322 MONTHLY WEATHER REVIEW. JUNE,1920 pressure need not be considered at resent. The range of mounted in a light invar frame (D), in such manner that movement required and freedom from vibration must be changes of length corres onding to changes of tempera- secured by the use of stron elements well supported. ture are engraved upon tB. e record-plate by the style (E). The ap aratus. describe% . herein is su gested as a The strips (T, T) are insulated from their support. btisis for Purther e,xperimental study. It flas not been The inner ends or ed es of the plate-carrier (C)and the constructed, but the princi le of bfr. Dines's smc.essfu1 frame (D), are securef under tension, to spring hinges engraving instrument has R een followed, and essential in the center of the tube (E"), and therefore restrict the parts already have been used to a limited extent in in- motions of the pressure tubes to an arc whose axis is instruments produced by Richard and other manufac- the center of the tube (E"). By this mertns longitudinal turers. Referring to figures 14, 15 and 16, the pressure- movements of tlie pressure tubes are prevented and element (B) is composed of two helical Bourdon tubes there are no pivots with the Tariable friction inevitable secured in a light frame (A), so that their free ends move when Bourdon tubes of this kind are mounted in the in opposite directions when there is a change of pressure. usual way, Another a plication of this device, in the A smgle tube could be used, but the double-tube ele- construction of R simpP e thermograph without pivots, ment 1s preferred.for the reason that thereby may be is shown in figures 17 and 1s. Here, circular motion secured greater compactness and rigidity. One tube about the center of the coiled element (T), is obtained carries the record-plate C),and the other the teniperature- by securing to its free end the frame (D). Adjustment element. The: latter consists of two or more strips of for rnuge is accomplished by changing tlie position of very thin bronze (T, T), connected by spring hinges and (.D)tis shown by the dotted lines. A GENERAL THEORY OF HALOS. By CHARLES5. HASTINQS. [Tale University, -day, 1920.1 SYNOPSIS. here and escape an undue lengthening of this paper by unnecessary repetition. The general theory of halos develo ed in this rper rests on t,lie (1) The ordinary circle about the sun of 2'2' radius, aseumptions that two kinds of simpfe icecrysta s-elongated Iies- sgonal rods and hexagonal plates-nre occasionally present in a toler- :Lttributed by Mariotte to the action of ice crystals sus- ably transparent atmosphere; moreover, that these crystals suhiding pended in the air and having faces inclined at 60°, the in uiescent air would necessarily fall into four groups. directions of their crystallographic axes being entirely '&e firstportion of the paper estdblishes the validity of the assump- fortuitous. This explanation of the commonest of all tions by re erence to well-recorded observations. The second portion is devoted to a development of the conequences halos is thoroughly satisfac.tor.y and universally accepted. from the presence of each of these groups for various altitudes of the (2) The 22'-parhellia, often called sun-dogs, are pm,- sun. It is there shown that all the authenticated featiires of coniples matic images of the sun right and left of it and at the halos are nitarally explained (escepting certain rare multiple con- same altitude. With a low sun they are at the angular centric circles) aa inevitable consequences of t,he hypotheses. In addition, this portion gives a new means of clwifpng the various distance named, but at a higher altitude the angular t;henomena. showhg unsuspected relationships a6 well as essential separation increases. They are not seen hi her than 50°. iversity in certain otlier casea whcre comniori origin wm Cornirrly At high latitudes they are more frequentf y noted than assured. any other feature and the explanation-also first ad- vanced by Mariotte-as due to hexagonal ice orystals I. with mistently vertical axes leaves nothing to be Dun the 72 ears which have elapsed since Bravais deairex ublishe37 his oeebrated and comprehensive work on cirole-a faint, oolorless circle every- galos man% observations have been accumulated- distant from the zenith and passing some 'even y means of photography-and much has This was attributed by Thomas Young been written m the esort to improve questionable points the faces of hexagonal prisms fallin in the theory presented by that admirable writer. As vertically. Bravais improved this theory bp the remara regards the esorts of the theorists it does not seem iinfair that crystals with their principal ases persistently hori- to say that they have been uite futile; st least, no solu- zontal would also contribute to this feature. 