D RA Y S O N I A

BEI N G AN ATTEMPT TO EXPLAIN AN D POPULARISE THE SY STEM OF THE SECON D ROTATI ON OF THE EARTH

AS DISCOVERED BY THE LATE

MA"OR- EN L DRAY SON G ERA A . W .

FOR FI FTEEN Y E ARS PROFESSOR RO YAL MI LI TARY ACADE MY WOOLWI CH ,

ALSO GIV IN G THE PROBAB LE DATE AN D DURATION OF THE LAST ’ GLAC A L ER OD AN D FURN S NG GEN ERAL DRAY SON S DATA I P I , I HI , FROM WHICH AN Y PERSON OF ORD IN ARY MATHE MATICAL AB ILITY I s EN AB LED TO CALCULATE THE OB L U T OF THE ECL TI C IQ I Y IP , THE RECESS ON OF THE E U N OXES AN D THE R T P I Q I , IGH ASCEN SION AN D D ECLIN ATION OF THE FIXED STARS FOR AN Y YEA AST RESENT OR UTURE R, P , P , F

DE O EY ADMIRAL SIR ALGERNON F. R H RS

'

K . C . B

E L O N G M A N S R E N A 0 0 . , G N D

R 39 PA TERN OSTE ROW, LON DON

N EW YORK BOMBAY AN D CALCUTTA , ,

P R E F A C E

IN the following treatise I have adopted the title Dray sonia in honour of a man whose scien tific attainments have

but been little known or recognised, whose death in September

1901 was r o to r mi l c a g eat l ss ast ono ca scien e, and who in

u u s l he i f t re day wil , I think, acknowledged as hav ng been a

- remarkable discoverer . I refer to the late Major General Al W r R Ar fred ilks D ayson, late oyal tillery, who,

i i ui hi s in add tion to d sting s ng him elf in his profession, was for fi t P s R M A W w f een years rofe sor, oyal ilitary cademy, ool ich, and for two years attached to the Royal Observatory at

' G u Practi al Mtlztar Sur ve in The reenwich, a thor of c y y g, Conmwn Si hts in the Heavens The Last Glacial E och E g , p , w

er'iences o a Woolwich Professor Thirt Thousand ears p f , y Y of ’ Earth s Past Histor r the y, ead by the aid of the discovery of

o Untrodden Ground I m o the sec nd rotation of the earth, , p rtant

Geolo ists Pro er Motton o the Fixed Stars and g , p f , etc.

ull diffi u I am f y aware of the c lty of my task, and of how imperfectly I can do ju stice to Drayson in attempting to

e d ul describe his syst m indee , I sho d not venture the attempt

not G n r s his were it that e e al Dray on, shortly before death,

u u u repeatedly rged me to write pon the s bject . Writing to me very shortly before his death, he said The reason why I thought that you ought to write something is that it would be a loss to astronomical science if the accurate calculations which you have made were allowed to be buried in your work book and among my papers . I refer especially to your PREFACE

20 - 0529 investigations to obtain the annu al motion of the pole ,

u C e r A . D . 229475 the ann al angle at . the zero y a ,

u ui the cycle years, the ann al precession of the eq nox

1 00 u u i u in 9 , the ann al dimin tion of the obl q ity and the variable rate of this decrease . ’ All these calculations are based on soun d geometry. In hi s again urging me in his last touching letter before death, when complaining bitterly of the unr easoning opposition he

S an d had encoun tered, he said I have pent between two

u hl . three hundred po nds in getting my books , pamp ets , etc ,

u i un s ur . p bl shed, and have received less than ten po d in ret n

- but ru Money making has not been my object, that t ths in nature should be made known . I can only claim to have

u ul done my best, tho gh whether good res ts will follow I

’ cannot say. I also can only claim to have done my best. My work in assistin g Drayson began after reading his

o n Ground Untr dde , and has been carried on almost entirely

’ Dra son s u hr by letter . y letters to me amo nted to t ee or

u d un his . four hundred, and were contin e til death From

’ this correspondence and from Drayson s works I learned a

u u li — great deal, and fo nd the occ pation enthral ng too much

’ k Shortrede s mir ms so, for in wor ing with ad able logarith , l which admit of accuracy to the fi of a second of arc and to "fi m

u ur i of a second of time, p and into the small ho s of the n ght,

n I considerably impaired my eyesight. I was i du ced to look ’ Dra son s h into y system by my old and distinguis ed friend,

n C u the late Sir Joh owell, who , when on d ty at Osborne, had

’

ra son s ro n o E . lent D y Unt dde Gr und to H. H the then Crown

Pr G fte ds E ss incess of ermany, a rwar the mpre Frederick, and

H . R . H. told me how great an interest had taken in the matter .

u H. R The s bject also has engaged the attention of . H. the

u C u W A D ke of onna ght, who, when at oolwich cademy as a

u u cadet, had st died nder Drayson, and was thus aware of i his great abil ty. I mention this as another instance of the PREFACE great interest always taken by members of our Royal Family fi in scienti c matters .

’ l sc Dra son s u I be ieve I have been a good holar of y , j dging ki ff from his nd appreciation of my e orts , for in an article of hi s orkshire Post some years ago in the Y , the following com mendation appears It is quite un necessary for me to refer fi m to the scienti c attain ents , especially in practical astro R N A mi . nomy, possessed by d ral de Horsey In the oyal avy

n ur these are well k own . I may say, however , that d ing the fifteen years that I was Professor of Woolwich I looked over several thousand examination papers on various qu estions in practical astronomy whi ch had been worked out by officers and cadets , who were excellent mathematicians , and to whom the practical working of spherical trigonometry was mere

’ but child s play, in no single instance have I seen anything equal in accuracy and neatness to the work accomplished by

’ Admiral de Horsey. The above flattering opinion of my attainments far exceed

u but s ch abilities as I may possess, I here insert it as a record

’ of General Drayson s appreciation Of the assistance I rendered him in astronomi cal compu tations from 1893 u ntil that dis

’ ’ 01 Dra son s tingui shed astronomer s death in 19 . y lamented death occurred withou t his receiving that pu blic recognition fi m di hi of his scienti c attain ents and scoveries w ch he merited, and which I trust posterity will accord him .

DE O EY . F. R . H R A. S 1 Gowns, Mar ch 191 .

C O N T E N T S

PREFACE

’ DRAY SON S THEORY OF THE SECON D ROTA TION OF THE POLE OF THE EARTH

ZERO YEAR

STAN DARD OF Trn E AND RIGHT ASCENSION

’ ‘ TEMPERATE GLACIAL EPOCHS

I N TR O D U C T I O N

DRAYSON’S SECOND ROTATION OF THE EARTH

' ’ E ur s mu o — t. v L L p e. GA I EO

A . D. t

I N the above diagram the circle is intended to represent the path traced by the pole of the earth in its course round a ° ’ " d u 29 25 47 f C cycle of years with a ra i s of rom , the E centre of second rotation . is the pole of the ecliptic distant ° Z u 6 f 0. abo t rom , which I have termed the zero year, is A D 2295 E the position the pole will attain in . . when and C are aligned ; when the obliquity of the ecliptic will be at its mi i um m dl n m , and the earth therefore at the id e point of Z’ its temperate epoch . represents the place the pole at tained G E B C at the middle of the last lacial poch, . . , ° ’ when the obliquity of the ecliptic was abou t 35 25 P the r u PE represents the pole of ea th at vario s periods ,

l u i u Pa the ob iq ity of the ecliptic at var o s times, the polar ’ di a OPa stance of (say) Draconis , and the angle the right Ca i o ascension of that star, and its d stance from the pole f A 2

i P i second rotation . Sim larly B is the polar d stance of (say) rsse M P 3 U inoris, the angle C B is the right ascension of that

G f . star, and Bis its distance rom the centre of second rotation The dotted line PA’ shows the direction of the first point of C r PA Aries at the beginning of the h istian era, and its direction about the present time . B ascen In describing the angles CPa. and OR as the right i u u s ons of those stars, it sho ld be added that they are so s bject

6 . 18 h. s correc to or h or , as the ca e may be, and to a tion for standard of time in order to assimilate them to the N u Al an d recorded right ascensions in the a tical manac, to G r the reenwich standard rate of sidereal time, as desc ibed VI I in Section . The following diagram is intended to Show the position of

i - G a P the ecl ptic and its pole at the mid l cial eriod, when the 9 i ui i u 35 wi obl q ty of the ecl ptic was abo t 5 , as compared th

- their positions at the present or nearly mid temperate period, in whi ch the obliquity is abou t

It will be observed that at the mid- Glacial Period the Arctic and the Antarctic circles come down to abou t lati tude and that the tropics of Cancer and Capricorn 9 u u u 35 extend from the eq ator to abo t latit de 4 .

N orth P ole

Equa to r Equator

So uth Pol e

EXPLAN ATION OF THE DIAGRAM

C the t is centre of second ro ation .

E the pole of the ecli tic at mi d- temperate period p . ' TT c at mid - m the e liptic te perate period . ’ E the pole of the ecliptic at mid - Glacial Period . ’ GG i t mid- a P the ecl p ic at Gl cial eriod. 3

The designation second rotation of the earth may be

but M - G open to objection, it is the name given by ajor eneral u d r Drayson, the a thor and iscove er of the system, which I shall endeavour to describe in these pages ; it is therefore B e sufi cient for my purpose . y what ver name the movement u i may be called, I refer to the revol t on of the pole of the u 0 Odd earth ro nd a centre in some years, instead t u of, as or hodox astronomers describe it, ro nd the pole of the ecliptic in abou t years . ’ As u Dra son s is un 1 I nderstand y system, it fo ded ( ) on u the ass mption that the stars, with some exceptions, are fi if xed ; or that their movements, any, are so small as to be inappreciable by observers on a planet so distant fr om 2 fi the stars . ( ) That, the stars being xed, their apparen t motions in right asce nsion and declination are alone due ” to the axis of the ear th altering its inclination about 20 3 hi annu ally . ( ) That t s alteration in the inclination of the axis of the earth is a movement in a small circle at a radius ° ' ” u 29 25 47 b r of abo t o n a point in the celestial concave, ° ’ u 6 0 0 f which point is abo t rom the pole of the ecliptic, and situated as hereinafter described in at present about

18 h . right ascension .

