times. Gradivus probably stands for Grandivus. In 2 Timothy. 172 170 Cato H. R 141, 2, Mars is invoked, Utique tu fruges frumenta vineta vir- Titus. 97 97 guhta grandire beneque evenire sinas. As from the verb averruncare we Philemon. 88 40 have Averruncus, an averting deity, so from Grendire, Gra(n)divus, a Closer agreement it would be unreasonable to expect. deity promoting growth. This sense is especially appropriate in Vergil, Aen. III, 85. This paper appears in full in the American Journal of Philology, No. 18, pp. 71—76. Functional D~/[erences of the Past Participle in the Pen- phrastic Perfects of the Latin, Old and Modern French, by A. M. ELLIOTT. On the Etymology of ~oi2o~,by M. BLOOMFIELD. [Abstractofa paper read at a meeting ofthe UniversityPhilological Association) April [Abstractofa paper read at a meeting of the University Philological Association, April 6, 1883]. 6,1883]. In this paper it was proposed to characterize the development of the No less than six distinct etymologies have been proposed for this word, past passive participle in its periphrastic use with habere (avoir) in the and none has secured for itself the acceptance of scholars generally. classic Latin, low Latin, old and modern French, down to the formation With the exception of Vanidek, who ventures to accept the pronominal of the present rule of position. derivation of the stern (from sva- the reflexive) no larger work ventures For the classic Latin the law of agreement is absolute whether the direct to accept any of the proposed etymologies. ‘Pick’s Comparative Lexicon object precedes or follows the participle; in the low Latin, the inviolability and the fifth edition of Curtius’s Etymology are silent on the subject. of this law is encroached upon but the participle still maintains the rela- The latest etymology propounded by Osthoff in the Morphologisehe Unter- tion of verbal objective to the object, while in the earliest period of the suchungen, Vol. 1V, p. 229, according to which ~bPuofis derived from old French the language goes back to its classic model and constant accord the preposition ipi (in ~8topKo~)=sk. abhi, and means ‘bei-gehbrig, again becomes the only legitimate construction. As the analytic tenden- zugethan,’ is based upon wide-reaching new theories about Indo- cies of the language grow stronger towards the middle French period the European vocalism which are far from certain. correct participial forms are lost sight of, until, finally, the traditions of Thus a suggestion which may secure for the word a Sanskrit equivalent the mother tongue are entirely broken down, the verb habere (avoir) has can be made without attacking any well-established explanation. There given up its fundamental meaning of “to possess” and, as a simple auxil- are two proper names in Sanskrit, Gobhzla and Rebhila, whose first iary, forms with the participle a single compound notion, a mere verbal syllable may possibly be the diphthongal stems go ‘cow’ and re ‘property’ locution. In thesixteenth century there arose a controversy among the lit- (Lat. rds). In that case the remainder of the words, -bhila, would be terati and grammarians as to the proper principle that underlay the then sound for sound the Greek ~t?~o-and go-bhila would be ‘fond of cattle’; varying mode of treating the participle. Those who wished to stick to re.bhila, ‘fond of wealth.’ Gobhila is a name which occurs in the Vedic the Latin usage made agreement under all circumstances a binding rule, period and is otherwise totally unexplained. while their opponents, the supporters of the modern drift of the language, held to the invariability dogma throughout. Out of these two antagonis- tic schools an eclectic school was formed by each of the former contending parties giving up half of their territory. The variability dogmatists kept On Some Points in the Relation of the Norman Dialect to participial agreement when the object precedes, the invariability dogma- Eligush Pronunciation, by H. C. G. V. JAGEMANN. tists held their non.agreement of form when the object follows the parti- [Abstractof a paper read at a meeling of the University Philological Association, May. ciple. It is thus that the burden of the Marot rule, the so-called rule of 4, 1883]. position, was saddled upon us, from which many of the younger gram- marians in France to-day are struggling to free themselves by a return In this paper an attempt was made to show that the pronunciation of to the invariability doctrine, in conformity with the analytic spirit of the Romance words in English can be traced back to certain phonetic pecu- modern language. liarities of the Norman dialect. The subject will be treated more fully - The views of Brachet, Darmestetter, and Bastin, respecting participial in a future paper. - usages in the transition period from the old to the modern conception of 142 JOHIATS HOPKINS [No. 25.

-[Notes in Philology Continued]. the chief excellence of this play. It is more consistent in plot than any other of Aristophanes’ comedies. In the Ayes, there is only 14.5 per Lyric and Non-lyric in Aristophanes. cent. of lyric. This is due partly to the great length of the play, and partly to the fact that deficiency in quantity is made up by variety and I was induced to undertake the metrical study of Aristophanes by the quality. The large proportion of lyric in the Lysistrata and the Thes- hope of finding some normal proportion between the lyric and non-lyric mophoriazusle arises from the number of vaudeville songs in these plays. portions of the different plays. As it was impossible for’ me, on account The Ranae is the piece of Aristophanes’ second youth. The maximum of lack of time, to study thoroughly the different systems of Greek (21 per cent.) of lyric is reached in this play. The two remaining come- Rhythmic and Metric, I based my investigations on the system of J. II. dies, the Ecclesiazusae and the Plutus, show a great fall in the propor- H. Schmidt, with which I was acquainted. The results reached, in the tion of the lyric element. The reason is evident. We have here the course of the investigation, very soon showed that there was no such transition from Old Comedy to Middle Comedy. normal proportion as had been supposed yet, owing to some curious phe- nomena that presented themselves, I continued the metrical study of C. W. E. MILLER. Aristophanes, and finally prepared the table given below.* For the explanation of thetable the following remarks will suffice: The As a chance word of mine led to Mr. Miller’s very laborious investi- upper part of the table gives the statistics of the lyric portions, and the gation, I will add that while the results do not present an ample reward lowerpart those of the non-lyric. The right column of each play indicates for the trouble taken, still they give us a surer grasp of what was already the ratios in per cent, of the metrical length of the different rhythmical known, and I have caused the tables to be reproduced, as they may be of portions of the play to the metrical length of the whole play. The left service hereafter. It is not likely that Schmidt’s analysis will he accepted column gives the number of bars of the different rhythmical portions, as final, but, after all, the proportions would not have varied essentially measured according to the standard of the Iambic bar of three morae. on any reasonable basis of calculation. The modest inferences drawn by The prose column was added for the sake of completeness, and, for con-• Mr. Miller are in accord with the current characterization of the various venience’ sake, was placed at the bottom of the table. pieces. Aristophanes makes a vast stride in his art from the Acharnians What, perhaps, on inspection of the table, would surprise us most, is to the Knights. The cretics are overdone in the former; in the Knights the comparatively very low per cent. of lyric in the Clouds. This ‘I there is a reaction. The two elements, the parodic and the political, think, may be safely attributed to the bad tradition of the Clouds, and it mirror themselves in the varying proportions, and we can see clearly may be accounted for by the loss of a considerable lyric portion of the that the lambico-trochaic verse is the ground form of comic lyric, going play. The loss of a choral song before line 889, which is supposed by over into cretic in the strongly political plays. The Thesmophoriazusae almost all editors of Aristophanes to have taken place, is thus put and the Ecclesiazusae have no cretics, the Nubes practically none, and beyond the shadow of a doubt, and the loss of another after line 1104, their range is philosophic and artistic mainly. Logaoedic is a style com- suspected by some to have taken place, becomes exceedingly probable. mon to tragedy and comedy; the other forms, dochmiac, dactyl, dactylo- In the Acharnians, Aristophanes exhibits a kind of Aesehylean vigor. epitrite, Ionic (proper) are really parodic. The lyric element is very large. The Equites shows a considerable B. L. G. decrease in this respect. The dramatic element, however, constitutes

* ACHAB. EQUITES. ~UBES. VESVAE. PAX. AVES. LYSISTR. THESM. RANAB. EUCLES. PLUTIIS. TOTAL. METRES. Bars. 31 Bars. 31 Bars. Bars 31 Bars. 31 Bars. 31 Bars. 31 Bars. Bars. Bars. 31 Bars. 31 Bars.

Trochaic 152 2.067 136 1.484 41 .471 505 4.906 190 2.319 419 3.823 689 8.491 326 4.554 684 7.387 153 2.021 . 3301 3-443 Iambic 461 6.309 374 4.083 226 2.261 316 3072 208 2.539 274 2.500 203 2.501 312 4.456 374 4.038 251 3.316 196 2.504 3201 3.343 Logaoedic 64 .870 416 4.541 311 3.130 354 3.432 204 2.490 408 3.723 200 2.461 401 5.602 231 2.495 301 4.001 2894 3.019 Ionic 124 1.204 - 12 .109 . , - 120 1.296 , - 256 .267 Dactylic 13% .181 .233 1.651 85% .779 430% 4.651 . 716 .747 Dact. Ep 2.018 . , . - .172 Spoudaic 1091< .114 Anapaestic 18b .181 ‘.576 . 1.074 3~1< .461 . 74% .806 . . - 306~ .320 Cretic 6.436 1.346 .031 160 1.554 186 2.258 iii 1.004 203A 2.501 . 31% .3-42 . 1291 1.345 Bacchic 47~’ .041 .031 6% .06L 5 .062 13% .186 - 31% .032 Dochmiac 85k 1.166 32 .311 53% .486 26% .372 16 .204 213% .222 Total Lyric 1255% 17.076 1070% 11.688 776% 7.781 1556% 15.12] 952%. 11.625 1588% 14.4941337% 16.481 1086 15.172 1946 21.016 707 9.341 212 2.708 12488% 13.027

Trochaic Dim 76 .836 96 1.090 52 .474 . . 40 .528 . 250 .269 Trochaic Trim . - . . 6 .079 6 .806 Tr. Tetrameter 56e 7.611 960 10.482 448 4.490 1064 10.331 1160 14.258 1240 11.380 376 4.634 240 3.351 326 3.456 80 1.057 . 646~ 6.743 Sync. Tr. Tetr . . 176 2.169 . .. - 176 .183 Tr. Tripody 6 .08] . 6 .006 Tr. Tetrapody 16 21] . - . . 11 .017 Tr. Hexapody . 6 .074 . .006 Iamb. Monosa .217 .022 .080 2 .010 .024 4 .031 2 .025 2 .026 . 38 .040 Iamb. Dim 12 .163 4 .04] 116 1.163 0. .091 16 .141 16 .197 84 .90] . . 256 .267 I. Trimeter 4950 67.310 4122 45.001 4561 45.768 4494 43.663 4164 50.831 5538 50.53] 4266 52.582 4548 63.537 5040 54.43] 5346 70.636 6018 76.884 53052 55.344 I. Tetram 48 .652 1096 11.961 1056 10.588 144 1.399 96 1.171 552 6.804 366 3.022 536 5.781 56 .740 296 3.781 4240 4.423 Sync. I. Tetr 206 1.943 16 .191 . . 216 .225 I. Monopody .016 . I .001 I. Tetrapody 8 .108 . 8 .005 I. Hexapody 48 .652 6 .071 6 .081 36 .38 96 .100 362 3.608 .375 Metr. Eupel . 361) Pact. Tetram 2118 .261 ...... 21’s .022 Dact. Hexam 392 4.271 616 7.511 112 1.022 56 .696 48 .511 - 1224 1.277 Elegiac 16 .191 . 16 .017 Spond. Dim 2% .03 . 2% .003 Anapacat. Dim...., .906 128 1.39] 541% 5.426 406 3.886 600 7.32- 3.091 210% 2.596 442% 6.184 253% 2.731 1619% 1.444 96 1.221 3l86~ 3324 An. Tetram 352 4.786 130118 14.201 1101% 21.061 2431 23.622 416 5.071 1845/s 16.831 098% 13.542 373% 5.215 992 10.711 1216 16067 1205% 15.391 13333% 13.909 Prose 16 .217 8 .08] .026 33% .401 216 1.97: 102 1.426 4 .041 6 .072 387% ______.404 Total Non-Lyric.. 6098% 82.920 3089% 88.31]Ii1199% 92.218 8736 84870 88.37 9370 85.501 6775% 83.512 6072 84.820 7313% 78.981 6861% 90.6~0 7615% 97.29: 833701< 86.972 Total Lyric 1215% 17.070 1070% 11.681 776% 7.786 1556% 15.121 11.621 1588% 14.49~ 1337% 16.488 1086 15.172 1946 21.011 707 9.341 212 2.701 12488A 13.027 Sum Total 7354 100.000 9160 100.001 1976% 100.002I l0292%~100.00C 8191 %jlOO.000 [0958% 100.001 8111 100.006 7150 100.006 9259%100.001 7568% 100.002 7827% 100.001 95855l~ 100.000

. AUGUST, 1883.] UNIVERSITY CIRO ULA RS. 143

NOTES IN MATHEMATICS.