1 shall tion of a dficulty.left by ravais, as far as known to show that proIpb1-j only such reflection as is total, hence ;B from the interior of the crystals, is generally effective. me has ever commanded , general acceptance. The eldorate mathematical discussions by Pernter of the (4) LJpper and lower tangent arcs to the 22O-circle to the 46' circle and of the, so called, arcs These are due to the resenc.e of crystals whose rincipal illustrate the rather sweeping state- ases are horizontal, tR e lateral faces having any xirection is a logical conclusion from premises in space. As the sun rises to an altitude of about 45' which no instructed meteorologist can possibly accept. t,hese two arcs unite and form a ring inclosing the 22"- Before advancing any new views regarding the highly halo and touchin it at its hi hest and lowest points. At complex phenomena involved it will be well to summarize very high sun tiisP ring, cafl ed the circumscribed halo what was known when Bravais finished his work. The by Bravais, approaches more and niore a true circle. number of features which lie considered and attempted may esis t alone. Admirable photographs to account for was about twenty. Of them we niuy T1iFtahen rinaat ew Haven, Conn., and at Chester, Pa., of the ignore one or two as not being sufficiently authenticated, halo of March 30, 1915, have been published in the MONTHLYWEATHER REVIEW.' Bravais gave .a very. but we must add two which are of unquestionable complete analysis of these features with tables which authenticit ; thus the total number remains nearly the same. UjYortunately, a small minority only of tliese may be used to find the position of any desired point - _---_ were satisfactorily explained. V\;e nay catalogue these 3 Map, 1915,43: 213-216 and October, 1915,43: 498-499. Unauthenticated | Downloaded 10/02/21 05:25 PM UTC M. W. R., June, 1920 [To face p. 323.1 Photo by Paul %hulk TEE SUN DOGS. FIG.7.-A reproduction of the remarkabk ph Unauthenticated | Downloaded 10/02/21 05:25 PM UTC M. W. R., June, 1920. o fac, ,,. FIG.lQ.,-Meteorograph in basket. FIG.ZO.--Meteorograph with cover removed, showing mechanisms. Unauthenticated | Downloaded 10/02/21 05:25 PM UTC JUNE,1920. MONTHLY WEATHER REVIEW. 323 with any assigned altitude of the sun. In the calcula- whelming numbers as to be effective. The other is a tions which are at the basis of the solutions given below little less evident although even more formidable; the I have saved mysqlf unnecessary labor by recourse to presence of any crystal not immediately effective in the these tables. production of a given feature obscures it. The condi- (5) Upper and lower tangent arcs to the i6O-halo. tions of development of rainbows.and of halos are, in a These are exactly tangent only in the cases of n solar sense, antithetic. In the former the more opaque the altitude of 22.1O for the former and 67.9" for the latter, background, provided that the is due to rain- but they may be conspicuous .when the sun departs drops alone, the more brilliant in tho several degrees from these statlons. Their fornis will latter a considerable a pear in certain of the solutions iven in this pa.per. mary requisite. Thus economy in the number of types &e theory and analysis of this qeature by Bravais of crysta.ls assumed in my theory is of the highest appears to be faultless. ini ortnnce. All theorists since the time of Bravnis mould cloubtless fn the theory presented here only two form of crystals include as a sixth feature of coniples halos finally and are postulated both of which are the simplest types of ice crystals and both of which are familiar to observers. The first is that of n hesagonal prism with a short prin- cipal asis--in short, hesagonal plate of which the thickness is a small frsction of its diameter. Such crystals I shall style the A ty e. The other €om is that, of n hemwiid prism of dich the length is much reater than tge diameter: it might be described as a and, as in the fex onal rod. This second form I shall designate as the 8 iype. Both types have dihedral ed es of 90" and of 120 , the former bein t.he angle at wiich the basal and side faces meet aiicfthe latter that kof the lateral faces : hut opbicxlly (as rega.rds transmitted light) they yield only prisms of 90° and of 60°, the rism of smaller angle being truncated by the plane wR ich forms the intermediate face of the hem from bein the case.