Some professional astronomers, who may have done me u the hono r to read the above few lines , will then perhaps lay down my paper saying that the system appears to be s i founded on hypothe es which are not proved, and wh ch are not in accordance with the long established teaching R of our greatest astronomers . ead su ch and su ch a work at page so and so and you will see how erroneous are your views ; we refuse to consider or even read argu ments which ’ our - are not founded on the dicta of orthodox text books . u un To those who th s reason I have no reply, less it be

’ ’ u t i hi C N on ra ion a/m di lor to q o e a l ne of Dante s T rd anto , g , ssa But ma guarda e pa . the many deep thinkers whose reputation and emoluments are not dependent on adherence

- w to orthodox text books ill perhaps read on , remembering that scientific truths are Often arrived at from apparently u u nfounded hypotheses, the proof of which is bro ght about 4

u u u u h by s bseq ent reasoning , and by the res lts of s c reason ing coinciding with facts which could not exist on any other hypothesis than the one first su ggested . If orthodox u ul a thority had alone been listened to , we sho d still have to admit that the earth was stationary, and that all the heavenly bodies revolved round the earth as a centre . I am not foolish enou gh to say Of my very li mited knowledge ’ D a son s t m ut but that r y sys e is absol ely exact , I do say that it appears to afford an easy means of calculating the i ui u obl q ty of the ecliptic, the precession of the eq inoxes , and the right ascension and declination of stars with preciseness

un r fu u for h d eds of years past or t re , and that it provides w a standard basis of time which ill not, as at present, be ul an always accum ating error . C orthodox astronom ers do any one Of these thi ngs ? Can it be claimed that the m 3m 35 6 8 present system of ti e is correct, seeing that of u rel ima inar time 1834 P p y g y were added in , that rofessor Stone finds a fresh accum ulation of error of u p to 1892 m , and that the best astrono ers admitted the whole ’ su bject having fallen into confusion ? General Drayson s or but system may be right it may be wrong, its results have shown ample cau se for its careful and u npreju diced u S u examination . If s ch examination ho ld be accorded, and the results I have mentioned be Shown to be correctly at

d fur wi our n u taine and ther, if th present k owledge s ch results O i k ur can be bta ned by no other nown method, s ely this alone

ul wo d go far to prove the correctness of his system . If English astronomical au thorities continu e to refu se it fair

consideration , there is a danger of foreigners claiming to

discover what Drayson asserted thirty or forty years ago . A u lready in a work recently p blished, entitled Astronomie M ‘ ’ Po u laire . : C ul p , Flammarion says est la Terre se e qui ’ " et ui m en est anim e, c est elle q acco plit pendant cette longue

p"riode u n e rotation Obliqu e sur elle - meme en sens contraire ’ ur de son mou vement de rotation di ne . This is precisely what Drayson stated some thirty years before Flammarion ; in reply to which an astronomical authority informed him u u u that if s ch was the case chaos wo ld occ r , and the earth 5

u n wo ld be smashed up. O this Drayson dryly observed that this was one of the objections urged against the daily rotation of the earth in former times . ’ The truth or fallacy of Drayson s system should be deter mi r mi but ned by ast ono cal research alone, it is interesting to note that modern geology confirms that system whi ch establishes with geometrical precision (not by m ore infer ce s as E en , as geology teache ) the date of the l t Glacial poch, showing that the coldest half of the cycle commen ced about ar i um u ye s ago, reached its max m abo t years ago when the Arctic circle came down to abou t the latitude of u A i u D rham and the ntarctic c rcle to that of Tierra del F ego, b and min e u 7545 . u ter at d abo t years ago This statement, p lished by Drayson twenty years before geologists would

d i u . u a mit it, was rid c led by them In a late p blication Drayson writes that at that time more than one dis tingui shed authority stated that although he did not feel competent to criticise my astronomical and geometrical argu ul ments, he co d positively state that the dates I gave for the duration and termination of the Glacial Period were n mi absurdly incorrect . He k ew that the period ter nated u mi about a q arter of a llion years ago, and lasted at least ’ a million of years . For every great advance in opposition to scientific authori ties there must be a martyr ; in former times this martyr im s r di ul was tortur ed or burned . In modern t e he is i c ed, di t his contra cted, or ignored, then years af er death is given ’ li e a statue . I am inc ned to believe with the lat Sir John mi un fi R E Cowell, and as a pro sing yo g of cer of the oyal ngi i w hi neers wrote to me some t me ago, that it n a generation , ’ in Dra son s if although probably not y l e, his system will be

- the accepted one of the text books . S E C T I O N I

DRAY SON ’S THEORY OF THE SECOND ROTATION OF THE POLE OF THE EARTH

As a pream ble to the endeavour I am abou t to m ake to explain ’ Drayson s theory of the second rotation of the pole Of the

s earth, I perhap cannot do better than reprint that which

u u 1894 w u s I wrote on the s bject in J ne , and hich was p bli hed at the tim e in the Isle of Wight Cou nty Press and in the orkshire Post w u Y , together ith a letter I had previo sly

- addressed to Major General Drayson .

THE GLACIAL PERIOD AS PROVED B Y THE SECON D ROTATION OF THE EARTH

A i Of ul m d scovery incalc able advantage to astrono y, although m ade and described in pu blished works more than u n twenty years ago , appears to be still nack owledged, and

ur m even branded as an abs d heresy, by so e professional astro u m ff nomers Of the day . In order to add my h ble e orts to

u u ifi u u i mi u ind ce q al ed and nprej d ced persons to exa ne f lly,

u all u test, and if tr e establish before the world the tr th of ’ G Dra son s eneral y system, I propose to bring the matter as briefly as so large a su bject will adm it to the notice of those ’ u u nacq ainted with Drayson s works . For this purpose it is necessary first to tou ch u pon certain fallacies Of orthodox astronom y which seem to be almost universally accepted u p to the present day .

Ou tlines o Astronom Sir John Herschel, in f y, stated that the

e. pole of the heavens (i . the pole of the earth projected to the celestial concave) describes a circle in the heavens rou nd the Of pole of the ecliptic as a centre , at a constant distance 23° 28’ in years . (Since that was written it has been i generally admitted that the d stance between the two poles,

i . e. l u l the ob iq ity of the ec iptic, varies . ) G A 1870 Sir eorge iry, writing to Drayson in September , says : The direction of the movement of the terrestrial pole in any one year on the surface of the globe is at right angles to the great circle connecting the place of the terrestrial pole ”

in . A with the place of the ecliptic pole that year gain, in October 1870 the same great authority wrote to Drayson : The state of m atters regarding the pole Of the earth and the pole of the ecliptic is thi s : the pole Of the earth does not u Of w revolve ro nd the pole the ecliptic , in the sense in hich ou un y derstand it . Su pposing the poles connected by an i arc of great circle, the pole of the ecl ptic has a small motion

’ in the direction Of this are towards the pole of the earth and m a s all motion transverse to it . The pole of the earth has no

m bu t motion in the direction of the arc above entioned, has i a large motion transverse to it . The d stance between the ne two poles is not invariable . O can only describe the above t Of di P did statemen s as a mass contra ctions . If always E u ur i move at right angles to , it wo ld be a geometrical abs d ty to say the distance between the two varied . In April 1893 a very high authority wrote to me ‘ AS m f a atter of act, the pole of the ecliptic does not change its position in space by more than abou t one degree on either side u of the mean, and the obliq ity of the ecliptic will only vary m u to the sa e amo nt, one degree approximately on either side ” of the mean . R A R Sir obert Ball , stronomer oyal of Ireland, in so late a work as The Story of the Heavens states that the pole hi of the earth moves in a circle, the centre of w ch is the pole Of the ecliptic ; and he illu strates this by a star map of Piazzi ’ u Smyth s, and gives years as abo t the period of the cycle of precessional movement . Viewing the contradiction that the pole of the earth moves at right angles to the pole of the ecliptic, and yet alters its 8 distance (and putting aside the geometrical absurdity of a w w O circle ith a movable centre) , it ill be bserved how hope lessly at sea the above au thorities are u pon the su bject . Against their inexplicable theories Drayson asserts and proves geometri cally that

r wi 1 . The pole of the earth does not revolve in a ci cle th the pole of the ecliptic as a centre . i 2 . The extent of variat on of distance between the two poles is not limited to about its maximu m variation being

r ius Of 3 . The pole of the earth desc ibes a circle with a rad ° ’ ° 2 4 r hi 6 di 29 5 7 from a cent e, w ch itself is stant from the pole of the ecliptic .

4 . The period of the cycle of precessional movement is u r about (since fo nd to be yea s, not years, and the pole of the heavens traces a different path am ong ’ the stars from that shown in Sir Robert Ball s Story of the

Heavens .

5 . The last glacial period is proved to have commenced

B . C. w u B . C. abou t , as at its height abo t , and ter 62 At a minated abou t 5 9 R C. the height of the gl cial period ° ' the obliquity of the ecliptic was 35 25 47 and consequ ently m n u u ur the arctic circle ca e dow to abo t the latit de of D ham, and the antarctic circle to that of Tierra del Fu ego .