On Farey Series, by J. J. SYLVESTER. part of the number they enclose is to be taken. Hence

rAbstract of a paper read at a meeting of the University Mathematical Society, May f(n) = ~8(n) = ~8(n)+ P [-~~]+f[~] 16, 1883]. The ordinary Farey Series is a succession of proper vulgar fractions arranged in order of magnitude, whereof the denominator does not exceed a given amount. The theory may be generalized and simplified by consid- In this formula, let n be a power of 2, say 21e; then we have ering the terms of each fraction as the coordinates of a node in a “r~seau.” If a simple and anautolomic closed boundary drawn on a tesselation be called a scroll, and any node within it be assumed as origin, a radius of in- definite length rotating about that point as centre, will pass through a series

of nearest nodes to it in succession, all lying within the scroll — and the coupled coordinates to thosesuccessive points, say (p, q), (p’, q/), . . . will form a certain series which in general but not universally will satisfy the equation pq’ —p’q = 1 or = —1 according as the order of magnitude is descending or ascending. The character of the series may be termed Farey if this law is satisfied throughout the entire succession and otherwise —mlog2— Non-Farey. The character obviously can only depend on the form, mag- nitude, position, and aspectofthe scroll and the position of the assumed cen- tre. The author ofthe paper showed that the position of thecentre was indif- Hence, transposing the term in log 2, = log 2m, and making in infinite, ferent except that it must be taken at some node within the scroll, and that we have the scroll might undergo uniform expansion and contraction about any in- 1 11 ternal node (and consequently also translation along any line of nodes) with- 1—0=—— L2( 1ffi 1 out change of character. Application of these principles was made to a 3 triangular or rectangular scroll (including Mr. Glaisher’s extension of the theory of ordinary Farey Series to a two-fold constant limit), to the case potentially indicated by Dirichlet where the scroll is formed by two It is easily seen that this may be otherwise written asymptotes to, and the branch of a hyperbola, and two other cases: the 1—0= + + 4{3(~4-~7) + ~(9.1~.11 + 13.14.15) theory is deduced without the use of continued fractions or indeterminate linear equations or any other algebraical process whatever, from the well known fact that all elementary triangles in a reticulation are of equal area + ~(17.I8.19 +... + 29.30.31) +.. and from the not very recondite theorem that a triangle may be divided into 4 equal and similar triangles by straight lines joining the bisections of its three sides and with the aid of a solid reticulation may be extended to triplets and so on indefinitely. It will be found fully set forth in Note A Proof of a Theorem of Jacobi, by ARTHUR S. HATH.. H, interact, part 2, Vol. V, No. 4, American Journal of Mathemalics. AWAY. [Abstract of a paper read at a meeting of the University Mathematical Society, April 18, 1883]. Namely, that On the Number of Intersections of Curves Traced on a Scroll (1 + sxe)(1 + eXe+Y~) of any Order, by W. E. STORY. X (1 + exb)(1 ±exb+h) . . . ~ e+b 82 +e—b [Communicatedto the Mathematical Society, May 16, 1883]. In a former communication I gave a formula for the number of inter- 2 = 1, Xh =(1~~x1L)(l~x2h)a + b, a, b, being any~= quantities~ 2 whatever. sections of two curves of any orders on a ruled quadric. I have applied whereThe emethod is to obtain a general term from the above product by the same method to cubic scrolls. Curves of any given order traced on a selecting i exponents of x from the first line, j from the second line, and scroll may be classified according to the number of points in which they k from the third line, giving ei+J(~ 1)1~Xme+eb by virtue of the relation meet any generator. It is evident that a given curve of order m on a A = a + b. The forms of in and n show that, for all possible selec- given scroll meets every generator of the same infinite system (excepting tions giving the same in and the same n, i and j are not independent, perhaps the generators of a certain finite system) in the same number of being connected by the relation i —j = in — n = 6 suppose. Then again, points, say i. Such a curve I call an m~. If then (mi, nj) denotes the since a2 = 1,

number of intersections of an m~ with an n~j traced on the same scroll of 5~+J — — so that the selections divide themselves order ji, we have (mi, nj) =mj+ni—,tej, at least if jc <~• If ~ = 1, into those giving positive terms (fi even) and those giving negative terms every curveof order m on theplane is an mm, and we have ~ n~) = inn, (fi odd), which, it is easy to show by correspondences, cancel each other as in the formula here given. 6.6 + 1 except when a certain relation exists between in and n, viz., in = 2 when there is but one selection giving a positive term. This is the thee.. 6.6+1 On an Expression for Euler’s Constant, by F. FRANKLIN. rem in question, as we see by making the substitutions m = 2 [Abstract of a paper read at a meeting of the University Mathematical Society, May nin6 6—1. The 16, 1883. 2 correspondences are those: The partition of If we denote byf(n) the sum of the reciprocals of the natural numbers in is composed of i unrepeated integers,j unrepeated integers, A unrepeated from 1 to n inclusive, lim [f(n) — log n] = U, and this may be taken as integers, the first two sets of which may be converted into an indefinite a 00 the definition of 0, Euler’s constant. partition with 6.6±1. less units of content [form the arms of elbows 1111 1 2 of a graph out of the integers in the two sets, least integer corres- ponding to least integer, until one set is exhausted, the remaining inte-

thatf(n) — ~8(n)=f[~],the square bracketsindicating that the integer gers of the inexhausted set which have no correspondents being succes- sively reduced by 1, 2, . . . 6 or 0, 1, 2, . . . — 6 — 1, the total of which

. 144 JOHNS HOPKINS [No. 25.

[Notes in Mathematics, Continued]. Putting now R’ = + 1/di + 4h2, and substituting both values of R in 6.6±1.1 succession, we get reduction is 2 j• In other words a (1: 1) correspondence exists 6.6 + 1 f ~2h(+ 29) + (Y+S~R,) =0, between an i, 3, k partition of m and a partition of m — 2 consist- ing of an indefinite partition on one hand, and a k partition on the other. (~±~‘~) + (~±8~ Such a bipartition is itself an indefinite partition, and conversely, an 6.6+1 as the equations of the axes when d = -i-, and similar equations when d is negative. If A = ~-, the first equation gives the transverse axis; if indefinite partition of rn — 2 involving 6 different integers gives A = —, it is given by the second equation. For when A is positive, the rise to (1 + 1)0 such bipartitions [obtained by placing successively zero, negative value of R gives the real directrices, and the second equation one, two, etc., unequal integers upon the k side] giving rise to as 6.6+1. =0, (which contains the negative value of R) gives the axis parallel to the many even as odd values of k except when 6=0 or 2 real directrices, i. e., the conjugate axis, and vice versa. Other well-known results easily follow from these formulae. Thus, if when there is but one such bipartition [0; ] Q. E. D. The connection (x0, y~) be the centre, we have between this theorem and the theorem respecting a bipartition composed of unrepeated odd numbers, the number of parts in the two having a x~=e2 (p’a—*) h2~~ab’ constant difference 6, is at once seen by considering that an i, partition 3 af—hg is obtained from a parallel bipartition composed of odd numbers by tak- 2(,f~ ing the greater half of each integer in one partition and the lesser half in the other. 4 —4A Directrix to center =~‘“ = R~R —

2 — ab)~ Semi-axes = ep” = \I(R —_— 2A A Note on Conic Sections, by 0. II. MITCHELL. 4s)1h—RA [Abstractof a paper read at a meeting of the University Mathematical Seciety, March Focus to center = e2p” = \j(hi — 21, 1883].

The following elementary method of showing the quadruplex nature of Semi-parameter = e(p” — e2p”) = ~/ 8A the focus, directrix, and eccentricity of a conic seems not to be found in + ~)5 The system of five equations in the six quantities e, ft, ji, p, x~, y’, taken the text-books. Let xa + yjz —p = 0 be the equation of the directrix with the sixth equation ft~ + ~2 = 1, has 2048 solutions. That is, alge- = cos a, jt = sin a), and let (x’, y’) be the focus. Then comparing 2 + (]I—y’)2 =e2(xa+y,t—p)2 braically speaking, a conic has 2048 each of directrices, foci, and eccen- (x—x’) with tlie general equation ax2 + 2hxy + etc. =0, we get the five equa- tricities. The process of elimination yields only eight distinct solutions. tions, Since the process consists only of addition and multiplication of the I —e2X2 a —e2?y.t A 1—e2~s2 b equations, it follows that the remaining solutions are either repetitions of k U A c’ A these eight, or are infinite. An examination of the equations shows that e2p2L—x’ g e2p/t—y’ f they can not have infinite solutions. Therefore the remaining 2040 solu- A U A — C’ tions are merely repetitions of the eight obtained. where k=x’2+y’2—e2p2.__Writing s=a+b, d=a—b R=4-Vd2 +4h2 ~ +4(h2—ab),

A = the discriminant, and 6 = the sign of — Rh, the following values of A Note on Binodal Quartics, by E. W. DAVIS. e2, ft, jt, p, x’, y”, are easily obtained: [Abstract of a paper read at a meeting of the University Mathematical Society, April 18, 1883]. 2R /R~d ~=± 4IR±d, Putting th~ equation of the curve in the form ___2+g2—i~c(R+s)— \ 2R 2fu~2g2u / —4A ~ f R—s L =p’-i-p”, say, the tangents from the node (xv) are given by ~ xf=e2(pa~~), yf=e2(p~s~~). or say by x — az. x — /3z. x — yz. x — 6z =0, For each value of R there are thus one value of e2, one (real) value of while those from the node (yz) are given by the angle a, and two values of p. There are thus fou~r directrices, two by4 + 2fy3z + (e + ab — h2)y2z2 + 2(af— hg)yz~ + (ac —g2)z4 = 0, entirely real, parallel to each other, the other two with a real direction or parallel to each other and perpendicular to the first pair, but at an imagi- — a’z. I’ — /3’Z. 1/ — 7’~ . Y — 6’z = 0. nary distance from the center. To each directrix corresponds one focus Let now and one value of e2. When A =0 the directrices are all real, the mem- = ~a, 8~ = ~a/3, s~ = ~a/3y, 84 = af3~6, bers of each pair become coincident, and the four foci are seen to be coin- while s’s, ~ S’~~ S’~, are the corresponding functions of a’, /3/, y/, e5’. cident with the intersection of the directrices. We readily find For the parabola the second form of the value of p is indeterminate, a=~!M, b 4 ~~1 8’M but the first is not. 1 f=27M, g—2 In the ellipse two of the four values of e are imaginary. When theellipse where 82 is real (sA K 0), the imaginary eccentricity corresponds to the imaginary —s/is2 4 and then ~2~/ ~/2~ directrices and foci; when the ellipse is imaginary (sA> 0), the imagi- 1 2 12

nary eccentricity corresponas to the real directrices and foci, and the real ~= 8(S 5f~8~8/4 A— 828’a+ eccentricity to the insaginary directrices and foci. 4 S~ M~~S2Ss+4,~i A1•, The equations of the directrices being found to be of the form xa + ~ together with the relations it follows that eft + y~t =p’ are the equations of the axes (ft and ji hav- 8182 —484 8~~8/3 ~4s/4 ing two values each), i. e., and ~ ) =0. 4 —83 ~

, . AUGUST, 1883.] C/NIVEJ?~ITY CIRCULAI?S. 145

For points of inflection we have tan 4’ a maximum; where ~kis the angle A Note on the Strophoids, by EDWARD BARNES. between j and a, and tan 4’is the coefficient of ici divided by the coefficient [Abstractof a paper read at a meeting ofthe University Mathematical Society, March d tan_4’ of a in the value of A, whence = 0 gives 21, 1883]. dt

Prof. W. W. Johnson has defined the strophoid (Am. Jour. of Math., (tan m — tan (n + o))(m tan (n + o) — n tan m) = 0. Vol. III) as the locus of the intersection of two straight lines revolving The first factor gives the infinite points. about two fixed points in a plane. The second factor substituted in the value of p gives Considering one of these curves as generated by a moving point and n ntanm. cci, applying quaternion methods, the equation reveals some interesting pecu- n—rn n—rn

liarities of this class of curves. which shows n — m points of inflection situated on a line perpendicular to Let the fixed points be A and B. n Let m and n be any two commensurable numbers, and o a constant a through a point D, such that AD = a. angular velocity such that no is the angular velocity about B and mo that The expressions for AC and AD show that C and D lie outside of A and about A. B respectively when the lines revolve in the same direction, while both At the time, I = 0, suppose the line revolving about A to pass through lie between A and B when the lines revolve in opposite directions. B, and the line through B to make an angle 0 with AB. For length of arc, Let P he the variable point of intersection. Then, if AP= p, AB = a (Ta = 1 for convenience) and i be a vector s perpendicular to the plane of revolution, 2 (‘1/m2 sin2 (n-J- 0)+ ni sin2 m— 2rnn siam sin (n+0) cos (n~m+O)dI sin mot —(acot+O) p=a+ ~( +0— mot) jsr a, J sin2 (n—rn +0) If we produce AP to A’ and BP to B’, where PA’= mTp, PB’ both lines revolving in the positive direction. nTBP, and call A’B’= L, we have 2 —(iuot+B) Or, by expanding ~ff a and writing n for not, m for mot, sin(n+0)cosm sinmsin(n+0 For the area swept by the vector p, sin(n—m+0) sin(n m+0) sa, tan (n+0) tanmtan(n+0 or, p= a+ sci. +fTvPAdt = ~fsin~(~n—rn+e)n~n+ o tan (n+0) —tanm tan (sa+0) —tanrn The direction of the tangent at any point is m sin (n +0) cos (n +0)—n sin m cos rn 2 (n—m+ 0) sin msin~ (n+0) —nsin2 m~ + Some Notes on the Numbers of Bernoujili and Erder,byG. sin2 (n—rn +0) S. ELY. These equations give an n-tuple point at A, an m-tuple point at B, (n, [Abstractof a paper in the Asasricen Jeurnet ef Zifeulsemetics, Vet. V, No. 4]. m) tangents at (A, B) dividing the space into (n, m) equal parts, and The article contains first formulae for the expansion of the n-tb powers n — m asymptotes similarly related. If the line through either A or B revolves in the negative direction, we of the trigonometrical functions; then the expansion of the p-th power,— have only to change the sign of m or a respectively in the above results. p being an odd prime number—of the secant is more especially considered; To find the point C where the asymptotes cut the line a, draw a vector by means of this expansion it is shown that the residues of the Eulerian w through A perpendicular to p and meeting j,. Then numbers, with respect to prime moduli, are periodic: as for example, that the numbers end alternately in 1 and 5; and finally that the same law of w = ~ + xj. when x is determined by the relation periodic residues holds with respect to certain composite moduli. Swp =0 =p2~xSpk. When A becomes an asymptote we have m AC=— a, n — m and since this is independent of I, all asymptotes cut a at C.