Having thus given some idea of existing orthodox theories u and of their contradiction , I proceed to f rnish a brief de ’ scription Of Drayson s system . For fuller details those who ’ are interested in the su bject should refer to Drayson s principal P Motion o the Fired s T . On the ro er Star hirt works , viz p f , y ’ Thousand Years of the Earth s Past History (Chapman Untrodden Ground in Astronom and Geolo K Hall) , and y gy ( egan to u s M — Paul CO . ) also the p bli hed papers of ajor General

n C Sir Joh owell . From a geometrical analysis Of the curve traced by the u 1800 pole of the earth d ring the past years, it proves to be ° ’ an arc of a circle which has a radius of 29 25 The centre of the circle is located in the heavens in about

10 results Of my calculations from data of many years back agreein g minutely with actu al present Greenwich Observations — results only now obtainable by constant observation, and which no astronomer can calculate u ntil he accepts and u ses ’ Dra ALGERN ON DE ORSE . yson s system . H Y

‘ M E 23r d A r il 1894 . MELCO B E HOUSE, COW S, p

EAR EN ERAL RA SON — As ou D G D Y , y are aware , I have dur ing several months been engaged testin g by numerous u u w ur calc lations the acc racy, or other ise, of yo discovery of i ur u Of the second rotation of the earth . Th s p s it has been

r li ou m a k enth al ng interest to me, and y y now like to now A the result . m ong these calculations (in all of which I have

u se w made no of solar tables , or rate per year) ere the follow

' z- h om A 22 5 2 u u D . 9 ing Starting the date . , I calc lated by yo r system what the obliquity Of the ecliptic would be for the On 1885 . year , working the problem by spherical geometry com paring my calculated obliquity with that recorded in the ” - N u Alm u d ff 0 07. a tical anac, I fo nd a i erence of only I then i eta U ae took the recorded R A. and decl nation of the stars rs ’ Majoris and alpha Draconis fr om Bradley s Catalogu e of 1st u 1755 all wi u Jan ary , and (as I have said for cases , tho t use w u making any of the rate of change , no fo nd only by u O f ul o . O perpet al bservation) I calc ated the R A. and De n

l s n these stars for the t Janu ary 1895 . O com paring my

u w N u A m u res lts ith those given in the a tical l anac, I fo nd a

ff 140 eta Ursee M 05 - 063 di erence, in years , for ajoris of only

R 8 - A . 1 6 6 . al ha 0 156 in and in Deen , and for p Draconis ” - in R A. 1 45 A k n l nis o . a ha and in De n gain, wor i g p Draco 1755 1875 120 u R. A. 1875 from to ( years) , I calc lated its for ° ’ 14 - - . 1 . 0 121 s . u 64 58 25 2 to be h m , and declination pl s .

u ul O These res lts I co d not compare with bservations, as , mi f 1875 N u A the star being o tted rom the a tical lmanac , e kn its position appar ntly was not own at Greenwich . Deter

i u la bda r m ned to apply a cr cial test, I selected the stars m U see

Mi N P si ma Octanti noris close to the orth ole, and g s close to u P u the So th ole, stars having an ann al variation in R A. 11

respectively twenty- fold and thirty- six- fold as great as the M r 18 0 u . C u lambda U a 5 average alc lating rs e inoris f om , I fo nd ” R 5 - - Decn . 1 0 its A . and in 895 to be within 0 249 and 0 65 respectively Of the results by Observation (and by rule of thumb for four years in advance) recorded in the Nautical

l s t n 18 5 u A . u i ma Oc a tis 7 lmanac Then , calc ating g from , I fo nd ” 5 0 0 - 2 its RA . and Deen . for 1895 to be within 4 251 and 8 N u As respectively of the a tical Almanac record . tronomers ff EA 43 3 will think little of a di erence of . 5 in the case of a 21413 star which , in the twenty years , changed , and which , ’ 44 u i Of being within of the pole, m st hang on the w res the transit instrument for a considerable time . I am fu lly aware that the above calculations are unknown to all astronomers to whom you have not explained your wi system . They are problems which any one th ordinary

ur . mathematical ability can work, if he knows yo system W u k w wi u u i itho t this no ledge, and tho t accepting yo r d scovery

‘

u . to be tr e, I believe no living man can work them To the A m R R A mi strono er oyal to the oyal strono cal Society, and to all the learned professors in the four qu arters of the globe

- n who adhere to their text book k owledge, I believe these pro ’ blems to be as insoluble as they would have been to Lobengula s

n m an . u mi medici e I am of a rather sceptical t rn of nd, deemin g that when in search Of scientific truth one should As ou hi u . take not ng on tr st y know, there are two or three minor points in one of you r pu blished works in which I differ — w m in opinion perhaps o ing to my inco petence, possibly — owing to your havin g been mistaken but these are trifles. u With regard to yo r system of the second rotation of the earth , u O if one or two calc lations only had agreed with bservation , ul bu t I sho d have said it was very extraordinary, might

But find possibly be a coincidence . when I that in no single

ul i O ul i u instance has calc ation fa led to btain res ts wh ch are tr e, and which are unobtainable by calculation from any theory differin g from your system ; when I fin d that by your great di ou u scovery, and by the system y have fo nded thereon , I am enabled to calculate with precision the obliquity of the Of u ecliptic, the precession the eq inoxes, and the polar 12

5 50 500 distances and right ascensions of stars for , , or more years past or future ; when I fin d that a precise and un changeable standard of time is obtainable from your systems us ur for all tim e to come instead of the present erroneo meas e, instead of the confusion admitted by Sir John Herschel, and the muddle in which all astronomers now appear to be u i ns di uis on the q estion of t me (for i tance, that sting hed O O s r Mr. R ff a t onomer, Stone, now adcli e bserver at xford, " has within the last few months discovered an error of 41 -5l ) i u is when, aga n, I consider that yo r system establ hes the period e one —hi of successive glacial epochs and the dat of the last t s, c m with geometri al precision, not by ere inference, as geology — teaches and when we note that modern geologists forsaking us their former theories abou t hundreds of tho ands, or even l s mil ion , of years having elapsed since the last glacial epoch — u u m now, years after yo r p blished de onstration of the fact, fix the period in accordance with your geometrical proof ul but when all the above res ts are considered, I can come u u ur to one concl sion , viz . that the tr th of yo system is estab lished u u u beyond all do bt, and that this tr th m st shortly force f ifi itsel on the scient c world . It is inconceivable to m e that the Royal Astronomical Society has not enthusiastically taken u p a subject which gives u its ru ift u —a s ch strong evidence of t th . To s s ch a matter — matter affectin g the basis of all astronomical calculation to the bottom is surely the first duty Of a learned society which ” fix R u has the privilege of the pre oyal . I sho ld have — — imagined as I believe you did that you had only to whisper ° ’ 29 25 47 in order to put astronomers on the qui vive to u t n s el cida e a discovery of enthralling i tere t, which, for a chaos u mill u u of s pposed proper motions of ions of stars, s bstit tes s ru a simple movement of the in t ment (the earth) , by which f m and rom which all astrono ical observations are made . i s As H story repeat itself. some 260 years ago Galileo ur i C 1 endeavo ed to rev ve the opernican system of 543, and explain ed the apparent diurnal revolution of all the heavenly i but u k bod es by the simple, then nac nowledged, fact of the ’ ou earth s daily rotation, so y in the present day explain the 13

absurdity of ascribing complicated so - called proper motion to the stars by the simple fact Of the second rotation of the ° ’ earth rou nd a fixed point di stant from the pole 29 25 47 a fact you prove by calculating results which Observations u dh show to be tr e, and which no astronomer who a eres to i but u li the ex sting orthodox, erroneo s , theory can accomp sh . Y ou will probably not be imprisoned nor made to swear on your knees that your system is not tru e you will not even be made to repeat once a week for the remainder of your life P but ul — the seven penitential salms , it wo d seem that as in — the days of Copernicus and Galileo you have the learned Y ou ll societies against you for a time . wi have been both

di R. A us n S. am ed and i terested in rea ng in the . notices of the ’ th M Mr i m 9 arch last . Stone s d scovery that the sidereal ti e of

1892 u Of 419 - 51 mean noon in was erroneo s to the extent . Mr — u u dl — . Stone clever astronomer as he ndo bte y is has prob

Oi u ably little knowledge , and no belief in, yo r system, and is perfectly innocent of the fact that the result Of his labours

di fi u Of ur is an ad tional con rmation of the tr th yo system . Since the au thorities at Greenwich in 1834 fudged in m 8 3 3 6 8 Of imaginary time to m ake their theories coincide

w . ith facts, the process has , I believe , not been repeated The Mr f r hi . u e ror therefore, w ch Stone dates rom the introd ction ’ V 1864 r accum of Le errier s solar tables in , has p obably been u 1834 On di lating ever since the time was corrected in . rea ng ’ Mr ul ur . Stone s paper I at once calc ated by yo system what would be the accum ulated error of the erroneou s Greenwich 1834 1892 i m system from to , and I made it agree with n a s all ’ u fraction of a second of Mr . Stone s res lt . I observe that ’

N di u Mr . u Professor Simon ewcomb sp tes Stone s acc racy, t — ur Mr . but no dou bt Stone is righ Sincerely yo s , ’ L ERN ON DE ORSE A A G . H Y, dmiral

’ Since writing the above I have tested Drayson s system

i e k conversely, . . totally ignoring his data and wor ing only from observed positions of stars as recorded in the Nau tical — — Almanac data which no one can dispute I calculated by my own independent method the radius of the circle described 14

u by the pole of the earth , the ann al motion of the pole, the angular distance between the poles of second rotation and un ul ecliptic, and other f damental items, bringing my res ts ’ out to agree with Drayson s data with sufii cient accuracy to hi Six i ul confirm their tru th . T s I did by d fferent calc ations ,

b a O i al ha viz . P et with olaris, rion s , two of p Draconis, and m two of alpha Virginie. These tests are to my ind con

u us ul ul n wi el sive , beca e their res ts co d not all coi cide th ’ Drayson s data if the latter were not correct .

The statement in the foregoing article, that the period of 31 69 f u . 7 one com plete cycle O precessional movement is abo t ,

u years , and the conseq ent apparent periodicity of the glacial

u u fi epoch is, I nderstand, q ali ed by General Drayson to the — I t di s di w . follo ing extent, viz is the perio city corre pon ng to

resent u the p motion of the pole , and s ch it has been for cen But vu u turies. if any con lsion of nat re, either in the past ’ u ur s u or in the f t e, ho ld alter the position of the earth s centre m of gravity, the gyratory otion of the pole, and therefore the ff i A e w u i . period city and intensity of the Ice g , o ld be d erent D E A. H . "an u ar y

’ In the above description Of Drayson s theory I have allu ded hi hh u to some points w ch he rightly wit eld from p blication,

n his but which are ow publi c property . I refer to method ’ m m Dra son s of easuring sidereal ti e . From y system it appears that by the orthodox doctrine that the pole of the earth m un a n m oves ro d the pole of the ecliptic error of ti e creeps in ,

m un u 05 - 7 u and a o ts at the present time to abo t per ann m , which error , if error it be , is entirely obviated by acceptance ’ of Drayson s system of the pole of the earth revolving round

An u di the central point herein described . ann al fference

Of 09 - 7 un but u so ds little, has to be taken into acco nt in all geometrical calculations wherein the right ascension is i a factor . Th s alteration in the annu al rate of sidereal time ’ is a discovery Of Drayson s which he wisely kept back from hi s published works and communicated alone to the late C m f Sir John owell and to yself . This dif erence of rate Of 15

’ time is not the least important Of Drayson s discoveries . In in u 1894 Wh n ou a letter to me Jan ary , Drayson writes e y have made this problem your own you will know that you are in possession of that which the astronomers of the whole ’ u world have never even dr eamed of . If it be ass med that ’ Sir John Herschel s addition of purely imaginary time ’ 3m 39 - 68 was l un Dra son s of correct, it fol ows that der y system an error Of some magnitu de will un der the Greenwich A ur system have to be corrected . short time ago I vent ed A R W C to write to the late stronomer oyal , Sir illiam hristie , to ask if I was right in my compu tation that an error in 1910

u u 54 see l him amo nted to abo t . I a so told that for the year

1892 418 - 283 O I had made the error , and that I had bserved

413 - 54 l e that Mr . Stone had made it . I hard y expect d a reply from so busy a m an ; but Sir William Christie very l f kindly rep ied at some length, to the e fect that it was not

Mr. considered there was any error, and that Stone had been i u l mistaken in su pposing one to exist . Th s s bject wi l be

in I more fully explained u nder its proper head Section VI . S E C T I O N I I

RADIUS OF SECOND ROTATION

I CAN scarcely do j ustice to General Drayson in attempting to describe how he determin ed the radi us of second rotation ° ' 29 25 47 u bu t m u u to be or thereabo ts , st endeavo r to do

s so . He appear to have been impressed many years ago by ascertaini ng from the records that the obliquity of the

l w fix un w w : ec iptic as not a ed amo t , as sho n by the follo ing

Recorder b O li uit . . q y P 24° 0’ 0 u . Strabo rocl s , etc Ptolemy 23 50 O Pappus 23 50 0 Ulu gh Beigh 23 31 58 Cassini 23 29 Flamstead 28 48 With correct refraction 23 29 2 - 5 Lacaille 23 28 19 Bradl ey 23 28 17- 6 Maskelyne 23 27 56 - 6 Bessel 23 27 54 - 78

23 27 36 -5

Nautical Alm anac 23 27 27- 38 23 27 22 2

23 27 20- 88 23 27 12 79

From the above records it appears that the obliquity had n m i been decreasi g at a di inish ng rate, and that in consequ ence the Circle described by the pole could not be round the pole u of the ecliptic as a centre , and m st be roun d some other

18

m Nautical Al anac, especially of those stars having a right

12 h . 0 . ascension within an hour of h and , from which he at ” first roughly took the annu al motion to be 20 - 1 and su bec qu ently but Of late years accepted my perhaps more ” ul 20 -0529 e complete calc ation of , which I ascertain d by the

method shown in Section III . ’ I fear the above explanation of Drayson s long labours to find his data is but a poor abbreviation ; but in order to ’ firm Dra son s ur 1894 hi s con y data, it occ red to me in that as data enabled him accurately to calculate the obliquities and N u Al positions of stars as recorded in the a tical manac, it ’ Dra son s should follow that conversely y data, if correct, should be ascertainable from authentic Nau tical Alm anac i ul records . I accord ngly made six independent calc ations from orthodox records of the positions Of stars at different

w a Of a U ae Mi d . perio s, viz t o of Draconis , one each rs noris O i w a V i O Of fi di and B rion s , and t o of irginis , w th the bject n ng ’ ’ u UP u Dra son s PP u the val e of the radi s of y cycle, the ann al u motion of the pole , and other res lting data . The mean of ° ' ’ six sul m OP 29 29 PP 20- O754 my re ts ade and , to u w but the precise acc racy of hich I do not pretend, which ’ u s go far to establish the general tr th of Dray on s system . A ful u u ler acco nt of these calc lations , with a table of their in ul w V . res ts , ill be given Section III ’ For more complete information about Drayson s m ethod fi hi s u u of nding data, reference sho ld be made to his p bli

in cations mentioned the preface to this work . S E C T I O N I I I

THE AN NUAL MOTION OF THE POLE

I N N u A m 1895 the a tical l anac , in the table of mean places ’ Of u Of stars , only ann al variation stars right ascension and

li N u A Of dec nation was given , whereas in the a tical lmanac 1898 two colum n s are inserted against both the right aseen l u sions and dec inations , respectively headed ann al precession n u m w and an al proper motion, fro hich it appears that the additional column s of proper motion were made between the

. As u two years named , however , the ann al precessions are esu O pr mably btained by observations at Greenwich, it may perhaps be assum ed that the amoun t of precession in cludes the proper motion, and that therefore , in ascertaining the

u i u ann al motion of the pole by the follow ng method . no acco nt Of need be taken the proper motion, if any .

TO find u f m m u ann al motion . of pole ro ean of ann al pre

in N cession (say) autical Almanac of 1898 . In the accompanying di agram let A0= annual precession of a star within one ho ur Of 0 h .

12 . or h right ascension, and let = AM AB =annual motion of pole c where the angle A is the si A amoun t of right ascension of the

0 12 . star from the meridian h . or h Ae B the expression AM y sin A the annu al motion of the pole has been computed for every star in the Nautical Almanac of 1898 (seventy- three in number) which is within one hour 20

l O 12 . u of h . and h of right ascension , the res ts being shown in the table at the end Of this Section . It will be seen that the mean of the results from the thirty- two stars whi ch are within one hour of right ascension O h . is and the mean Of the forty- one stars within one hour of right 12 u ascension h . is The mean of the res lts from the whole seventy- three stars will be found to be ” ” 20 -O52918 20 - O529 u u , say , which by a c rio s coincidence P bu t is precisely the amount Of aberration given by eters, how arrived at is beyond my knowledge . If it be granted that the above method of fin ding the

ua u ann l motion of the pole is fairly acc rate, there is a C AM— corollary which is not without interest . Since siilA

A0=AM >< Sin A Sin A it follows that , and that i s

This means that with the annu al m otion of the pole ascer tain ed to be either the ann u al precession in de ’ clination un f can be fo d rom the star s right ascension , or the right ascension can be foun d from the precession in declination . In the above computation for finding the annu al motion of the pole I have for obviou s reasons only taken stars within

u Of e uin oxial u . m a O one ho r the q col re I y, however, bserve AO that the expression AM applies equ ally to stars what sin A

u ever their amo nt of right ascension . For example, I take

7 C ur at random the star ) enta i, whose right ascension is in N u A 1898 14 . 29 In given the a tical lmanac of as h . ’ Let it be required to fin d that star s annu al precession in

li f AC=AM Sin dec nation rom the expression x A. Log AM 13 021772 Log sin right ascension 9- 9008594

Log precession 1 - 2030366 Whence precession 15 96014 by Nau tical Almana c

Difference 0- 002 14 21

iff g- This d erence of less than T o os of a second of are is negli ible ln g , and its smal ess tends to prove either the accuracy of the Nau tical Almanac or that Of the ascertained annu al motion u of the pole, or the acc racy of both . ’ P l u ossibly I shal be told that I have fo nd a mare s nest, and that it has been known all along that the right ascension of a star and its annu al precession in declination are functions Of u u the ann al motion of the pole, and that s ch motion can u in N u Al be fo nd the a tical manac, and is properly termed

. but fin d in aberration It may be so, I have failed to any ’ on u Outlines o Astronom formation the s bject in Herschel s f y,

- N u or other text books , or in the explanations in the a tical

ur Almanac . I vent e to think that the term aberration is

m Of us suffer f m not a happy one . So e may ro aberration of M i intellect perhaps I do . y d ctionary describes it as ’ l but a ienation of mind, there is no aberration in the works i of the Great Architect of the un verse . His laws are precise

and immutable . In conclu ding this section on the annual motion Of the u u r pole, I may say that strong reasoning wo ld be req i ed to ’ shake my belief in Drayson s assertion of abou t forty- five fi years ago , and con rmed by the French astronomer Flam hi marion some t rty years after Drayson, as stated in the Intro du ction Of this work : that the one single motion of the pole t is w u of the ear h , ith certain exceptions, the sole ca se of the us hi w l apparent motion Of the stars . Let hope that t s il not i but be claimed as a French d scovery, be rightly awarded to

Drayson . As an additional proof that the one single motion of the pole is the cause of the apparent precession Of stars in right " i Of ascension and declination, I append a d agram the northern ’ f G Dra son s hemisphere, copied rom an original one of eneral y , which purports to Show that whilst the centre of second C fi P rotation ( ) is a xed point, , the pole of the earth, has ’ moved on an arc with O as a centre fr om P to P between 140 A D P A . D . . . 1895 the time of the astronomer tolemy and , and that this motion of the pole has caused the so - called