NOTES IN PHYSICS.

On Professor Langley’s “Selective Absorption,” by C. H. Our atmosphere is composed principally of oxygen, nitrogen, watery KOYL. vapor, and carbonic dioxide. It follows then, that when there are not clouds or suspended haze, the sky may be, as far as pure absorption is [Abstract of remarks at a meeting of the University Scientific Association, May 2,1883]. concerned, almost perfectly transparent to the visible rays of solar energy, During a series of years, beginning with 1859, Prof. Tyndall carried on but to the longer waves opaque, to a degree dependent upon the amount experiments which demonstrated the great absorptive power of water, of dissolved aqueous vapor. carbonic dioxide, and the vapor of water in the infra-red region of the Until within a short time actual experiments upon the absorption ofthe spectrum, and which also demonstrated the non-absorptive character of earth’s atmosphere as a whole have been of little value because of deficient these substances in the visible parts. Other investigators have, almost apparatus, but since the invention and application to this work of the without exception, reached the same conclusions, and it now appears bolometer by Prof. Langley we are able to arrive at approximate results. beyond dispute that pure water with its vapor and pure carbonic dioxide In his late paper he shows that the ratios of energy in different wave-lengths deeply absorb the long-wave rays but exercise little influence upon the stopped by our atmosphere are not by any means such as we should expect shorter. The same series of experiments proves also that dry oxygen and from the laboratory experiments above mentioned, but that if c~, ~ ~ dry nitrogen either singly or mixed are almost without effect upon any represent the amounts of energy transmitted, (r’) to our atmosphere, (c/f) part of the spectrum. through it on a clear day with a noon sun, and (c”’) with a low sun, the

) ) 146 JOHNS ffOPKINS [No. 25.

[Notes in Physics, Continued]. quoted, that these short waves are not absorbed in the ordinary accepta- ratios will be about as follows for three representative wave-lengths, in tion of the term. What tnen becomes of them? the ultra-violet, in the green, and in the infra-red, In 1869, Tyndall demonstrated that if ordinary light fall upon a cloud of suspended matter in sufficiently great subdivision, the long waves pass V. G. R. through unhindered while the blue are reflected, and from this he deduced ~ .375 .500 1.000 an explanation of the color of the sky. In 1880, 1 published a brief paper experimentally extending these results to ordinary coatings of oxides of c’ 353 1203 309 the metals, projected upon charcoal by a blew-pipe flame. From these it was shown that an oxide in thin layers might reflect only a beautiful blue; that if the coating naturally absorbed blue, it reflected in prepon- e” 112 570 235 derance in thin layers the next longer wave-length; and that, in fact, the amount and character of reflection depended upon the size of particles and thickness of layer. No quantitative measurements were made, but ~ 27 225 167 from the magnificent character of the blues obtained, I concluded that nearly all the incident light of that wave-length was reflected. Apply- demonstrating immediately the fact that though some 54 per cent. of long- ing this theory to t~e sky we have an explanation not only of its blue wave energy is transmitted at low sun, only about 8 per cent of short- color and of its sunset tints, but also of Prof. Langley’s results that through wave radiation reaches us under similar circumstances. Theintermediate the lower air, full of these floating particles, the rays of shorter wave- rays are transmitted in amounts proportional tosome direct function of the length do not penetrate. It is not selective absorption; it is selective wave-length. It seems almost certain, from Tyndall’s experiments above reflection.

COMMUNICATIONS TO THE HISTORICAL AND POLITICAL SCIENCE ASSOCIATION.

Spanish Plots in the Southwest, by C. H. SHINN. The conclusion, after weighing the evidence against the conspirators, is that their plots were more nearly successful than is commonly supposed, [Abstractofa paper read at a meeting ofthe University Historical and Political Science Association, March 9,1881]. though they were neutralized to some extent by British and French machi- nations during the same period. It is also believed that the region under The region studied was that south of the Ohio and west of the Allegha- consideration, at the period named, presents a comparatively untouched nies in the period from .1780 to 1803. field for historical inquiry. Hitherto it has been abandoned to mere an- The paper was an attempt to describe the intrigues of Spain to disrupt the American Union. The social and political condition of the South- nalists. It deserves such literary treatment as Francis Parkman has west at the close of the Revolutionary war was described,,and the claims of bestowed upon the French r6gime in the Northwest. Spain were defined. The development of discontent in Kentucky and Ten- nessee was encouraged by Spain’s subtle and three-fold policy of (1) annoying restrictions to American citizens as such; (2) generous con- Immigration, by C. H. SHINN. cessions, contracts, and monopolies to colonists and secret friends; (3) [Abstractofa paperread at a meeting ofthe UniversityHistorical and PoliticalScience promises that she would help maintain an independent Western Republic. Association,March i6, 1883]. The development and final failure of this secret policy were traced. The correspondence of MirS and de Carondelet, successive governors In this paper were discussed the more important questions connected of Louisiana, with their subordinates and co-conspirators on American with the right of the individual to change his dwelling place, and transfer his allegiance from one government to another; also the effect of immi- soil, the nature of their plots and the nearness of their success, were con- sidered. Indian combinations on the frontier of Georgia, the great Yazoo gration upon the United States. Three cases of migration were consid- land schemes, Sevier’s “State of i~’rankland,” the various important ered: (1) that of a man moving from one county of a State to another political movements of the time and the motives and character of the county of the same State; (2) that of a removal from one State to another; leading plotters were examined. Jealousy and lack of confidence were and (3) that of a removal from one country to another country. The con- shown to have existed. General Wilkinson’s speculation, tobacco syndi- clusion was that the right of an individual to leave his native land is absolute; but the country to which he offers hiniself has the right to cate, receipts of Spanish gold, cipher letters to MArS, and other schemes decide whether he is a desirable citizen. The exercise of this right is seem, in the light of all attainable evidence, to have been dangerous and disloyal. His associates and their methods of “creating public sentiment” among the duties of a government. Complex social and political ques- were described. The general conclusion was that all pensioners of the tions are involved. The evils of over-population, leading to emigration, Spanish government, and many others deserved punishment at that time. the effect of great disasters, and other causes transferring population, were The evidence of the Louisiana records and contemporary testimony bear discussed. The arrivals of 1881 (669,431) were considered (1) as regards nationality and race; (2) as regards sex and occupation ; (3) as regards heavily against the adroit Wilkinson. In 1795, while the Treaty of San Lorenzo el Real was being negotiated effect upon the national life. The causes of the preponderance of the Ger- man element were analyzed. The occupations, and sections of the country (signed October 27), Judge Sebastian met Don Gayoso, a Spanish envoy at New Madrid, and discussed methods of separating the West from the that chiefly absorb unskilled labor; the effect of surroundings on the new- Union. In 1797, Baron Carondelet sent Thos. Power to Lexington, Ky., comer; the questions of climate and native vitality; the probably wise limits of immigration were next considered. Attention was drawn to with a letter to the conspirators, which, in brief, (1) advised his friends in the West to form an independent republic; (2) promised that the troops possible changes in industrial or commercial centers, and to the disturbing of the new government should be armed and eqtiipped by Spain, and paid influence of trades unions. The end of this great migration to the United $100,000 in gold; (3) advised about boundaries; (4) promised aid against ‘States is not far off. Renewed colonization, on a large scale, of the the Indians; (5) agreed not to interfere with the framing of laws; (6) world’s waste placesis everywhere foreshadowed. Recent political events, reports of exploring parties, organization of great commercial companies, the envoy declared that Spain did not intend to carry out her treaty obli- gations. The conspirators found themselves too weak to venture to make all point towards this end. these proposals public. Lesser intrigues continued till the purchase of Louisiana in 1803. AUGUST, 1883.] UNIVERSITY CIBCULAPS. 147

The Office of Public Prosecutor, by F. J. GooDNow. was two and one-half per cent., and the exemption was $2,000. There does not seem to have been much complaint about the income tax during [Abstract of a paper read at a meeting of the University Historical and Political Science Association, May 4, i883]. the first few years of its imposition, but from 1867 numerous charges The paper began with a discussion of the two chief methods of pro- were made against it. cedure in criminal investigations, the litigious and the inquisitorial, and By an amendment of 1864, each person liable to the tax must make his of the application of these methods in the systems in vogue in France, returns under oath, while under the earlier law no oath was needed, England, and Scotland. Especial attention was given to the historical unless demanded by the assessor. Also, by this law, penalties were development of the office of public prosecutor in England and in Scotland. imposed for neglect or refusal to pay the tax, and for delay in payment. In most of our American commonwealths and in the judicial system of But the most important innovation on the original law was made when the national government, there is a minor prosecuting officer, who in every person was allowed to deduct the exemption and pay only on the most cases is called the district attorney, in others the state’s attorney, excess. This principle seems so manifestly just, that we can only wonder commonwealth’s attorney, county solicitor, circuit solicitor, prosecutor of that it did not prevail at first. But such was not the case; neither was the pleas, deputy attorney-general, or assistax~t attos~ney-general. This it retained in the later law of 1870. office was not brought with us from England, as there was none such there In this country, the amount of income was determined by self-assess.. at the time of the colonization of Anserica, or even in 1776. The origin ment, while in Germany the officers make the estimates from apparent and development of the office can be discovered by an examination of the resources; but that the former method is the better is shown by a recent statutes, especially of the older States. In each of these, except Connec- trial of the system in Berlin and Hamburg. ticut, there was in 1776 an attorney-general. As the business of his office The total amount paid in income tax was $376,290,400.67; other sources increased, other attorneys were deputed to perform his duties at times and of internal revenue, $1,259,445,718.06~ customs duties, $1,573,460,613.34; places at which he could not be present. In Virginia, a law of 1788 total revenue from 1862 to 1872, $3,209,196,732.07. provided for the appointment of such deputies by the attorney-general The above figures show that about eleven per cent. of the taxes col- himself. In 1800, it was provided that they should be appointed by the lected for the years 1862 to 1871, inclusive, was obtained from the income courts respectively, a second step in their development; their duties were tax. Now, when this tax was removed, one class was largely relieved still confined to the lower courts. In 1808, the system was extended to from taxation, and the burden was thrown on the people according to the higher courts; in 1867, the office of commonwealth’s attorney was their consumption of the taxed articles; butsuch a tax bears more heavily made elective. on the poor and on the middle classes than on the rich, hence an income The course and extent of the development of the office in each of the tax is needed to equalize and supplement other taxes which bear especially thirteen original States was described. An account of the tenure and on the poor. duties of public prosecutors in all the present States was given. The By comparing the income tax of 1866 with that of 1867, it is found introduction oil the office into the judicial system of the national govern- that 220,000 persons had an income of between $600 and $1,000; and in ment by the Judiciary Act of 1789 was accounted for; it was undoubtedly 1867, 50,388 persons had an income of over $6,000. The cost of collecting borrowed from the• State governments, under which it had by this time was probably not much over two per cent., and certainly not over three, become partially developed. and as the average cost of collecting all taxes was over four per cent., Statistics were given to show that under the Scotch system, with an this tax comes nearest’ Adam Smith’s fourth canon of taxation. The official prosecutor, the number of innocent persons who suffered lengthened usual objections to and arguments for an income tax were brought forward imprisonment was, in the average of three years, only one eighth of all in this country, but no new principles were developed. Finally, under persons detained in jail for trial by the crown counsel, whereas under the the present system of taxation, the people are bearing burdens almost in (former) English system, the proportion was one-third. proportion to consumption, which violates the first principle of equal taxa.. tion, namely, equality of sacrifice.

The Income Tax in the United States, by II. W. CALDWELL. Taxation in Maryland, by C. M. ARMSTRONG. ~Abstract of a psper resd at a meeting of the University Historical and Political [Abstr”ct of a paper reid at the meetings of the University Historical and Political Science Association, May4, 1883.] Scieflce Association, May 18 and 25, 1883]. The Act imposing an income tax became a law July 1,1862, and was The object of Maryland legislation on the subject of taxation seems to not finally repealed until 1872, although, in the meantime, it underwent have been to require a direct contribution to the public treasury from many modifications. There seems to have been very little opposition to every person in the State who enjoys any pecuniary revenue, or who owns the income tax. Some discussion occurred in Congress on two phases of property of any value. But the law falls far short of accomplishing this the hill: whether all incomes should be taxed, or whether small incomes purpose. Many persons enjoy large yearly incomes, profits, and earnings, should be exempted; and second, whether the rate should be uniform or on account of which the State receives nothing directly or indirectly. progressive. The decision was in favor of an exemption, and all incomes Ground rents are a clear profit to the owner of the ground, and he pays below $600 were not to be taxed. Afterward the exemption was raised no tax at all, much less a tax ‘according to the revenue he enjoys.’ A to $l,OuO, and then to $2,000. number of professional men earn $20,000 a year, or even more, and pay The tax was progressive from 1863 to 1867, but from that time until its no taxes. On the other hand, the owner of leasehold property in Balti- repeal the rate was uniform. In this respect, the same policy was pur- more city is required to pay a tax which often amounts to 25 per cent of sued as obtained in other countries, tending everywhere to a uniform his net income. He must own nearly half a million dollars worth of such rate. The original policy of progressivity was adopted on account of its property in order to derive a net income of $20,000, and on this he will support by Charles Sumner, and on the authority of the French econo- pay nearly $7,000 taxes. Yet, while this is true, the owner of this class mist, M. Jean Baptiste Say, who argues that a tax of ten per cent. on an of property does not, as is generally supposed, pay the largest tax in pro- income of $10,000 will not occasion a greater degree of sacrifice titan a portion to his income. This undesirable distinction is reserved for the less rate on smaller incomes, or a higher rate on larger incomes. How- holder of State bonds, who, if his bonds bear 6 per cent., pays 25 per cent. ever, there is danger of abuse of this principle, and justice seems to demand of his net income therefrom in taxes. But if they bear only 4~ per cent. that the rate should be uniform. interest, his taxes amount to nearly 27 per cent, of the income. And this The first bill imposed a tax of three per cent. on incomes between $600 class of property is strictly assessed at its full value every year, while but and $10,000, and five per cent. on incomes over this amount. By the little real estate has been assessed since 1876, and this for the most part is amendment of 1864, the rate on incomes between $600 and $5,000 was assessed at less than its actual value. The case of shares of stock in cor- five per cent ; between $5,000 and $10,000, seven and one-half per cent., porations is much the same as that of State bonds. and on incomes over $10,000, the ratG was ten per cent. Further modifi- An adjustment of the rates of taxation so as to bear most heavily upon oati.ns were made until the last twe years, 1~70 an~ 1871, when the rate these presumably least able to pay is a marked feature of the Maryland 148 JOHNS HOPKINS [No. 25.