See di agram at en d o f book . 22

first point of Ar ies to alter its position about thus giving the stars an apparent motion in right ascension and declina ff hi u . tion , w lst in tr th they have not moved The e ect of this one motion of the pole and of the change in the first point of Aries may perhaps be compared to that Of a dial in which the num bers representing the hours (not the dial) have been slowly turning in the direction of the hands of a watch, and ° so have changed their position about 20 in a period approach ing twenty centuries . In the diagram referred to the num erous small arcs marked ’ from Z to Z approximately Show the apparent alteration Of u the right ascension and declination of stars at s ch points, u u whereas in tr th it is the zenith of s ch stars, not the stars themselves, which have moved . To be more exact, the curves Show the direction rather than the correct amount Of w the movement, o ing to the protraction of a portion of a flat u t r f sphere on a s rface and the distor ion a ising there rom . A reference to the precessional movement in the table of

fi N u A hi S xed stars in the a tical lmanac will, I t nk , how the general accuracy of the apparent motion thu s depicted in

s the diagram . The truth of thi appears incontestable when it is considered that the otherwise unaccou nted for and variable changes in the positions of myriads of stars are all exactly explained by the one annu al motion of the pole of the earth . I am very sensible of the imperfection Of my explanation ’ Of Dra son s y diagram, and can only hope that in the fu ture the su bject will be m ore fully considered and better j ustice

done to him by those more capable than myself . 23

AN N UAL MOTION OF POLE DEDUCED FROM AN N UAL PRE CESSION I N DECLIN ATION I N 1898 N AUTICAL ALMAN AC

An nual

’ Annu al Motion of Star s N ame . he Precession . Pole of t

Earth.

02 Aquam y Tou cani y Pisciu m x Piscium

B . A. C. 8213 Phoenicis

a Pisciu m y Cephei 8 Sculptoris 27 Pisciu m

a) Piscium 2 Ceti

a Androm edae B Cassiopeiae y‘ Pegasi o Octantis i l. Cet gTou cani 44 Piscium 3 Hydri a Phcenicis 12 Ceti

e An dromedze 8 An drom edae a Cassiopeiae B Ceti 8 Pisciu m 20 Ceti y Cassiopeiae An dromedae y. a Sculptoris e Piscium i) Octan tis 4 Ursse Maj oris B Crateris 8 Leonis 24

Right me Star 9 N a . ion . Pole of the Ascen sion . Process

Earth.

v Leonis

B . A. C. 4007

8 Centauri e Corvi 8 Crucis 8 Ursae Mejoris 7 Corvi B Chamwledntis

B . A. C. 4165

B Corvi

a Cenum Venet 6 Virginis

Mean of the above seventy - three stars

26

whole period Of rotation is thereby determinable , and will be 360° 1296000” or annu al angle 40 - 81143

Wh u Of =31 755 - 814 u ence the d ration the cycle , , say abo t

years . ’ The mean of my six reversed calculations to fin d Drayson s m f bu t data ade the dur ation O the cycle years , those calculations have no pretence to precise accuracy (see

Section VI II . ) THE ZERO YEAR

TO find m u ui the zero year , the year of inim m obliq ty ’ Of r Dra son s the ecliptic, is a matter of simple geomet y, if y

m - syste and his before mentioned data be accepted . fi ur 0 In the foregoing g e , let be the centre of second rota E Of P Of tion , the pole the ecliptic , the pole the earth on any Z of given year , and let represent the position the pole in the E A 0 ale . w w 0. zero year , hen aligned ith and lso let be the position Of the pole of the earth at the beginningof the C hristian era . On reference to the diagram it will be manifest that the number Of years from P to Z mu st depend on the angle

Z =P E u fin PC C . d For example, let it be req ired to the zero ’ Dra son s u year from y data , and from the obliq ity recorded in 1898 the N autical Al manac of . In the triangle OPE we have 0P=29° 25 ' 47 CE ° ' ” ° ” 0 O EP = 23 2 - 8 find 6 7 8 9 0. , and to the angle 23 27 9 6 0 0 cosec o 29 25 47 cosec 2 14 56 58 52 56

29 26 28 sine C=4° 29’ 52 23 27 9

5 59 19 sine 269’ 52

— ” Log cosine g 16192

S E C T I O N V

THE OBLIQUITY OF THE ECLIPTIC

To fin d the obliquity for any given year we have in the accom panying figure the two sides OP and OE respectively 29° 25’ 47" ° ’ and 6 0 and the inclu ded angle

POE fin d hi EP to the t rd side , the

obliquity .

For m ui exa ple, let it be req red

to fin d the obliquity in 1900. fin d POE First the angle , and transposing the expression to fin d I V the zero year (Section . ) we have angle POE (zero year—year angle ” — 1900) 40 - 81143 ’ " 28 30 - 283

With POE thus found we have two sides and the inclu ded

find i EP = os angle to the th rd side tan ¢ tan OE . C O and cos OE - cos (OP Cos EP 95

9 02 16202 9 - 9976143 9 9986740 9 9625693 9 0202942 19 9601836

a 9- 9976288

CP 29 25 47 Log EP 9- 9625548

— - (OP da) 23 26 52 37

’ " Wh u - ence obliq ity in 27 8 3 . 29

r du e In the above case, as in othe s , I feel that some apology is to su ch mathematicians as may honour me by reading this work for having inserted the details Of simple trigonometrical

u ae e A B 0. form l , which to them are matt rs as familiar as , , M u w u y exc se is that I am riting also for the yo ng, whom I hope to entice into a stu dy of the subject .

’ THE AN GLES POE AN D OPE

As the angle POE is required in all calculations for finding u OPE the obliq ity, and as the angle will play an important part when dealing with sidereal time and right ascension , a table of these two angles for the beginnin g of each century is appended . ri E s OP CE In the t angle O P with the two side and , known as s O u a s constant , and the angle fo nd for any ye r as de cribed in hi i l OPE t s sect on, it wi l be evident that the angle for the same year may be found . I also append to this section a diagram showi ng the obliquity ’ curve on Drayson s system for the first 2500 years Of the i w u Of i ui Christ an era, together ith the amo nt obl q ty and Of its corresponding precession Of the equinoxes for the beginning Of each century. 30

THE AN GLES POE

OPE YEAR A. D. BLI UITY OF THE ECL I PT ON AN A Y I s Q IC " U R t. ’ Of the Christian Era on General Drayson s System Of the 2 41 i Rota

’ 1 and. Rotation 2 5- 3 5 47

of and . Rotation

tl cir-c le rou n d Ce ntre

- taken ao osz g] .

3 3 95 3 .

32

0 - 1 1174 i un whence in the earth travels , wh ch amo t 2000 may be considered a constant for years or more, and should be subtracted from the precession found by the pre cession triangle in which PP' is

the ann u al motion of the pole, ui the angle Q the obliq ty, and Q ’ P Q the approximate precession . PP , = - 11 hi We should thu s have precession 0 1 74 . T s sm Q r u E might be correct if the pole travelled in a ci cle ro nd , ’ Of but Dra son s the pole the ecliptic, as a centre, as by y un O system the annu al revolution is ro d as a centre, the annu al motion m u st be redu ced to the am ount it woul d be if it were direct towards the fir st point Of

TO m if hi : P Aries . exe pl y t s From in the accompanying figure draw PA EP at right angles to , and therefore towards the first point of Ar ies draw PB at right angles Al AB to OP . so draw at right BP angles to AP . Let represent AP l an exaggeration Of the annu al motion . Then wil be the redu ced annu al m otion required for computing the precession . As APE BPO EPE m and are right angles, and is com on

APB =OPE u to both, the angle , which latter can be fo nd for any year as shown in Section v .

Thus in the triangle ABP right - angled at A we have

= ' PA PB cos P . Whence

Annu al moti o >< cos1ne OPE n 0 4 1174 . si n Obhqui ty

For example : let it be required to fin d the precession in

1900 1910 ul O s and in by the above form a, b erving that the u —0 11174 t ann al motion and are constan s . 33

1900. 1910.

” ” Given N . b - A. o li uit - 8 O3 Given N . A obli uit q y . q y 3 5 8 1 102 7 ~ 28 Angle OPE l 9 30 as found ( in Sec ion . as found in ti t v ) ( Sec on v. )

Lo - ann l m - g ua otion 1 302 1 772 Log annual motion 1 302 1 772 Lo cos P g 9 9999088 Log cos P 9 - 99991 12

1 1 3 020860 1 1 - 3020884

Lo sin obli uit - g q y 9 5 998660 Log sin obliquity 9 5 998444

1 - 7022440

” - ” 60 375 56 50 - 37836

0- 1 1 174

Precession 50- 26382 Precession 50 26662 DO b a . N ut. Almanac Do. b m y y N aut. Al anac 50 25865

Differe nce 000008 Difference 0- 00797

A similar calculation for the year 1898 with the Nautical

" ° ' ” Alman ac obliquity 23 27 8 - 98 and the angle P (computed ° ’ ” V 1 10 4 - as shown in Section . ) 8 6 gives the following result

Precession by this method 50 2 6318

N u A 50 - Do . by a tical lmanac 2633

Difference 0 ' 00012

Assuming the Nau tical Almanac obliquities an d preces be ul s sions to correct, the above res t respectively show only e ——— u - co arc abo t r ut ow, n w , and fl gog of a se nd of difierent from the Royal Observatory figures given in the Nau tical Al hi O i e manac ; t s in my pin on is an additional t st, and goes far to prove the accuracy of my method of finding the pre ’ fu ur u Dra son cession for any year, past, present, or t e, nder y s system . To this sec tion is appended a table which I calculated some ten years ago to show the obliquity and precession for the

m Of u t o A. D . 2700 s com encement each cent ry, and ; al o a table of yearly diminution of obliquity from 1851 to 1950 ’ a un der Drayson s system . These t bles will perhaps lead to n more accurate investigation , and may be of i terest even to ’ un f Dr s those who do not admit the so dness O ay on s system . c 34

The data from whi ch the tables are compu ted are the ° ’ radiu s OP 29 25 the annu al motion Of the pole OE the di stance between the centre of second rotation and POE un the pole of the ecliptic and the angle , as fo d for

- each year from the above mentioned data . In the foregoing examples of a m ethod Of fin ding the Of whi precession , and also in the table precessions ch follows, the direction Of the first point Of Aries has been assumed to be at right angles to the pole of the ecliptic as generally ’ but u Dra son s fir accepted, as I nderstand y system the st point Of Aries should be considered to be at right angles to

OP i Of Of , the l ne between the pole the earth and the pole un second rotation , in which case the precessions before fo d ” ” u s 1898 50 - 27383 1900 50 - 2744l wo ld be re pectively for , for , and for 1910 fi u O i These g res, in my pinion , are l kely to be more correct than those which agree with the am ou nts given in the N autical

iff u Of Almanac . The d erence between the res lt the two systems is about in the year 1900. If it be accepted that the first point Of Ar ies is at right

ir Of Of angles to the d ection the centre second rotation , the item cos OPE may be eliminated from the form u la for fin din g w l the precession, and the expression il then be A mu al " P - 1 11 4 recession i 0 7 . sme Obhqul ty

s s w l s The prece sion , ho ever, given in the fol owing table are calculated on what I believe to be the orthodox assumption ° fir Of Ar 90 m Of that the st point ies is fro the pole the ecliptic . 35

OB LIQUITY OF THE ECLIPTIC AN D PRECESSION OF THE EQUI N OXES AT THE BEGIN N IN G OF EACH CEN TURY

‘ Difi in 2nd . Diff. in bli u t P O i . rocession . q y 0 1 0 ears I fifi 1 0 s. y . . 0 yr

24 ° 1 ' ” K 0 7 d. 4S 55B6

- 1396 ” 24 (5 26 - 6 8 . 9 48 - 6982

2 11 ~ 6 ° 1350

24 2 55 - 0 48 ' 8332 202

' o h ~ 59 32 5 c c 48 9634

193 ' l 254

: h - ~ 23 56 18 a c 49 0888 0050

184 - 1204 : n 53 14 c i 49 - 2092

175 ' w

o O o ~ ~ 50 18 C c d 49 3243 0055

166 o - 1096

°D - ' 23 47 32 C 49 4339 0056

156 m - 1040 1 ' o - h c £ 49 5379 44 56 l o 146 o

1 o ~ 23 42 29 m c 6 49 6360

137 w - 0922

o h ° 23 40 12 c c 49 7282

o b ° ' c c 49 8 141 1 17

1200 23 36 10 ' H 49 - 8938 107 b 1300 23 34 20 d 49 ° 9669 97

c ° - 32 42 10 c 50 0336 0070

o 1500 23 31 15 10 ~ c 50 ° 0933

1600 23 29 58 10 - 1 50 - 1464 ~ 0070

o - - 1700 2 3 28 5 1 t 10 1 50 1925

" 27 54 ° m 50 ~ 2317

h - - 0071 1900 23 27 e 50 2637

s 2000 23 26 32 a 10 - 6 50 °2886 '0177

: ° 2100 23 26 d 10 - 2 50 3063

4 2200 23 25 5 1 - 36

OBLIQUITY OF THE ECLIPTIC AN D PRECEssm N OF THE R — d EQUIN OXES AT THE BEGIN N IN G OF EACH CENTU Y cont .

fi i

bli Precession . O uity. q POll yr:

° ' ' 2300 23 25 50 -3201

2400 23 25 52 - 9 10 - 1 50 3 160

2500 23 26 s - 9 10 - 8 50 3 049

- 0186

2600 23 26 35 ~7 10 - 2 50 2 863

2700 23 2 7 12 -7

In the above table some irregularity will be Observed in u ff Of ur the col mns headed Second Di erence, which , co se, should not be ; the reason for su ch irregularity in calculations will be Obvious .

ANN UAL DIFFERENCE OF OB LIQUITY FROM 185 1 TO 1950

Year Annual Year Annu al Year Annual D n" A. D. i . A . D. Diff . A. D.

” " 0 -458 0 - 385 S E C T I O N V I I

STANDARD OF TIME AND RIGHT ASCENSION

BEFORE i u s Of i consider ng the q e tion t me, I may perhaps, i u u Of m w th the garr lo sness age, take per ission to make a short

- i . ur s u d ssertation Some sixty fo year ago , when frozen p r V u u u u C at Fo t anco ver, abo t a h ndred miles p the olumbia R Of m u u iver , and with plenty ti e for tho ght, I arg ed with

un Ofli cers w a us my yo g brother , no all de d, that the conf ion u of time with longit de was a mistake, and that, as a lapse Of time is measured by the nu mber Of beats Of a pendul c t a u u of a er ain length in a certain l tit de, time m st go on

‘ whether or no the Observer changes his longitude on the u u and earth, and that conseq ently there sho ld be one the An ur Of a same time at all places. ho time means a l pse Of and that time will have elapsed whether the u observer has moved or is stationary . I am m ch interested to Observe in the Press that it is proposed to adopt the sam e — time as at Greenwich over a large part of the Continent a change whi ch woul d greatly add to the convenience Of the

u i travelling p blic, and wh ch gives me hope that in the distant future the day will come when a watch pointing ’ to twelve hours will represent twelve O clock all over the civilised world . u Al though not bearing directly on the s bject of time, it may not be out Of place to remind my young readers with regard to cardinal points that there is no east and there is no west in the solar system or in the universe . The terms to east and west are merely planetary, and refer only the direction in which an Observer on a planet can note the i apparent rising and setting Of the heavenly bod es . There u is a north and there is a so th, so called from the direction 38 of the respective poles Of the earth produced to the heavenly

But u i Of sphere . j st as an observer stand ng at one the poles ul u wo d have no east or west, so in the heavenly sphere s ch

- x points are non e istent . C u Of l oming to the q estion sidereal time, the ec iptic in a terrestrial globe is u sually shown to cross the equ ator in the meridi an Of Greenwich ; but this has no particular sigui

fication i u u , as the ecl ptic m st be shown to cross the eq ator

. SO somewhere far as I have learnt, the zero meridian for right ascension is that meridi an which passes thr ou gh a point on the heavenly sphere which would be indi cated by a straight line from the centre of the earth throu gh the centre of the ’ ° sun at the instant Of the sun s polar distance being 90 at n the vernal equinox . This poi t on the heavenly sphere is

fir Of A w u called the st point ries , and as so termed beca se it was situ ated some centuries ago at the beginning Of the fir n sign Of the zodi ac called Ar ies . The st poi t Of Aries is ° l u 20 m now, I be ieve, abo t or more fro that position, and has an annu al and varying motion . The above description Of the zero point of annu al sidereal time may or may not be u correct , as I have no pretence to be an a thority on the subject . ’ According to Drayson s system the axis Of the earth changes " its inclination about 20 - 0529 in each year on a small circle ° ’ di 29 25 47 f O Of stant rom , the centre second rotation . It can be shown by a diagram that if at the vernal equin ox in any year the centres Of the earth and sun and a fixed u di point in the heavens, s ch as a stant star, were aligned, at ’ the next year s vernal equinox the same distant star would " hi is u - not be aligned . T s beca se the change Of abou t 20 O529 ’ in the di rection Of the earth s axis would by that movem ent ’ ° alter the condition that the sun s polar distance shall be 90 ui at the vernal eq nox . The practical result Of the alteration ’ in the inclination Of the earth s axis is that the condition of ° 90 w ulfil polar distance ill be f led, and therefore the vernal ui ur l Of eq nox occ a little before the a ignment the distant star .

i di ff Of fir Of Th s erence in the position the st point Aries ,

Of u u w termed precession the eq inoxes , is a q antity hich varies

40

Of the assu m ption that the pole of the earth travels round m the pole Of the ecliptic in a period Of so e years , Of fi m u instead , as he af r s , ro nd the centre of rotation m in so e years , and says that for a correct standard If Of tim e it should be measured with O as a centre . in ’ the diagram P and P be the positions Of the pole Of the u Of l earth in two consecu tive years, the ann al error rate wil be the difference between the angles OPE and OP’ E which

u 10 - 66 in 1910 amo nts to , or in time On the su bject Of a standard measure of tim e I write with

s m difiiden ce o e , and prefer where practicable to quote ’ Drayson s own words . In a letter to m e dated 3rd January

1894 m e in , Drayson gives the above diagram, referr g to P Of u 5644 B . C . the date abo t , in which is the position

5644 B . Of C . O the pole at date , the pole the second rota ° ’ t PO= Z9 25 E u Of ion , tr e position pole of the ecliptic, OE= 6° EOP =90° , and W Of P i hen the pole the earth is at , a daily rotation w ll caus e O to transit before E by an interval Of time m easured by EP the angle O. Wh P ’ wi en the pole has been carried to , a daily rotation ll cau se O to transit before E by an interval Of time measured ’

EP O Z A . D . 2295 by the angle , and when the pole reaches

E m u u O and will transit si ltaneo sly . u Of O Of The s ccessive transits , the centre the circle , give a ur u s uniform meas e or standard of time . The s cces ive tran

Of E su m hi sits , therefore , give a variable mea re of ti e , w ch also has a variable rate dependin g on the variation in the angle EPO as the pole is carried round from 5644 to

2295 . A . D . The intersection of the equ ator and ecliptic giving the equinoctial point (first Of Aries) is the point from which u right ascensions are co nted, and as the pole is not movi ng at 41

right angles to the arc joining it with the pole of the ecliptic , the su ccessive transits Of the pole of the ecliptic do not corre s ond w u f p ith the s ccessive transits O O. The variation in the angle EP’ O from year to year and from century to century becomes therefore a very important u u O u m item, beca se the s ccessive transits of give a nifor standard of tim e ; hence the su ccessive transits Of E give less

u Of u r than a niform standard time, and the meas re of ight ascension is affected thereby . ’ The change in the angle EP Ofrom century to century can ’ ° ’ be easily calcul ated as follows OP = 29 25 47 ” = 22 - 2 — - and the an gle at O ( 95 date) x 40 9. Hence with two ’ sides and the inclu ded angle the angle EP O can be found . ° ’ ” Thu s for l st Janu ary 1887 this angle=1 12 58 1787 1 30 45

‘ Diiferen ce un r 1787 188 : 0 1 47 for a h d ed years, to 7 7 ” 1067 ur 10 - 67 that is, for that cent y, or per year . The rate w ui u m bu t u u ill not be q te nifor , near eno gh to niformity for practical u se . f fi N ow for the application O this fact . A date mu st be xed fi l st u 1887 u on as a zero , and I xed on Jan ary , the J bilee ” m - . Of 10 67 year , therefore easily reme bered The correction for the erroneou s standard Of time will be minu s for dates u t 188 previous to 1887 and pl s for dates af er 7.