[Communications to the Historical and Political Science Association, Continued]. system. Itis so with the tax on the State bonds. It is true of the traders’ sequently. Pending these demands, and succeeding a remarkable increase license-tax, which amounts to 1~ per cent. of the value of the stock where in our production of breadstuffs, there came a period of prosperity, of the dealercarries an amount of the value of $1,000, and, as the value of the cheap money, in which a portion of the national debt was funded at a stock is greater, the per cent. paid in taxes is less, until on a stock of the low rate, and a remarkable expansion of means of internal communica- value of $40,000 it is only ~ of 1 per cent. The rates for some other tion took place, the Erie Canal being opened. This succession of events, licenses, as wholesale liquor dealers, to keep an ordinary, &c., are arranged which closely resembles the period succeeding the tariff legislation of upon the same principle. 1867, led to a demand for revision, and when granted by Congress, con- There is a popular idea that all, or nearly all, of the revenues which flicting opinions resulted in an Act satisfactory neither to protectionists come into the State Treasury are’ derived from the direct tax of 18~ cents nor free-traders. on the hundred dollars ordered by the statute to be levied annually on From the Presidential election in 1844, closing this period, when Penn- property and gathered by the collectors. This is an error. The State sylvania was carried by the cry of “ Polk, Dallas, and the tariff of ‘42,” derived from this source during the fiscal year which ended Sept. 30, 1882, no great Northern State was carried by a tariff issue until 1880, when the $898,867.18. Of this sum, $789,128.15 were paid through collectors, and Republican party owed its success chiefly to the appeal made, in the $109,739.03 were paid directly to the State Treasurer. The license taxes closing weeksof the canvass, on this issue. The Congress then elected, yielded $517,354.69, and other taxes, as on commissions of executors and had a working protectionist majority in the Senate, while the House was administrators, collateral inheritance, &c., $207,970~56. These taxes found overwhelmingly for protection. . When it met, in December, 1881, no their way to the treasurythrough various channels, some directly from the doubt existed that if any chan~es were made in the tariff, they woUld be taxpayer, some through clerks of courts, &c. in the direction of higher ‘duties. Weeks passed without action, and it was finally decided, in March, to report a bill confining the necessary reductions of revenue to internal taxes. Meanwhile, short crops had raised the price of food fifteen per cent., decreasing enormously the free The Revised Tar~fi~ in its relation to the Economic His~ share of the national income available for the purchase of manufactures after food and rent are paid. But of our adults, at least five-sixths buy tory of the United States, by TALCOTT WILLIAMS. their food. The increase in the cost of food decreased the sale of manu- [Abstractof a paper read May 30, 1883, before the Seminary of Historical and Political factured articles, and raised food imports for 1882, to $47,949,546, exclu- Science.] sive of sugar, spices, tea and coffee. The distress caused by high food and The Revised Tariff (Act of March 3, 1883,) bears the same relation to the low sales of manufactures, led to a demand for action on the tariff, our economic history which the tariff revisions of 1824 and 1828 and which took the shape of a commission for investigation in the recess, and accompanying changes, bore to the industrial development which began a report -at the next session, a proceeding which practically made the with the close of the war of 1812. Any discussion of the tariff history of general election of 1882 an appeal to the people on this issue. This appeal this country necessarily begins with the close of a struggle, in many was taken at the end of a crop year (1881—2), in which there had been senses our second war of independence. Before .that time, as Benton grown, as compared with 1880—1, three-fourths as much wheat, two-thirds says, protection had been an incident, since then an object. as much corn, potatoes, and pork, one-seventh less cotton, and everything Aside from the great change wrought at this period in the trade and else in proportion. While the acreage of cereal crops was one-third commerce of the world by the freedom and peace of the seas, and the larger than in 1877, the total cereal crop was smaller, so that 30000,000 consequent growth of shipping, which brought our Atlantic coast nearer acres were cultivated without increased return. Wool and cotton manu- Europe than it had ever been before, the United States itself passedthrough factures were depressed, and the visible supply of print-cloths doubled in three great changes. Its position as a food-producing nation became six months. Pig iron remained stationary, but steel rails fell from $60 clearly defined during the Napoleonic wars. Embargo and war together, to $45 a ton. Strikes failed to advance prices, and some trades, like rub- its manufactures grew apace under a prohibition of foreign imports for ber, found it wisest to suspend altogether. When the railroad reports six years, and at the same time they passed through the general change came in, it was found that the New York Central had not earned its divi- following the introduction of machinery, which substituted factories and dend, the eastward tonnage of the trunk lines for 1882, to September 1, powerful manufacturers for the individual, and therefore weak, industries was two-thirds that of 1881, and, as a result of all this, the aggregate fall of the domestic loom and forge. Lastly, the revolt of the Spanish Ameri- in stocks from July 1,1881, to September 1, 1882, was greater than for two can colonies was accompanied by a period of disorder which lessened years after September, 1873. These causes produced the Revised Tariff, their commerce and deprived our seaboard of a trade relatively and often which, like all other tariffs, was a result and not a cause. When Con- absolutely larger early in the century than it has been since, leaving the gress met, the blind pressure for a revision had taken shape in an intelli- exchange of food products with Europe the typical characteristic of our gent demand for lower raw materials. The draft Act submitted by the commerce. Commission, enabled both Chambers to take up the discussion of a new These changes combined to render the period which began in 1814, tariff pan passu, and the evidence presented gave a larger body of facts and whose tariff legislation commenced with the Act of 1816, a period than Congress has ever before had in acting on customs duties. The Act, controlled by conditions still current. The Act of 1816, whose specific as finally passed, failed to meet the demand for lower raw material on terms and careful schedules make it similar in form to the Tariff now in iron ore, in many other respects it did, and in precision it was a great force, many of whose phrases are drawn from it, and differing from any advance on any previous tariff. From a protectionist stand-point, it was preceding it, was drawn under the influence and direction of manufac- notable for its admission that some industries had had enough of protec- turers who found their industries, already in operation, seriously threat- tion and could stand a reduction; it is remarkable in our economic his- ened by the large imports of 1815. Here, as elsewhere in our history, tory for the resumption of economic influences in our legislation, inter- protection is obtained after an industry is started. rupted by the demands ofslavery for solution, non-sectional votesbeing cast High duties have rarely been granted in the United States, for protec- on a tariff question for the first time since 1828. Its political lesson is tive purposes in specific cases,until some manufacture asked them. Begin- the promise and prophecy it carries of additional reductions as inevitable ning with relatively high duties and an expanded currency, manufac-. in the near future as in 1833. tures had, for a brief period, apparent prosperity. Serious depression ensued, and as the ad,ninistration and effect of a tariff had by this time secured public attention, higher duties were demanded in 1820 and sub- AUGUST, 1883.] UNIVERSITY CIRO ULARS. 149

NOTES IN BIOLOGY.

On the Relation of Bilateral Symmetry to Function, by or left of the middle point of the measuring rod is, within the field of E. M. HARTWELL. direct vision, constant and in the same sense as the error of the hand in simultaneous, impulsive movements. (c). The error of the eye is [Abstractof a paper read at a meeting of the University Scientific Association, May 2, 1883]. greister in the field of indirect than in the field of direct vision. C—If the experiment be made exactly as in the first case described, under The correlation of bilateral symmetry in structure with bilaterally A, with the exception, that impulsive movements be made with the equal functions in the bodies of vertebrates, especially man, was taken right and left hand alternately leading at an interval of one second or as the general topic of this paner. four seconds in advance of the other, then— (a). The excess of error is Attention was called to the clear recognition on tbe part of the ancients far greater than in the case of simultaneous,, impulsive excursions. of the disproportionate powers of the two sides of the body. Assyrian, (6). The error is in a sense opposite to that given under A. (c). The Egyptian, and Greek sculptures for the greater part depict right-handed excess of error is greatcr for the left hand, in right-handed persons, men; and in some instances the right side of the body is represented as than for the right, and vice versa: and this excess for the left is greater asymmetrical with the left. The speculations of Plato and Aristotle of when the right leads than when the left leads. Hyrti, and of Charles Reade, were instanced as types of the various D.—If a person, with his eyes shut and his arms and hands extended, hypotheses advanced to explain right and left-handedness. Observations attempt to bring the middle points of the tips of two thimbles, equally made by scientists upon the differences in color markings on the two weighted, and peculiarly armed for the purpose of securing a graphical sides of the body, in dogs and horses; upon the inequality of the right record, together by simultaneously impulsive movements, it is found— and left sides of the skulls of civilized races; on the disproportion, as (a). That symmetrical movements are more exactly executed when made regards size, the number and depth of convolutions, and the number in a plane continuous with the median plane of the body, and above and of motor fibres, found to exist between the right and left sides of the in front of the head, than when made to the right or left of that plane. human brain; and upon the differences in the functional powers of the two (6). The right hand in such movements in the median line takes a posi- eyes of a single person, were cited as tending to show that unequal and tion in advance of and above the left among the right-handed, while the unbalanced functions accompany asymmetrical organs. It was held that left is similarly advanced above the right in the case of the left- asymmetry, and the inequality of function correlated with it, is to be handed. accounted for as a variation, due to specialization, from the normal type. E.—By using a dynamometer designed to test and record the clenching The ancient views of the office of the brain, based upon the doctrine of power of the hand, it was determined that— (a). A maximal clenching animal, vital, and natural spirits, were contrasted with the modern theory movement with one hand is weakened if a symmetrical maximal move- of localization of the functions of the brain, based upon the study of its ment be simultaneously made with the other hand; but that a maiimal, anatomy, physiology, and pathology; and the principal arguments for simultaneous, unsymmetrical movement has no effect. (b). Submaximal and against the notion that the brain is a double organ, were outlined. movements have an effect opposite to those of maximal movements, in The main portion of the paper consisted of a preliminary report of a that they produce summation and not weakening. The right hand in research conducted by the writer at the suggestion of and in conjunction dexterous persons has more power of interference with the left than with Dr. G. Stanley Hall. In this investigation, which was still in pro- the left has with the right; and the reverse is true in case of the left- gress, it had been attempted to determine, in some degree, the nature and handed. Fatigue reduces the error of the stronger hand more than the extent of the functional differences between the two sides of the body in error of the weaker hand. right and left-handed persons. F.—The reaction time of the stronger side, i. e., the right in the right The results of the investigation may be stated as follows: handed and the left in the left-handed, is longer than the reaction time A.—(a). If a person sit, with his eyes shut, before a table upon which at of the weaker side, an arm’s length from him a measuring rod is fastened in a horizontal position, and attempt to make, with his index fingers, exactly equal and simultaneous excursions along the rod from its middle point; that person, if he be right-handed, will generally make wider excursions to the right than to the left; while if he be left-handed, the excess of error On Ciliated Epithelium in the Human Kidney, a Note b~’ will be toward the l’eft. (b). The per centage of error increases to a A. H. TUTTLE. distance of from 80 to 40 c. m. from the middle point of the rod, and [Abstract of a paper read at a meeting of the University Scientific Association, April then diminishes. (c). The movement in the above case is made from 4, iSSI]. the shoulders, the arms and hands being fully extended—but if the Ciliated epithelium, long known to exist in the renal organs of the movement be from the elbows, or the wrists, or simply with the index lower vertebrates, has recently been detected in the kidneys of several fingers, the excess of error subsists in the same sense but not in the mammals by Klein and others. The fineness of the cilia and the small- same degree. (d). Inasmuch as the excess of error is scarcely affected, ness of the lumen of the convoluted tubules in mammals render their’ if, instead of making simultaneously impulsive movements, the attempt demonstration comparatively difficult, and it is essential that material em- be made to make the excursion of the second hand equal to that of ployed for this purpose should be put into hardening fluids while perfectly the first, immediately the excursion of the first hand is completed; fresh; a condition in which the human kidney is not usually obtained. it would seem that a difference in the amount of central innerva- An opportunity recently occurred of examining a number of human tion for the right and left sides is the chief factor in producing the kidneys obtained in an unusually fresh condition at post-mortem exami- excess of movement of the stronger side. nations of smallpox patients. The parenchymatous swelling of the renal B.—(a). If the person observed, with his eyes open, stick a pin with one tissues occasioned by the disorder enlarging the lumen of the tubules, hand into a measuring rod fastened as described under A, on the same and rendering the structural elements unusually distinct, the examination side of its middle point as the hand that bears the pin, and then attempt of exceedingly thin sections (mounted in glycerine) with a Zeiss one- with the other hand, even after careful sighting, to measure off an twelfth homogeneous immersion objective showed plainly the presence of equal distance on the other side of the middle point of the rod, there cilia upon the epithelium of portions ofthe convoluted tubules. will be an excess of error to the right if he be right-handed, and vice A fuller account will be published in the forthcoming number of “Studies versa. (6). The error of the eye in judgments of distance to the right from the Biotogicat Laboratory” of this University. 150 JOHNS HOPKINS [No. 25.