EXAMPLE I

Let it be requ ired to fin d the right ascension Of B Ursae 1818 Min oris for the 1st Janu ary . Having calculated OB as before PO= 29° 25’ shown , we have ° ’ PB the polar distance 15 6 2 - 4 A Of 1818 as per Nau tical lmanac , and 21° 50’ Hence in the accompanying diagram we have P0 P 0 find , 6 , and 6 to the angle ° P u 46 , which will be fo nd to be ’ 4 . 7 111 . 50 57 or in time 3 h . s As this star is in the third qu arter Of right ascension the 42

18 ur hi angle P must be subtracted from ho s , w ch gives

14 52 . 9 6 . . h . m s as the approximate right ascension ‘ Between 1818 and 1887 are 69 years to be corrected for " - erroneous standard Of time at 10 67per year . ” = S° 16 49 l in time .

4 52 . 9 6 8 . 1 h . m

— 49- 1

By calculation 14 51 205

4 5 1 20- 69 A. 1 Recorded N .

- 0 0 0 19 difference in 69 years .

EXAMP LE II

TO fin d the right ascension of B Draconis on 1st January 1 5 89 . Given OP=29° 25’ OB= 9° 17’ and PBthe polar

distance in 37 (See di agram in Example I . ) fin d OP With the three sides the angle B, which will be ° ’ " found to be 8 0 32 ° ’ 2 1 3 32 m . 8 0 h . . Take from 18 0 0

17 27 57- 9

Between 1887 and years . = ’ 2 ” x8 years 1 5 in time . 2 5 9 B u 17 . 7 . 7 ro ght down h m s . Correction +5 69 R 3 59 u . A . by calc lation

3 55 RA . N A. by .

’ 0- 04 di ff erence .

About the year 1900 I received from General Drayson the following further explanation of his system relating to a correct standard Of sidereal time 43

STAN DARD OF TIME AN D RIGHT ASCENSION

Without entering into a long and elaborate explanation Of a d I ma the st n ard of time, y state that astronomers have assu med that they have a true standard Of time by aid of a Of e x knowledge one complet rotation of the earth on its a is . But e , what is a complet rotation of the earth on its axis, ‘ and how can it be measured 4 In consequ ence of the second Of w i rotation the earth, every star ith n the circle described by the pole will transit once Oftener during an entire revolu tion u wi r of the eq inoxes than ll those stars outside this ci cle . Hence it follows that the only tru e and uniform standard of time whi ch represents a tru e rotation of the earth is that point in the heavens at which the pole Of second rotation is Of is located . As the position th point has been hitherto unlm own x t the , there e is s at present time a slight error in the supposed rotation of the earth amoun ting to about 08 - 711 per year . The right ascension Of stars is the term used to defin e the interval Of time shown by a chronometer between the transit Of a zero point in the heavens and the transit of the star . An y error as small as 08 - 711 per year might go on accumu i us e lating durin g several years, and m ght then be adj t d at all the observatories without the outside public kn owing any u 1833 thin g about it . S ch was the case between the years

1834 3m 38 - 68 ur r and , when of p ely imagina y time was O u u . u inserted to balance acco nts tsiders, nless possessing v u an Observatory, and ha ing the best instr ments, chrono di meters, etc . , have no means of scovering the right ascension Of the stars other than accepting that which is given in the k is in N autical Almanac . A person may now there an error ul ti must the standard measure of time, and yet for calc a on he take the data given in the Nau tical Almanac in order to work t ou details . For example 87 N u I selected the date 18 as a zero , and in the a tical 1887 u at Almanac, , I fo nd that the star Draconis had ° ’ 54 5 - 84 Decn . N . 64 7 . 1 . 19 743 . B A . 14 h . m s 44

° ’ I knew that PO= 29 25 47 From N autica l Alma nac I

a OPa r u Obtained P and the angle , and f om this data I co ld a An calculate Ca and the angle PO . d

as cul hence , I have proved, I can cal ate the

R A. Of P . D. . N . and assigned this and other

stars for a hu ndred years and more . But the interval Of time Of transit u f between a. and O is meas red year a ter year by a chronometer whi ch does not ’ u Of give the exact val e the earth s rotation, and hence there is an accumulating error which for any 1900 w ff u other date , say , ill give a slightly di erent val e for

an l POa a m 1900 the g e and the side C . Yet by aking the E zero the same accu rate resu lts can be Obtained . xample

N u t Al m 1900 a. s. a ical anac, , Draconi ° ’ R A 4 - 1 . 1 N De 64 5 1 13 35 . . 40 . . 8 8 . . cn h m . s

From this N au tical Almanac data I Obtain the following ° ' L OPa =59 34 46 - 8 N u A m a tical l anac . Pa = 25 8 46 - 65 OP = 29 25 47 . From this N autical Almanac da ta I find ° ’ ” = - by calculation that Oa 26 36 9 1 and ° ’ ” L : O 54 54 54 for 19000. These two valu es differ slightly from the u u 1887 u val es fo nd for the zero , beca se the standard m easure Of tim e between

1887 1900 u m is and sed by astrono ers in error . ° ’ m z 25 4 19000 . PO 29 7 I now have y constants for , viz ° ’ ” ° ’ Oa = 26 36 9 - 1 L O=54 54 54 a , and For Draconis (see 54 Untrod n . de Ground p , ) I have taken the angle O to vary

40 - 9 f ul N P. D. RA O per year, and I now calc ate the . and . a 1 5 Fro ze o Draconis for 7 5 . m r Between 1755 and 1900 there are one hu ndred and forty ’ " - = five . 145 40 38 50 A 00 years x 5 . ngle O in 19 54° 54’ angle O in 1755 — 53° 16’

N P. D a u . 1 From above calc late . Draconis 755 45

L cos - = - 5 9 77675 77 cos - 9- 95 14028

L ta 2 - n 6 36 9 6996798 - 1 6 402 8

- — 4764375 12 45 1 9 cos 9- 989148 0

1 9- 9405508

9- 98 1343 1

- = - N . P. D. 2 cos 9 9592077

1755 b a - . 24 2 6 4 4 y Br dley 7 .

P 1 755 . H c R t A s For angle at en e igh scen ion 1 755 . ” Sin 3 - 5 =9 - 9038698

Sin 26 36 9 o l 9 65 10826

1 9 - 55495 24 — Sin 24 26 47 - 616835 1

- 9 9381 173 sin - . 0m . 32 3 8 h . h h . s. . . m h . m . s .

” — - 1 8 4 3 32 3 =l 3 59 27- 7 1 45 years x 0 Deduct 1 4 3 - 09

1 5 - 1 3 7 44 6 R A. 175 5 u by calc lation .

1 3 5 7 46- 3

0 0 1 - 69 145 s for year .

From this calculation I think it will be made clear that

e hi ful u A . D . 1887 th re is not ng wonder or special abo t . It is unfortun ate that by the erroneous standard of time now used

r recorded observations o RA . u I cannot, f om f at vario s dates ,

n Obtain always the same value for O . I therefore cannot tell exactl Of l i y, and have no means te l ng, what is the exact ’ Ca distance of , as I am dependent on the astronomer s clock

A. u . ul s for the assigned R. at vario s dates I sho d he itate to determine the valu es of Ca and L C from records previous to

“ 3 “ 3 9 w a e mo a n i nde e d in , but how adjusted I

. _n u Mr even now, beca se if . there is an error of 41s in W t i i l d . time, I may be m s e ha can say is, that given the

D. u N . P. conventional RA . and at any date, I can calc late —five these items for a hundred and forty years to one second, 1887 1900 no matter whether I make , , or any other date my zero . 46

There seems to be a slight misunderstanding as to what

. W A. has been termed the correct R. at a given date hen I fi 1887 u N u have xed on a date, say , I m st take the a tical Al m manac clock at that date , and set y imaginary chrono e meter to exactly the same time for that dat . Hence on the As l st u 188 . Jan ary 7 the two clocks agree , however, the but difierence rates of the two clocks are not the same , have a " u 0 - 711 ul di f of abo t per year , there wo d be a f erence of

05 - 711 u 1888 of 1st u on lst Jan ary , on Jan ary

1889 . , and so on 1900 m r If I take as y zero , I set my imaginary ch ono

m m N A . n meter to the sa e ti e as the clock, as show by the

f w . u R A. o stars , and then ork as before It is not a q estion A ” A R . u R . of what is the correct at any date, beca se is

R A. ur not a finite qu antity like polar distance . is meas ed f m fir Ar ro an imaginary st point of ies as a zero , and by a clock which has a certain rate . Another clock which has a

flerent ul difierent di rate wo d give a result . Although at the date 2294 - 75 the two points E and 0 u m u u wo ld transit si ltaneo sly, it does not follow that the two u A clocks wo ld agree at that date . stronomers know nothing ’ abou t the point C they keep their chr onom eters going at a rate corresponding to what they assume to be a tru e rotation of m u hr the earth , and if they ade no readj stments their c ono

m at 2294 - 75 ul u iff 03 - 711 eters wo d show j st the d erence of ,

. um etc . , for each year that it now shows To ass e that at

2294- 75 r ul the two chronomete s wo d agree, and then to work 1 m 22 4 755 9 75 1755 . back to and correct the error fro to , viz

111 245 - m 5 6 7 d ff 7 56 8 u . + , and show a i erence of is not so nd

w m 1st u If e had two chrono eters , which we set on Jan ary

1887 A 05 - 711 , and chronometer had a rate of per year

ff u di erent from chronometer B , what right have we to ass me

that at 2294- 75 the two chronometers would agree One of m fi u u y greatest dif c lties and ncertainties is , whether the point

C fi m e is xed, or whether it has a slight ovement in some dir c Wh u tion . ilst it wo ld take a great force, or alteration of the

centre of gravity of the earth , to alter the position of the in the earth u poles of daily rotation , it wo ld requ ire only a

48

t 1 u af er or before 887, plus or min s as before stated in this section . The diagram which follows and its explanation will perhaps best show how the right ascension of a star is deduced from ' the angle CP star. A table showing the di stan ce of some stars from the centre u of second rotation is appended . The calc lations were made by General Drayson .