CORRESPONDENCE. i. e. such symmetric functions are subinvariants; as I learned from your Extracts of Letters to PROFESSOR SYLVESTER, from Mu. J. memoir on subinvariants. HAMMOND, of Buckhurst Hill, Essex, England. I am afraid that I cannot put the thing before you in a manner at once March 14, 1883.—. . . As the matter now stands, it seems to me that short and intelligible, but by following up this hint I have obtained the in order to obtain correct results a generating function for syzygants is same generating functions as are given in sec. 4 of your memoir for degrees required as well as one for covariants. It would not be difficult to write 2,3,4(viz., x2 x1 (1 x1 and down such a G. F.* for syzygants of degree 5 for any Quantic, but how 1—x~~ (1—x2)(1—x3)’ —xl)(1—xl)(1—x4) / can all syzygants whose degree is higher than 5 be found? I cannot tell. passing on to degree 5 found the same results as given in my letter ot’ What was called the automatic method of tamisage in my letter of March 8th. After that I went on to degrce 6 which I have hot suffi- January 23, suffers from this perhaps more than the method of the 4th ciently studied yet but in which I found several syzygies (none of them section of your memoir on subinvariants. I give the tamisage by this so far as I can remember new). method for the Cubic, Quartic and Quintic that you may see an example The following simple examplcs may illustraite my method of working. of the work: Multiplying both numerator and denominator of the repre- Denote ~alj3myn . . . by (I, m, n, . . 1x3 1 + a Then (3) (2.2) = (6.2) + (3.2.2) sentative generating function (1—a4) (1 —alxl)(l — axl) by 1—a’x’ we (2)(3.2) = (5.2) + (4.3) + (3.2.2) have lax ,which may be called a fully gives a syzygy of deg. 5, wt. 7, (1—a4)(1 —c2x2)(l—axl)(1—alx3) (3)3=(6) +(3.3) rcpresentative form ef generating functions, inasmuch as all the ground- (2)3 — (6) + (4.2) + (2.2.2) forms are representcd in the denominator and the only syzygant in the gives a syzygy of deg 6, wt. 6. numerator. Similarly the fully representative form for the Quartic is in these examples numerical mult~pliers are neglected. I — a6x’ 2 In considering degrees 3 and 4 it is shown that (3.3) and (4.3) are ground-forms. I am now in some difficulty; I cannot arrange the results The case of the Quintic is far more complex, but here it may be proved I have from time to time announced in anything like a connected form, that any ground-source of weight w is of lower degree than that ground- so that I cannot help thinking that my next paper when it comes to be syzygant of the same weight whose degree is a maximum; and if the written out will be a sadly disjointed and incoherent affair. I will try postulate •were true any ground-source of weight w would be of lower once more to put these things in a connected shape, and if I am still un- degree than any syzygant of the same weight. We are now led to reject successful will send them as they are “with all their imperfections on their all terms of the numerator of the representative generating function, head; ‘ but they will be little better than rough notes. except those in the first positive block. The remaining terms are P. S.—April 17.—I have an idea not very clear at present that it will 1 + a3(x3 +x5 + x5) + a4(x4 + x5) + al(x + x3 + x~) + a6(x’ +x4) eventually be possible to obtain all the ground-sources of a given degree- + a7(x+x3) +a5(x2 +x4) +as(x3 +x5) +a18(x2 + x4) .-f- a11(x—j— xl) 4- a12x2 +a’3x +~al4x4 + a’6x2 +a’s. weight both in number and position and that when this is done to each ground-source will correspond a given partition of the weight not con- Multiply now both numerator and denominator by 1 —a3x’, rejecting negative terms in the numerator; this destrays the terms a1x3, a5x4, a5x5, taining a unit. Thus for deg. 3, wt. 9, there will be the two partitions (3.2.2.2) and (3.3.3), the first of which corresponds to the cubic proto- a10x4, and a14x4, and places an additional factor (3.3) i. e. 1 — a1x3 in the denominator. morph of wt. 9 and the second corresponds to a cubicovariant of the 7-ic. Continuing the process with (3.5), (3.9), (4.4), and (4.6) instead of (3.3) If I can only distribute the ground-sources and syzygies properly among each multiplication will only destroy a simple term in the numerator; and their respective Quantics I think there will be no difficulty after that. there remains in the numerator 1+a5(x+xl +x~) 4-a6(x2 +x4) +a~(x+x5) +a5x2 +a5x3 +a18x2 Extract of a letter to PROFESSOR SYLVESTER from PROFESSOR a1 ~— a1 ~. —f-- 1 (x -4- xl) a1 2x2 —i--a1 3x —f— a1 5x2 -]-- CAYLEY. Continuing the process with (5.1) destroys the terms a5x, a18x1, a”x3, a12x2, and a16x2. - Cambridge, April 6, 1883.—It seems to me that in the N. G. F.* there There is now left in the numerator is no possible way of taking account of the syzygies which present them- 1 + a5(xl + x~) + a5(x2 + x4) + a1(x+ x5) + a5x2 selves in defiance of the fundamental Postulate, but that this can be done —f-. a5x3 -.f—a11x--I-- a’3x —f-al5. with the R. G. P.f—in fact that the R. G. F. is capable, what the N. G. F. If the process were now continued by multiplying by (5 3), (5.7y, (6.2) is not, of telling the whole truth. Take the quintic; in the developed each step would only destroy one term in the numerator and intro- N. G. F. we have a term 4a5x4, and there are in fact of this deg-order 8.4 duce one factor in the denominator, and so the process is at an end. the four terms b2g, bin, 41, gh, [a, 6, c. . . w the 23 covariants], and these being in fact asyzygetic, we have in the R. G. F. a term There is a rather absurd erratum in my note of December 4th, for repre- 41(1—ag2) sentative ground-form read representative generating function. 1—a.1—b. l—c.1—g. l—q.1 (see 10th Memoir)t; *Generating Function. but suppose there had been a syzygy between b2g, bin, dj, gh—and con- sequently for the deg-order 8.4 a new covariant z; then the term in the

April 16, 1883.—. . . Every spare moment of my tin~e has been spent E. G. F. might have been written in searching for a method of finding the syzygies of Binary Quantics. z(1—agl) This method I believe I have found for the Quantic of the infinite order, 1 — a. 1—b. 1 — c. 1 — g. 1 — q. 1 — but I anticipate considerable difficulty in distributing the syzygies among and the new form of the R. G. F. would have put in evidence the 24 the lower Quantics. covariants a, b, c. . . w and z. Of course, writing therein z = a5x4, we In Vol. XIII. of the London Mathematical Society’s Proceedings and in should obtain the N. G. F. in its original for,n, and there would be no another paper not yet published, I proved that the symmetric functions longer any trace of the new covariant. It would thus seem that the true P1 P2 P3 question is that of finding the expression of the R.. G. F., but to do this Zal~3rnyn. . . of the roots of 1 ~ + — ~ +. . . = 0 satisfy the differ- we require first to know the number and form of the extra-syzygies. . ential equation d d d * Numerical Generating Function. .0, t Real Generating Function. 4 On Quantics. provided no unit occurs among the indices t, m, n, etc., AUGUST, 1883.] UNIVERSITY C’IRCULAPS.. 151

The Peabody Library Building. After having given many years to the study of library economy and library architecture, after having visited nearly all thegreat libraries of the Statements, utterly erroneous and misleading, in regard to the capacity world, and examined plans innumerable of both the old and new styles of and cost of this library building, have been widely circulated, and I have building, I have been forced to the conviction, that, for any library, like been repeatedly urged to correct them. In these statements the capacity that of auniversity; where the readers are to have access to the shelves, the of the library is put at 150,000 volumes and the cost of storage at $2 per central hall with surrounding alcoves is by far the most convenient and volume. I have gone carefully over the calculations once more, and find the most beautiful of all library structures; and that it can be made as the capacity of the main hail for books to be 300,000 volumes, allowing economical as any yet devised which will furnish the same amount of but eight volumes to the running foot on the actual shelving — all that light, air, and general accommodation to readers and attendants. It is our large volumes will permit. The other rooms in which hooks are the only form of library that admits of fine architectural proportions and stored will hold, on the same basis of 8 books to the foot of actual shelving, decoration; and surely the settings and surroundings of books are as suita- 28,000 volumes, making the capacity of the library 328,000 volumes. ble for ornamentation, are as legitimate objects on which to display artis- The cost of the fire-proof marble wing containing the library, including tic beauty and taste as title-pages, paper, print, margins, and bindings. shelving and furniture, was $342,000. Seven-fifteenths of this wing, by A grand hall, filled with the gathered wisdom of ages visibly set in alcoves actual floor measurement, are occupied by art galleries and lecture halls; chastely but richly ornamented, will impress the young student with a and must have cost at least one-third of the whole, or $114,000, leaving respect for books and a sense of their importance which he will never the actual cost of the library building $228,000, or less than 70 cents per forget, and which no multiplication of “stacks” will ever give. I can volume for storage instead of $2. but think that the present rage for “stacks” and warehouse packings — -But the capacity of libraries is usually estimated on the basis of 10 fit only for popular circulating libraries — is a temporary mania which books to the square foot of shelving instead of 8 books to therunning foot. must soon pass away. The falling of dirt and the rising of heat through This library, on account of its many folios and other large books, the perforated or grated floors required for light in the warehouse plan of averages at present but 8 volumes to the running foot. Allow 10 books building, and the danger of leakage and drip from glass roofs placed over to the running foot, and the result will be a capacity of 410,000 volumes the books, are fatal objections to their use. Solid floors alone, as this and a cost of 56 cents a volume for storage; but make the usual count of library has shown, will keep the highest alcoves at as low a temperature 10 books to the square foot of shelving, and the capacity becomes 600,000 as the lowest, and that is a fact of the utmost importance in library volumes and the cost of storage 45 cents a volume. In regard to the architecture. statement that this library is so constructed that it can never be enlarged, it may be said that the lecture halls and art galleries can all be thrown PEABODY INSTITUTE, May ii, 1883. N. H. 1VIORISON, Provose. into it, and thus its capacity for books be more thaa doubled.

THE DIRECT INFLUENCE OF GRADUAL VARIATIONS OF TEMPERATURE UPON THE RATE OF BEAT OF THE DOG’S HEART. By H. NEWELL MARTIN, M. A., M. D., D. Sc.

(Abstract reprinted from the Proceedings of the Royal Society of London, No. 223, 1883). In the investigations described, the method of experiment was such as Uniform artificial respiration was maintained. to completely isolate physiologically the heart of the dog from all the As the result of many experiments, it was found (1) that the isolated rest of the body of the animal, lungs excepted. dog’s heart beats quicker when supplied with warm blood, and slower This was accomplished by occluding the right and left carotid and sub- when cold blood is supplied to it; (2) that the rate of beat depends much clavian arteries, the aorta just beyond the origin of the left suhclavian, more upon the temperature of the blood in the coronary arteries than on and ligaturing both venn cav~ and the azygos vein. In consequence the its temperature in the right auricle or ventricle; (‘3) that when defibri- only fraction of thu systemic circulation left open was that through the nated calf’s blood is used to feed the heart that organ cannot be kept alive coronary system of the heart; no organ but the heart itself has any blood as long as when defibrinated dog’s blood is employed; (4) that no matter sent it, except the lungs. Hence the cerebro-spinal nerve-centres and the how long an experiment lasts the defibrinated blood, circulated again and sympathetic ganglia very soon die, while the heart remains alive, in good again through heart and lungs, shows no tendency to clot; hence fibrino- working condition, for two hours or more. The right auricle is supplied gen is not produced in those organs. uniformly with defibrinated calf’s blood, conveyed to the superior vena The question answered by the first of the above results was the one for cava from Mariotte flasks. The blood, after traversing the pulmonary whose solution the research was undertaken. The experiments show that, circuit, is finally pumped by the left ventricle into a cannula, which is in spite of its highly-developed extrinsic nervous apparatuses, the heart tied into the aorta just beyond the origin of the left subclavian artery. of the mammal does, so far as its rhythm is concerned, in its own nervo- From the distal end of the canaula a wide rubber tube carries the blood muscular tissues respond to temperature variations within wide limits to an exit cannula seven or eight feet above the level of the heart. By (42o~27o (3.), just as the frog’s heart or that of the embryo chick does. raising or lowering this exit, and by raising or lowering the level of the To account for the quick pulse of fever, we, therefore, need not look Mariotte flasks feeding the heart, arterial and venous pressures could be beyond the mammalian heart itself. We require no theoretical assump- changed at will, or maintained very nearly constant. tion of any paralysis of inhibitory, or any excitation of accelerator Venous and arterial pressures being kept constant, the temperature of cardlo-extrinsic nerve centres. the blood supplied to the heart was gradually changed by raising or lower- ing the temperature of the water contained in the vessels in which the feeding Mariotte flasks were immersed. The paper of which the foregoing is an abstract has been selected The pulse rate was recorded by a Fick’s spring manometer, and arterial as the “Croonian Lecture” of the Royal Society of London for the pressure by a Marey’s mean-pressure mercury manometer, each being present year, and will appear in full in the next volume of The Philosophi- connected with the central stump of a carotid artery. Temperatures cal Transactions. were read by means of a thermometer tied into the root of the left sub- clavian, so that its bulb projected into the aortic arch. 152 JOHNS HOPKINS [No. 25.

THE ECLIPSE OF THE SUN ON MAY 6, 1883.

(Reprinted from The Times, London, July 2, 1883). During the last few days additional information has been received both determine the real limits of the corona by means of any simple analysis from the French and American eypeditions sent out toobserve the eclipse of the light from any part of the regions surrounding the sun. When of the sun on the 6th of last May. The more we learn about the results spectroscopic eclipse work began it was imagined that if a part of the cir- of the expedition the more we see that most excellent work has been done, cumsolar region, say 1 deg. from the sun, was brought on to the slit of and, as we surmised in our previous article, new questions have been the spectroscope, and a bright line spectrum obtained, here was evidence brought to the front as well as old ones probably settled. Let us deal that the corona extended to 1 deg. from the sun. It was only some time with some of these seriatim. One matter, outside the domain of solar after such observations as this were commenced that it was found that the physics, but yet of extreme interest to the astronomical world, is con- earth’s atmosphere was so flooded with coronal light that even the dark cerned with the possible existence of a planet or planets nearer to the sun moon itself gave such a record. This fact was most strongly brought than Mercury. Such a planet has been “discovered ,“two or three times, home to us in the eclipse of last year, when the coronal spectrum was only to be lost again; its existence has been predicted from general con- photographed extending right across the dark moon, and the result ob- siderations, but yet, strange to say, it has not revealed itself when it has tained in 1871—namely,that the corona was chiefly built up of blue light— had every opportunity of doing so, for instance in the photographic record was clearly confirmed by the fact that the photographs revealed that the of the sun which is now being slowly introduced, at a sufficient number of strange, weird, lurid light, so special to eclipses, was really nothing but places on the earth’s surface to make the story almost a continuous one. the reflected blue coronal light in our air. This question was seriously taken in hand at the late eclipse by Dr. Jans- These things being premised, we can now come to Professor Hastings’s sen, the head of the French party, by MM. Palisa and Trouvel6t who observation, lie was among the first many years ago to recognize the accompanied him, and by Professor Holden, who was in charge of the importance of observing the spectrum of different parts of the sun side by American party, in consequence of the enforced absence of Professor side in the spectroscope, and for this purpose he, as well as others, pre- Young, to whom the charge had been in the first instance offered. pared a special piece of apparatus allowing him to study the chromosphere The result of this combined attack is to show that there was no body on two opposite parts of the sun’s limb at the same time. This was the near the sun brighter than a star of 5~j magnitude. Professor Holden’s instrument he used at Caroline Island this year. What he set himself to conclusion depends upon eye observations. Dr. Janssen’s depends upon do was to carefully watch during the eclipse the apparent height of the photographs of the whole region near the sun to a distance of 15 deg. all corona, as determined by the lengths of the chief line in its spectrum at round it. Such self-confirmatory evidence as this is of the highest value, the two opposite points of the moon’s diameter at which totality com- and must be held, we think, to suggest that the body seen by Watson in menced and finished. Of course, if each line were really due to an actual 1878 was in all probability a comet, as was, indeed, suggested by the definite corona of the sun, the position of its extreme summit, and its appearance of the comet seen in Egypt last year. Had the comet then length would not greatly vary, but if the s~ectroscope revealed a flash of observed been less bright than it was, so that the nucleus alone had been light, now on one side of the moon and now on the other, produced by visible, the discovery or the confirmation of the existence of an intra- some such action as that to which v~e have referred, then it is obvious that Mercurial planet would in all probability have been ‘announced to the the position of the summit of each line would greatly vary, its length world. varying in equal proportion. The question put to the sun, it will beseen, Next in point of view of general interest to this work with regard to was of a most definite character, and Professor Hastings found that there the intra-Mercurial planet, we may refer to some observations made by was immense variation in the lengths of the lines. At the beginning of Professor Hastings, which are of very great value taken in conjunction totality the 1474 line had a length of 12’ on the east side, while on the with prior work. In order, however, that the full importance of Pro- west it was seen short and faint. During the progress of the eclipse this fessor Hastings’s observation may be clearly grasped, it is necessary to go differetice in length disappeared, but was reversed at the end of totality, briefly over the history of eclipse work since the year 1869. It was only the change being greater than that which would result from the moon’s really in the eclipse of that year that we began to know anything about motion alone On the strength of this variation, Professor Hastings gives the corona, and it was only in the eclipse of 1870 that we began to appre- out the view that this paying out of light, first on one side of the dark ciate whata very difficult problem was presented to us by that phenome- moon and then on the other, is an effect of diffraction at the moon’s edge. non. The then Astronomer Royal and Professor Macdier, to cite some He, however, goes further than this, and, as we gather from his telegram among the eminent authorities writing after the eclipse of 1860, had come to. Professor Young, proposes to abolish the external corona altogether to the conclusion that the corona was mainly a non-solar phenomenon. from our text-books. Here astronomers, while acknowledging the inge- That part of it, however, was undoubtedly solar was admitted by all, for nuity which suggested the above observation, will not follow him, because the reason that it was seen before and after tota[ity. In the eclipse of he has not sufficiently taken into account the vast difference between the 1870 the idea that part of it was really non-solar was enormously strength- visible corona with which he has been dealing and the photographic ened by a comparison of observations made by different astronomers. Its corona, which, as we have already stated, is a thing quite by itself and shape seemed to change as the moon swept over it, and this, obviously, if possessing characteristics of its own but in any case it is very curious it were true, implied some action of the moon’s edge and reflection by and interesting that not only the boundaries, but even the existence of something between the observer and the moon. In 1871, when the Gov- the solar corona is again in question, and it may happen that our view of ~rnment of India and the British Association took steps to have the corona the chemical nature of the outer corona will have to be revised. photographed atthe same~timethat it was carefully observed by the naked There is another matter, and one in which the American and French eye, the strange fact was first clearly indicated that the corona seen by the observers are entirely at disaccord. This, however, is of little importance, eye was a perfectly different thing to that recorded on the photographic as the question raised was really settled by the photographs obtained in plates. The explanation given at the time was that the coronal light was Egypt last year. The Americans say that in the coronal spectrum the much more actinic than ordinary solar light of the same visible intensity, only dark line observed was D, whereas .Janssen, in his telegram to the so that in the eye and on the photographic plate twO different images were Paris Academy, announces the discovery of the Fraunhofer spectrum and built up by different qualities of light proceeding from ,different sources. the dark lines of the solar spectrum in the corona, adding that this indi- Hence the view was distinctly enunciated that the corona seen duiing cates the existence of cosmical matter round the sun. The French observa- eclipses was a dual phenomenon, partly solar, partly non-solar in its ori- tion, judging from the photographic results obtained in Egypt, is much gin, the true solar corona being filamentous with variously-curved stream- nearer the truth than the American one, but at the same time it must be ers, the visible corona being non-filamentous and consisting mainly of acknowledged that the eye observation is one of extreme difficulty. Itcan- radial lines and rifts, extending to different distances from the edge of the not, however, be said that the French observation is entirely~accurate, for, moon. Such observations as these show how extremely difficult it was to although., no doubt, there are dark spaces in the coronal spectrum, it is not AUGUST, 1883.] UNIVERSITY CIROULAPS. 153

probable that all of them will correspond with the Fraunhofer lines. From place, so enabling them not only to give out light of their own, according the careful quantitative polariscopic observations made in 1878 in America, to their special nature, but to reflect the light from the regions around we know that up to a certain point the amount of reflected light increases them to the eye of the observer on the earth. with the height of the corona, which may be taken to mean simply that NOTE—This article, which indicates a writer exceptionally familiar with the ohserva- the temperature in its higher regions is so reduced that its constituents tions ofpast solar eclipses, contains several inaccuracies. Of these, the only one of great have given up their simple gaseous nature and combined to form concrete mosnent is the statement regarding the polarization of the coronal light. Contrary to particles, which are capable of reflecting light more strongly than gases the statement here given, the@bservations of Professor Wright and myself proved that are. On the theory referred to in our previous article this is at once the polarization decreases from the moon’s limb outwards. These are the only observa- tions to which he can referf The fact is of great theoretical importance. readily and simply explained by the supposition that a reduction of tem- C. S. HAsTINOs. perature enables the association of the finer molecules of matter to take

LIST OF WORKS IN THE LIBRARY OF THE PEABODY INSTITUTE RELATING TO ASSYRIAN, BABYLONIAN, CHALDIEAN, ETC., TEXTS AND INSCRIPTIONS.

When the information was received that Professor Haupt would join the staff of the Johns Hopkins University next autumn as Professor of the Shemitic Languages, inquiry was made at the Library of the Peabody Institute in respect to t.heir collection ofworks in Assyriologyand the related branches. TheLibrarian has beenso kind as to furnish the following list, which is now published for the information of those who may wish to follow Professor Haupt in his courses at Baltimore during the ensuing year. (Seepage 129 ef Circular 24). BIRCH, S. Records of the Past. London, 1873-81. 12 v. 12o. OPPERT,J. Exp3dition scientifique en Mesopotamie. v. 2. BOTTA, P. E. Lettres sur sea d6couvertes 8 Khorsabad, prls de Ninive. Paris, 1845. 80. Inscriptions cun6iformes. (Rev. Arch6ol. 1848.) Mdmoire sur l’Scriture cunSiforme assyrienue. (J. Asiat. 4ser. v. 9,10, 11.) Las inscriptions de Dour-Sarkayan. Paris, 1870. fo. D6convertes I Ninive. (J. Asiat. 4 ser. v. 2, 3, 4.) M3moire sur las inscriptions des Ach6nm6nides. (J. Asiat. 4 ser. v. 17, 18, 19.) and FLANDIN E. Monument deNinive. Paris, 1849-50. 5 v. ifo. • Trait3 babylonian sur brique. (11ev. Arch3ol., n. s., 1866. v. 14.) BaANDIs, J. Ueber den historisqhen gewiun . . . der assyriachen lnschriften. Berlin, and MIiNANT.J. Las fastes de Sargon. Paris, 1863. fo. 856. .80. Grande inscription du palais du Khorsahad. Paris, 1863. 8vo. Bunese, E. A. History ofEsarhaddon. London, 1880. 80. PETTIGREW, T.J.- Account of a bilingual inscription. (Arebteologia, v. 31.) BURNOUF, E. L. M8moires sur deux inscriptions cunSitormes. Paris, 1836. 4o. PLACE, U. Ninive at lAssyria. Paris, 1867. 3v. fo. Surdeux inscriptions cunOiformes trouv5es pr5s dHamadan. (J. Asiat. 3 ser. v. 2.) PRARTORIUS, F. Bemerkungan zu ainigan inschriften Sargons. (Deutach. Morg Gesells. CsewoLsoN, D. A. Ucher Tammnuz u. 5. w. St. Petersburg, 1860. 80. Zeits. v. 27.) Coxmc, W. H. Cylinder of Ilgi. (Roy. Soc. Lit. Trans. 2 ser. v. 9.) RAWLINSON, SIR H. C. Cuneiform inscriptions of Western Asia. London, 1861-75. CazossAT, E. DR. Classidcation des caract5ras cunliformes babylonians et ninivites, 4 v. ifo. (Vol. 5, 1880, will be received next autumn.) Paris. n. d. 40. Bilingual readings—cuneiform and Phcenician. (Roy. Asiat. Soc. Jour. n. s. v. 1.) DicLiTacie, F. Assyrisehe studien. Leipzig, 1874. 80. Memoiron theBabylonian and Assyrian inscriptions. (Roy. Asiat. Soc. Jour. v. 14.) ENEBERG, C. Inscription de Tiglath Pileser ii. (‘.7. Asiat. 7 ser. v. 6.) On the inscriptions ofAssyria and Babylonia. (Roy. Asiat. Soc. Jour. v. 12.) HAGER, J. Dissertation on the newly discovered Babylonian inscriptions. London. Notes on paper casts ofcuneiform inscriptions from Behistun. (ArebRologia. v. 34.) 1801. 40. Persian cuneiform inscriptions at Behistun. (Roy. Asiat. Soc. Jour. v. 10, 11.) HAUPT, P. Die sumerisehen Familiangesetze in Keilschrift. Leipzig, 1878. 40. Selections from historical inscriptions of Chaldea, etc. London, 1861. fo. -, HINcacs, E. On the polyphony of Assyrio-Babylonian cuneiform writing. Dublin, SAINT MARTIN, A.J. Nouvelles observations sur las inscriptions dePersapolis. (Acad. 1863. 50. • des Inscript. M6m. v. 12. pt. 2.) LAYARD, A. H. Inscriptions in the cuneiform characters from Assyrian Monuments, Dun m8moire relatifaux antiques inscriptions de Parsepolis. (J. Asiat. 1 ser. v.2.) London, 1851. fo. - SAULCY, L. F. J. C. nse. Iteeherches analytiques sur las inscriptions cun3iformes du Discoveries in the ruins 6fNineveh and Babylon. London, 1833. 80. syst5ma m6dique. Paris, 1860. 80. Nineveh and its remains. London, 1849. 2 v. 80. Lexique de linscription assyrienne de Behistoun. (J.Asiat. 5sar. v. 5.) Monuments ofNineveb. London, 1833. fo. Traduction de linscription assyrienne de Behistoun. (J. Asiat. 5 ser. v. 3.) LENORRANT, F. Las dieux de Ilahylone at dalAssyrie. Paris, 1877. 80. Fragment du texte assyrienne de linscription de Bisitoun. (Rev. Archlol. 1849. La plus ancienne inscription en lan,,ua Assyrienne. (Rev. Arch. n. a. 1873. v. 26.) Inscriptions trouv3es I Khorsabad. (Rev. Arch3ol. 1849.) Lattres assyriologiquas. Paris, 1873-74. 2 v. 40. SAYCE, A. H. Assyrian grammar for comparative purposes. London, 1872. 120. Essai sur un document math6mnatiqua chald6en. Paris, 1868. r. 80. Lectures upon the Assyrian Language. London, 1877. 50. Etudes cunSiformes. (J. Asiat. 7sar. v. 9.) On the cuneiforminscriptions ofVan. (Zait..Vergl. Sprachforsch. v. 23.) Inscriptions cunSiformes in6dites. (Rev. Arch. n. 5. 1869. v. 20.) SCHEADER, F. Assyriach-Babylonisehe Keilinschriftan, Lsevv, M. A. Uaber die von Layard aufgefundenen chalditiachen Insebriften (Dentsch, Die Assyrisch-Babylonischen Keilinschriften. Leipzig, 1872. 80. Borg. Gesells. Zeits. v. 9.) Kritiscbe untersuchung der Grundlagan ibrer Entzifferung. (392 pp.) (Deutach. Loseerseseisese, A. nse. Sur las inscriptions cunSiformes de lAssyrie. (Rev. Arch3ol. v. 4.) Morg. Gesells. Zeits. v. 26.) LOTTNER, C. Remarks en the nation by which the cuneiform mode of writing was Die Basis derEntzifferung der Assyriseb-Babyloniachen Keilinschriften. (Deutsch. invented (Philol. Soc. Loud. Trans. 1858.) Morg. Gesells. Zeits. v. 23.) MAURY, A. Linscription cundiformue da Behistoun. (Rev. Arebdol. v. 3.) Kailinsebriften und das Al~e Testament. Giessen, 1872. 80. MENANT, J. ExposS des diSments de la grammaire assyrienne. Paris, 1868. r. 80. SCHULTZ, F. E. M3moire snr le lac de Van. (J. Asiat. 3 ser. v. 9.) Annales des rois dAssyrie. Paris, 1874. 50. SMITH, G. Assyrian discoveries. London, 1875. 80. D3couvertas assyriennes. Paris, 1880. 160. Assyrian eponym canon. London. 80. Inscriptions assyriannes. Paris, 1839. r. 80, Chaldean account of Genesis. London, 1876. Ellments depigraphie assyrianne. Paris, 1864. r. 80. History of Assurbanipal. London, 1871. 4o. Inscriptions de Hausmourabi, rol de Bahylone. Paris, 1863. r. 80. Phonetic values ofthe cuneiform characters. London, 1871. 40. Notice sur quciques cylindres orientaux. Paris, 18~8. 80. History of Sennacherib. Tr. from the cuneiform inscriptions. London, 1878. 80. MoRDTMANN, A. D. Entziffarung der armanisehan Keilinsebriften von Van. (Deutach. Chaldcaan account ofthe deluge. London, 1872. fo. Morg. Gesells. Zeits. v. 26. 31.) and RENOUF, P. L. P. Lists of Assyrian and Egyptian texts. Records of the past. Ueberdie Kailinsebriften zweiter Gattung. (Dautsch Morg. Gesells. Zeus. v. 16. 24.) vols. 1-10. MUENTER, F. Versuchuaber die kailfoermi4en Insebriften ze Persepolis. Kopenhagen, SPIEGEL, F. Altpersische Keilinsabriften. Leipzig, 1862. 80. 18 2. 120. TALBOT, H. F. New translation of the inscription of Bellino. (Roy. Soc. Lit. Trans. Nosnus, E. Assyrian dictionary. London, 1868-72. 3 v. r. 80. 2 sar. v. 8.) Memoir on the Scythic version of the Behistun inscription. (Roy. Asiat. Soc. Jour. Translation of an inscription ofNebuchadnezzar. (Roy.Soc. Lit. Trans. 2 ser. v. 7.) v. ii.) Translations ofAssyrian inscriptions. (Roy. Soc. Lit. Trans. 2 ser. vols. 7, 8.) OLSEAUSEN, .7. Pruefung des charakters der in den assyrisahen Keilinsebriften Comparative translations of the inscription of Tiglath Pileser I. (Roy. Asiat. Soc. enthaltenen sa,nitischan Sprache. (Berlin Akad. Wissens. Abhandl. Philol., 1864.) Jour. v. 18..) OPPERT,J. Elalon des mesuras assyriennes lixd par las textes cun6iformes. Paris. On the inscription of Kimamumurabi. (Roy. Asiat. Soc. Josmr. v. 20.) 1875. 80. Additional notes on Assyrian inscriptions. (Roy. Asiat.Soc. Jour. v.18.) Inscriptions assyriennes des Sargonides. Paris, n. d. 80. VAux, W. S. W. Nineveb and Persepolis. London, 1850. 80. El3mants de la Grammaire assyrienne. Paris, 1868. 80. WALL, C. W. On the different kinds of cuneiform writing in the triple inscriptions of Etudes assyriennes. Paris, 1857. 80. the Persians. (Roy. Irish Acad. Trans. v. 21.) Histoire des empires de Chald8e at dAssyrie. Paris, 1870. 80. Etat actual du dechiffrement des inscriptions cun~iformas. Paris, n. d. 80. Sec also Catalogue of the Peabody Library under Assyria, Babylonia, Chaldm, etc. 154 JOHNS HOPKINS [No. 25.

LIST OF MODELS OF MATHEMATICAL SURFACES BELONGING TO THE JOHNS HOPKINS UNIVERSITY.

These models are of plaster, excepting Nos. 17, 25, 26, 27, 28, which are constructed of 28. Two circular cones, thread model showing portion of one sheetof outer cone and both threads. sheets of inner cone,wills tangent plane to outer cone; both bases can beinclined and the upper base rotated as in No. 27, B in limiting position shows both systems of generators of the SURFACES OF THE SECOND ORDER. same hyperboloid touched by hyperbolic paraboloid (radius of 1. Right circular cone, showing elliptic, hyperbolic, and paraholic sections (diameter of upper base 10 cm., radius oflower hase 20cm., altitude of cones hase 18.5 cm., altitude 29.5 cm). 22.5 cm.). 2. Sphere (radius 4.5 cm.). 29. Elliptic cone, showing principal sections (semiaxes ofbase 10.4 cm. and 5.4 cm., alti- 3. Ellipseid, showing principal sections (axes VS j/2: 1, Major semiaxis 5 cm.). tude of cone 11.5cm.). This is theasymptotic cone to Nos. 12-16 4. “ lines of curvature (axes as in No. 3). 30. “ showing lines ofcurvature (dimensions as in No. 291. 5. “ “ principal sections (axes j/3: j/2: 1, Majorsemiaxis 9 cm.). 31. Elliptic cylinder, showing twisted cubical ellipse (semiaxes of base 4 cm. and 2.3 cm., 6. “ lines ofcurvature (axes as in No. 5). altitude 10.5 cm.). 7. “ principal sections (semiaxes 6 cm., 4.15cm., 1.05 cm.). 32. Hyperbolic cylinder, both sheets, showing twisted cubical hyperbola (altitude 10 cm.). “ geodetics through two umbilics (axes V3: y’d: 1, Major semi- 31. Parabolic cylinder, showing twisted cubical hyperbolic parabola (altitude 10.3 cm.). axis 9.4 cm.). 34. “ showing twisted cuhical parabola (altitude 10.3 cm.). 9. “ ofrotation (prolate spheroid), showing geodetics (axes 3: 2: 2, semiaxis of rotation 8.75 cm.). OTHER SURFACES. 10. “ “ (prolate spheroid), showing two varieties of envelope of geodetics 35. Cubic surfacewith 4 real conical points, 6 real 4.fold and I real single straight lines, through a common point (axes 3: 2: 2, semiaxis of rotation 4 real 8-fold, 6 real 2-fold and I otherreal triple tangent plane. 6 cm.). 36. Wave surface for optically uni-axial crystals, one octant of outer sheet being removed 11. “ (oblate spheroid), showing two varieties of envelope of geodetics taxes 8.8: 7.8, nearly the ratio for cale-spar, dimensions 9 cm., through a common point(axes 3: 3: 2, semiaxis of rotation 8 cm.). 3.5 cm.). 37. Wave surfacefor optically bi-a tat crystals, outer sheet removable (axes 12.2 cm., 8.3 12. Hyperboloid oftwo sheets, showing principal sections (transverse semiaxis 2 cm.,, cm., 6.2 cm.). The ellipsoid corresponding to this surface is see No. 29.). No. 7. 13. “ oftwo sheets, showing linesof curvature (axes as in No. 12). 38. “ “ foropticallybi-axialcrystals,two octants, showing ellipsoidal and 14. “ ofone sheet scud asymptotic cone, showing principal sections (semiaxes of spheroidal lines on both sheets (semiaxes 12 cm., 9 cm., 6 cm.). gorge ellipse 4 cm. and 2.1 cm., height of model 23 cm., see 39. Dupins cyclide, ring variety (dimensions 17 cmn., 17 cm., 6 cm.). No. 29). 40. “ “ horn “ ( “ 18.7 cm., 15.3 cm., 5.7 cm.). 15. “ of one sheet with esy ptotic cone, showing hoth systems of rectilinear 41. “ spindle “ ( 11.5 cun., 11.4 cm., 9.7 cm.). generators (axes as in No. 14~. 42. “ parabolic” ( “ 15cm 135cm 10cm.). 16. “ ofone sheet with asymptotic co e, showing lines of curvature (axes as in 43. Hummer’s surface (16-nodalquartic) with 16 real nodes. No. 14). 44. “ “ “ 8 17. “ ofone sheetwith asymptotic cone, thread model showing hoth systems of mm mm 4 rectilinear generators, threads stretched hetween two parallel 46. Central surface ofan hyperboleid of one sheet; two models show the two sheets of the elliptic sections (axes of gorge ellipse 4.2 cm. and 2.6 cm., surface separately, and a third represents the two together heightof model 24 cm.). (axes of hyperboloidS: 2:1, the last being the conjugate axis.) 18. Elliptic Paraboloid hounded by section perpendicular to axis, showing principal 47. Focal surface of a system of rays, nearly coincident with the central surface of an sections (sesniaxes of base ellipse 9.5 cm. and 6 cm., height of elliptic paraboloid; two models show the two sheets of the model 20 cm.). surface separately, and a third represents the two together. 19. “ “ showing elliptic sections perpendicular to axis (dimensions as 48. Susface ofrotation ofconstant positive curvature, meridian curve meeting the axis of in No. 18). rotation. 20. “ “ showing linesof curvature (dimensions as in No. 18). 49. Surface of rotation ofconstantpositive curvature, meridian curve not meeting the axis 21. Hyperbolic paraboloid (eqnilateral) hounded hy circular cylinder shout the axis of rotation. showing principal sections (diameter of cylinder 14 cm.). 50. Surface of rotation ofconstant negative curvature, meridian curve meeting the axis of 22. “ “ showing hoth systems of rectilinear generators (dimensions rotation. as in No. 21). 51. Surface of rotation ofconstant negative curvature, meridian curve not meeting the axis 23. “ “ showiisg hyperbolic sections perpendicular to axis (dimen- of rotation. sions as in No. 21). 52. Heticoidal surfaceof consta I positive curvature 24. “ “ sbowing lines ofcurvature (dimensions as in No. 21). 53. ‘. “ “ negative 25. “ “ thread model showing both systems of rectilinear generators, 54. Surface ofrotationof constant mean curvature (unduloid), showing geodetic lines. threads stretched hetween two parallel parabolic sections 53. Surface of rotation of constant nusan curvature (nodeit), showing geodetic lines: one (dimensions 28 cm., 17 cm., 20.2 cm.). model represents the surfacegenerated by a complete period of 26. “ “ thread model showing hoth systems of rectilinear generators, the meridian curve, and a second representsthe ring generated threads stretched between opposite sides of agauche rhombus hy the1oop. jointed at two opposite vertices (side ofrhombus 32 cm.). 56. Surface qfrotation ofconstant mean curvature (catenoid), showin, geodetic lines. 27. Circular cylindecwith tangent pl’mne, thread model both hases can heinclined to make 57. Susface generated by rotating the tractrix about its asymptote, showing geodetic lines elliptic cylinder, and upper base can he rotated to make hyper- and an asymptotic curve. holoid of one sheet tonched hy a hyperbolic paraholoid along a 58. Surface whoseequatio ‘is 4s ~ nun (u, is), ~, u, is being used as rectangular coordinates. common generator shows also a ruled quartic surface with 39. Catenaries on a sphere. line of striction (radius ofcylinder10 cm., altitude 26 cm.). 60. Hemispherical bowl with loci of aprojectile, showing also the locus of lowest points cor- responding to different horizontal velocities. July 1,1883.

SYNOPSIS OF THE RECENT SCIENTIFIC JOURNALS Published here. American Journal of Philology. Edited by PRO- the number of derivatives is no test of the autochthonous character of a FESSOR GILDERSLEEVE. Vol. IV. Whole No. 13. word. Egueta, a kind of sulphur, is derived from AGH, m choke.’ ropy6~ is a derivative of 0-AR, as also Popy6; and mliouac, bf(dm are for bPio~uac and Article 1.—The Color System of Vergil, by THOMAS R. oFin and connected with ohovoc PRIcE. In the Notes, ThNToN WARREN shows that Gradivus was originally This paper was prepared for the Philological Association of the Johns Grandivus and that Mars Grudivus was in the beginning a god of growth; Hopkins University, and read before that body on the 14th of April, 1882. H 1~NRY NETILESHLI’ maintains that the title bucolic caesar-a was rightly An abstract will be found in the University Circular, No. 15, p. 205. given to the cadence to which Theokritos was so partial. The Greek gram- rasrians had begun by characterizing a particular kind of hexameter- as Article H—Historical and Critical Remarks, introductory to ‘bucolic’[and] ‘when the name bucolic had been attached to a hexameter a comparative study of Greek Accent, by MAURICE BLOOMFIELD. of which the first word formed a dactyl and in which the fourth foot also A treatise of 42 pp., of which a rdsum6 is given in University Circu- • ended a word, the phrase bucolic carsuera may easily have been attached lar, No. 22, p. 66. to the particular cadence in the fourth foot’ ; for J. IR. HARRIS’S ‘Trans- position in Seneca’ see University Circular, No. 22, p. 69; ‘whilst being Article ILL—Etymological Studies, II, by J. P. POSTGATE. reviewed’ is cited by H. E. SHEPHERD from the memoirs ofGeorge Selwyn Liceo and ticeor are traced to distinct roots; ticeo goes back to the root (1779). of ?uvicrccv (intrans.) m leave off,’ ticeor is referred with Corsson to RIK, This number contains Reviews of K6r-tinq und Koschwilz’s Franzbsiselee ‘reach out.’ Compare potliceri, licitari, bpi~’cas~ac, digilo ticeri = ~vpaiv Sluedien; of Votlmbtter-’s Sammiung Franzdsischer Neudruche; of Wende- opi~aas1~ae. Trio in septentrio (for *tri/to *trigo from TRAGH), is the tin For-ster’s Attfr-anz6sische Bibliothek, by A. M. ELLIOTT of Gas-nell’s dragger of the plough, the ox. £fodus is for surdus (comp. pddo for sr’p~u) Beowuif, by J. A. HARRISON; of Ruthe~fo~~d’s Babrius and Slur-ms rrpiv, and is connected with seresco, ser-enus, aipacov for aFipccov, defruturn. by B. L. GILDERSLEEVE; of Schuckburgh’s Lysias, by C. D. MORRIS; of Airr6g is referred to du (1Pm), hence the ‘living, breathing’ man himself; L. T. Sunith’s edition of Gorboduc, by H. WOOD; of Steudemund’s Due though, if this is true, the consciousness was lost very early. Bo2~j3o’~ is Gommedie Par-allele di Difito, by MINTON WARREN. derived from I3op (0-A. R) and means m eatable.’ The derivatives from but- The Reports give abstrnctsof Gernoania. Hermes, ZeiischrifI der deulschen bus (Lat.). which seems to be a borrowed word, are late and Pm.chnical and Mor-gentdndischen Gesellschc’fI, Journal Asiati even if they were not, we can see by the many derivatives of machina that 1mue, and Mnemosyne. AUGUST, 1883.] UNIVERSITY 011WULAPS. 155

DEGREES CONFERRED, 1883.

Doctors of Philosophy. MAURICE FELS, of Philadelphia, who pursued his preliminary studies under Mr. E. Cohen. WILLIAM J. ALEXANDER, of Hamilton, Ontario, A. B., Uni- Principal Studies: German, History, and Political Economy ; — versity of London, 1876. His principal subject has been Greek, Latin, Philosophy, and Physics. the subsidiary, Latin. He submitted a thesis on “ Participial Periphrases in Attic Prose,” which will be prepared for publica. D. STERRETT GITTINGS, of Baltimore, who pursued his prelimi- tion in the American Journal of Philology. nary studies with Mr. H. W. Luckett. Principal Studies: Latin and German ; — Greek, French, and WILLIAM C. DAY, of Baltimore, A. B., Johns Hopkins Univer- Chemistry. sity, 1880. His principal subject has been Chemistry, the sub- ordinate, Physics. He submitted a thesis on “ The Oxidation of W. BEATTY HARLAN, of Churchville, Maryland, a former fi—Cymenesulphamide,”. which will appear, in modified form, in student of St. John’s College. the American Chemical Journal. Principal Studies: Chemistry and Romance Languages; Mathematics, Mineralogy, Physics, English, and Political Econ- WILLIAM P. DURFEE, of Berkeley, California, A. B., University omy. of Michigan, 1876. His principal subject has been Mathematics, his subordinate, Physics. He submitted a thesis on “Symmetric GEORGE T. KEMP, of Baltimore, a former student of the City Functions,” of which portions have already appeared in the College. American Journal of Mathematics. Principal Studies: Chemistry and German~ with History, English, and Ethics. ,—Physics, Biology, GEORGE S. ELY, of Fredonia, N. Y., A. B., Amherst College, 1878. His principal subject was Mathematics, his subordinate, GONZALES LODGE, of Baltimore, a graduate of the City College Physics. He submitted a thesis on “Bernonilli’s Numbers,” of in 1881. which portions have already appeared in the American Journal of Principal Studies: Greek and Latin ; — Physics, French, and Mathematics. German. KAKICILI MITSUKURI, of Tokio, Japan, Ph. B., Yale College, WILLIAM E. STRATTON, of Baltimore, a former student of the 1879, who here pursued studies in Biology, and has since been City College. called to the Professorship of Zo6logy in the University of Tokio, Principal Studies: Biology, German, and Chemistry ;—French Japan. His thesis on “The Structure and Significance of some and English. Aberrant Forms of Lamellibranchiate Gills,” has been published HENRY W. WILLIAMS, of Baltimore, who pursued his prelimi- in the Monthly Journal of Microscopical Science. nary studies under Mr. W. S. Marston. BERNARD F. O’CONNOR, of Baltimore, Bach. ~s Lettres, Uni- Principal Sludies: Mathematics, German, and History ;—Latin, versit6 de France, 1874. His principal study was the Romance Physics, and Logic. Languages, the subordinate, Latin. He submitted a thesis on HENRY V. WILSON, of Baltimore, a former student of the City “The Syntax of Ville-Hardouin.” College. (6) Principal Studies: Romance Languages and German;—Physics, Bachelors of Arts. Chemistry, Biology, and Latin. WILLIAM J. WITZENBACIIER, of Hagerstown, Maryland, a WILLIAM S. BAYLEY, of Baltimore, a graduate of the City former student of the Washington County High School. College in 1879. Principal Studies: Mathematics and German~ Principal Studies: Chemistry and German ;—French, Mineral- History, and Political Economy. ,—Latin, French, ogy, Physics, with History, English, and Ethics. (10)

APPOINTMENTS, 1883-4.

Fellows. JOHN DEWEY, of Burlington, Vt., A. B., University of Ver- mont, 1879. Philosophy. WILLIAM M. ARNOLT, of New Brunswick, N. J., B. D., Rut- gers Theological Seminary, 1882. Greek. JAMES R. DUGGAN, of Macon, Ga., A. B., Mercer University, 1877; M. D., Jefferson Medical College, 1879. Chemistry. GUSTAV BISsING, of Baltimore, A. B., Johns Hopkins Univer- sity, 1882. Mathematics. WILLIAM S. FLEMING, of Wetumpka, Ala., A. B., Davidson College, 1878. Greek. ADAM T. BRUCE, of New York City, A. B., Princeton College, ARTHUR L. FItOTHINGHAM, of Rome, Italy. Shemitic Lan- 1881. Biology. guages. ARCHIBALD L. DANIELS, of Kendallville, Indiana, A. B., Uni- ELGIN R. L. GOULD, of Oshawa, Ontario, A. B., Victoria versity of Michigan, 1876. Mathematics. University, 1881. History. W. S. B., University of Wiscon- ELLERY DAVIS, of Baltimore, ARTHUR S. HATHAWAY, of Decatur, Mich., S. B., Cornell sin, 1879. Mathematics. University, 1879. Mathematics. DAVID T. DAY, of Baltimore, A. B., Johns Hopkins Univer- WILLIAM H. HOWELL, of Baltimore, A. B., Johns Hopkins sity, 1881. Chemistry. University, 1881. Biology. 156 JOHNS HOPKINS UNIVERSITY (JIRCULARS. [No. 25.

HANS C. G. VON JAGEMANN, of Naumbnrg, Germany, Naum- HOMER W. HILLYER, of Waupun, Wis., S. B., University of burg Gymnasium, 1876. Modern Languages. Wisconsin, 1882. Chemistry. EDWARD H. KEISER, of Allentown, Pa., S. B., Swartlimore FREDERIC S LEE, of Canton, N. Y., A. B., St.’ Lawrence College, 1880. Chemistry. University, 1878. Biology. GUSTAV A. LIEBIG, JR., of Baltimore, A. B., Johns Hopkins GONZALES LODGE, of Baltimore, A. B., Johns hopkins Univer- University, 1882. Physics. sity, 1883. Greela. C. W. EMIL MILLER, of Baltimore, A. B., Johns Hopkins ALBERT G. PALMER, of Baltimore, A. B., Johns Hopkins University, 1882. Greele. University, 1882. Chemistry. CHARLES A. PERKINS, of Ware, Mass., A. B., Williams Col- lege, I 879. Physics. ERNEST M. PEASE, of Boulder, Col., A. B., University of Colorado, 1882. Latin. LEwIs T. STEVENS, of Baltimore, A. B., Johns Hopkins Uni- versity, 1882. Biology. B. JAMES RAMAGE, of Newberry, S. C., A. B., Newberry College, 1880. ilistory. LEWIS W. WILHELM, of Baltimore, A. B., Johns Hopkins University, 1880. llistory. ALBERT 11. TOLMAN, of Chicopee Falls, Mass., A. B., Williams College, 1877. English. Graduate ~Scholars. ARTHUR YAGER, of Georgetown, Ky., A. B., Georgetown Col- FnANK DONALDSON, Jr., of Baltimore, A. B., Harvard Uni- lege (Ky), 1879. Political Economy. versity, 1879; M. D., University of Maryland, 1883. Biology.

PROCEEDINGS OF SOCIETIES.

8cientific Associatwn Papers read: May 2.—Fiftieth regular meeting. Professor Sylvester in the chair. Thirty members The Office of PublicProsecutor, by F. J. GooDsow, Professor (elect)of Administrative present. Law in Columbia College, New York. (Abstract onp. 147). The Income Tax in the United States, by H. W. CALDWELL, Instructor (elect) ofHis- Papers read: tory in the University of Nebraska. (Abstract o p. 147). Note on the Distributionof Heat in the Spectrum of an Incandescent Solid Body, by HA. ROWLAND. May ll.—PresidentD. C. Gilman in the chair. On the Relation of Bilateral Symmetry to Function by B. M. HARTWIcLL. (Abstract Papers read. eup. 149). Hu~o Grotius, the Founder of Modern international Law, by ARTHUR YAGER. Review of the Results Obtained by Fouqud and Michel Lhvy, of Paris, in the Syn- ReviewNotices of the 30nth Anniversary of the Birth of Grotius, by Dr. J. F. JAHE- thesis of Rocks, by G. H. WcLLxAoes. SON. America as a Field for Church History, by Dr. PHILIP SOSIAFF,of Union Theological Seminary, New York. Philological Association. May 4.—Forty-seventh regular meeting. Professor Gildcrsleeve in the chair. Twenty- May 18.—Dr. H. B. Adams in the chair. seven members present. Paper read: Taxation in Maryland, by C. M. ARMSTRONG, Esq., of the Baltimore Bar. Papers read: The Laws of Tone-Color in the English Language, by A. H. TOLMAN. (Abstract en May 23.—Dr. H. B. Adams in the chair. p. 140). Papers read: On a Plautine Pun, by M. WARREN. (Abstract on p. 141). Taxation in Maryland, continued, by C. M. ARMSTRONG. (Abstract on p. 147). On Some Points in the Relation of the Norman Dialect to English Pronunciation, Review of Certain Results of the United States Census of 1880, by JOHN C. ROSE, by H. C. G. JADEMANN. (Abstract eup. 141).. Lecturer (elect) in the University of Maryland. A further Note on the Stichometry of Euthalius, by J. H. HAscius. (Abstract eup. May 30.—Dr. H. B. Adams in the chair. 140). Paper read: The Revised Tariff in its relation to the Economic History of the United States, by Historical aiui Political Science Association, TALCOTT WiLLIAMS, of the editorial staff of the Philadalphia Press.. (Abstract ems p. 148). Aprit 6.—Dr. H. B. Adams in the chair. Papers read: Mathematical Socicty. Topical instruction in History, by Professor WiLLIAM F. ALLEN, of the University April 15.—Professor Sylvester in the chair. Nine members present. of Wisconsin. (To appear in a work en Methods ef Teaching History, edited by Dr. G. Slantey Hall, and published by Gian and Heath). Papers read: German Methods of Writing and Teaching History. (Letters rrom a Unieersity Stu- A Remark on a Farey Series, by W. B. STORY. Note On Binodal Quartics, by B. W. DAVIS. (Absts~act assp. 144). dent its Germany, read by H. B. Adams). A Proof of a Theoreus of Jacobi, by Correspondence, by A. S. HATHAWAY. (Abstract April 13.—Dr. H. B. Adams in the chair. on p. 143). Papers read: On a Theorem in the Fundamenta Nova, by J. J. SYLVESTER. The Limits of Co-operation, by B. R. L. GOULD. (Part I. of a Monograph hereafter to On the Intersections ofCurves drawn on Quadrics, by W. B. STORY. be reportedin the Ussiversity cireulars). Historical Rsmarks on i’albot County and the Eastern Shore, by Dr. SAMUEL A. .Muy 16.—Professor Sylvester in the chair. HARRIsON, of Easton, Maryland. Papers read: On aim Expression for Euler’s Constant, by F. FRANKLIN. (Abstract on p. 143). April 20.—Dr. H. T. Ely in the chair. A Remark on the Intersection ofCurves drawn on a given Ruled Surface, by W. E. Customs ofLand Tenure among the Boys of MeDonogh Institute, Baltimore County, STORY. (Absirstet en p. 143). by JOHN JOHNSON. On Farey Series, by J. J. SYLVESTER. (Abstract enp. 143). Socialistic and Co-operative Features of Mormonism, by the Rev. (1. D. B. MILLER, of St. Mark’s School, Salt Lake City. Metaphysical Club. April 27.—Dr. H..B. Adams in the chair. May 8.—Thirty-first regular meeting. Dr. G. Stanley Hall in the chair. Twenty-two Papers read: members present. Machiavalli, the Founder of Modern Political Science, by EDnAR GOODMAN. Papers read: The Induenca of John Locke upon Political Philosophy, by B. J. RAMAnE. Rhythiss in the Classic Languages, by B. L. GILDERSLEEVE. May 4.—Dr. R. T. Ely in the chair. Wundts Logic of Chemistry, by I. RENSEN.

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