First Po int o f Aries

’

R. A. 1st u 1887 accordin to N autical Almanac Stars Jan ary , g standard of time. = — l R a. s B Pa 6 . . A. of l t u dr . A. C Naut A m . . in q a ant of h — 3 6 2nd 18 h. CP, . 7 3rd — 8 8 4th 18 h. +CP .

1887 find N u Al a ac For years other than , to the a tical m n R A CP t u . . the angle s ar m st be corrected for the yearly error

s u a - c u u of time, which (for the pre ent q rter ent ry) is abo t

03 -711 r 1887 lus per year f om , this correction being p for minus u years after that date, and for years previo s to it . 49

DISTAN CE or SOME STARS FROM THE CENTRE or SECON D

ROTATION

N f ar ame o St .

R A. N . P. D.

Deneb K aito s

B Gemin orum

a Draconis

Zu ben esch

a Scorpn

Ras Algethi

“ irdi a Capricorni Secu nda G 50

’ DIFFERENCE B ETWEEN ORTHODox AN D DRAY SON s TIME

Error in Time an d R A . er cen u r p t y.

I n Are. I n Time.

8 6 08 . secs. 8 6 08 .

” 31 - 74 70- 1 17 0 70117 00351

37 -01 704 68 0 70468

- 00298

4 1 - 50 70- 766 0- 70766

45 127 71 - 018 0- 71018

- 00201

48 - 29 71 -2 19 0- 712 19

-00150

50 - 54 71 - 369 0-71369

- 00099

52 - 02 71 - 468 0-71468 0004 9

56 - 43 67- 762 0- 715 17

2294 - 75 (I n 94 - 75 years) 0-71520

THE ANGLE PCZ OR POE AT THE FOLLOWI NG PERIODS

° ’ ” 9 0 34 - 87 2000

7 52 33 - 74 2100

6 44 32 - 59 220 0 °

5 36 31 -45 2294 - 75

4 28 30 - 31 51

l w ’ The fo lo ing diagram Of Drayson s cycle of second rotation and accompanyi ng table are intended to show the period

2 86 A . D. 9

3 A -D 39075

B . Gy m

at which the an gle CPE an d its annu al diflerence will respec mu and um e — tively attain their maxi m minim , the latt r the — annual difference being the principal factor for obtaining a standard rate of time . The diagram is based upon the following data ° ’ ° = CE=G u PO 29 25 47 , the ann al angle at

- Of u u A. D . 2294 5 and the zero year minim m obliq ity 7 .

PRINCIPAL PERIODS OF CY CLE

Year Obli uity. . q

47” 0° 0' 0 increasingto - 12 6 2 9 0 19 1 0 4 0 2 1. 2 0 or 55 3 16 57 decreasingto 2294 5 80 0 0 0 23 25 47 0 0 0 A. D. 7 increasing to 92865 72 90 79 15 462 1 28 51 12 16 57“62 decreesingto ‘ 0 180 0 0 35 25 47 0 0 0 A . D. 18172 65 52

ANNUAL DIFFERENCE (m TIME) OF ANGLE OPE FOR EACH

NN AL P IO F O 1 00 To 2400 A . D DECE I ER D R M 5 .

Year Ann u al Year Annu al Diff D A . D. . A . . 5 3

ANNUAL DIFFERENCE (I N TIME) OF ANGLE OPE FOR

H D . EAC Y EAR FROM 1850 To 1950 A .

Year Annu al Year Annu al Year Annu al ih‘ D . A. D. Diff . A . D . Diff. A . D.

secs.

1850 0- 71016

0-71 101 S E C T I O N V I I I

PROBLEM TO FIND DRAY SON ’ S DATA FROM RECORDED ORTHODOX OBSERVATIONS

u I N Section II . I have endeavo red to explain how and by

m s u what eans Drayson a certained his fo ndation data , espe

ciall m u OP . y the a o nt of the arc , viz the distance between the pole of the earth and the centre of second rotation, and CE w , the distance bet een the centre of rotation and the pole f i O . the ecl ptic The above two arcs Drayson, by trial and

m u m error and possibly by so ewhat r de ethods , ascertained ° ’ ” ° ' to be respectively 29 25 47 and 6 0 Bu t whilst fixing the above am ounts to the nearest second as the best approxi m u u m w i ation he co ld attain to the tr th , by ethods to h ch I cannot pretend to do j u stice withou t extensive references to his u p blished works , he in later years admitted to me the possibility of those di stances being m ore accurately deter min im fir m vi ed and, I think , limited h self to a con ction that the distance between the pole of the earth and the centre of ° second rotation m ust be between 29 and ’ It occurred to me in 1894 that if by Drayson s data the u obliq ity of the ecliptic, the right ascension and declin ation Of stars and other items can be fou nd with mu ch accuracy u u for any year, past, present , or f t re , it should follow that ’ by reversing the process Drayson s data can be obtainable r N u A m n f om a tical l anac and other recog ised au thorities . Thi s I have endeavoured to do by six somewhat complicated — u l w a a calc lations with the fol o ing stars Draconis , Ursae Mi r O a V u no is, B rionis , and irginis, the res lts of which are u given below in tab lated form . In that table it will be seen u ul that, altho gh the res ts vary, they all six point to a fairly

57

PROB LEM WITH [3 ORI ON I s

’ an exam ple of the method I adopted to test Drayson s

w - data, I give the follo ing extract from my work book of

1894 - 5 us w R , ing t o recorded positions of B Orionis ( igel) in the sou thern hemisphere at an interval of seventy- five years

fift - five between them, and an interval of y years between two recorded obliquities .

Given

- 1820 N u A 5h . 5m . 53 56s. RA . , a tical lmanac ° ’ ” 5 0 - 2 u P 1820 N A . 81 3 So th olar Distance ,

- 2 458s. 9m . 9 A 5h . RA . 1895, N . ° ’ ” 1 40 36 - 32 1895 N A . 8 Sou th Polar Distance , ° ’ ” Ai 23 27 36 - 5 O u 1840 . bliq ity , Sir G ry ° ’ 23 27 10 - 41 O l ui 1895 N A . b iq ty ,

Correction of right ascension for annu al error 05 - 711 Of sidereal time .

From the above data it is required to find

P di u . 1 . C ra s of second rotation

CE l . 2 . pole of ec iptic to centre of second rotation

An u AM . 3 . n al motion of pole ( )

A u Of 4 . nn al angle at centre second rotation Al C’ E mi 5 . Zero year . ignment of and and year of ni

m um obliquity .

6 u of . . D ration complete cycle iff 7. Accum ulated d erence or error of sidereal time

fr om 1834 to 1892 . 58

’

find P fin d CP . To C B. To B

- 294 588 . R. A. m . 5h. 5 . 9 m . 53 56s. R. A. 5h

5 9 23 76 6

’ CP B0 50 36- 24

’ ” - - Corr ction . l U 6 4 x ear 10 x 8 ears. e 7 7 67y s. y ' ’ 2 05 1 25 - 464

9 9 47 - 68 5 - 698

’ TO fin d Radiu s OP

cos PBcos (CP ct) where tan cos qt

’ and in the A CP B

cos CP ’B

Let UP (which equals

Then from ( 1) an d ( 2) we have 1‘ — cos (ac c) cos b cos c — ( SW) _ m cos (ao d) cos a cos d

Whence tan (13+50+d) cotan yo d)

" r I n this equation the wil x at first e lu ded m effor y y ts, an d I was in de ted to the kin dness of ir W v b S . N i en , then Director of Stu dies at Greenwich for its s , olution . 59

find 0. d - 6 fi To To nd d.

’ c=t - 6 8 1 2 1 14 - 01 Tan an a cos CPB Tan d=tan b cos CP B

- 10 8298457 10- 8347599 1 62 49 35 - 6 1

9 - 98932 62

- 10 8 1798 78 10- 8240861

- 01 -6

cos b- cos 0 cos a - cos d

- 9 1606414 Cos a 9- 1654516

9 1770486 Cos d 9- 1710861

18 - 3376900 18 3365377

18 - 3365377

0-0011523

m = 1 - 0026567 m+ 1 2 0026567 m 1 00026567

Resuming the former expression to find

~ 1 a c = cotan 3 Tan ( +% +d) 2 (c d Cotan ai 12

3 - 4243425

10- 4087605

0- 3016066

10- 1071539=Log tan

- 8

59 51 - 65

° ’ x=5 1 59 51 - 65 - 8 90 0 O

141 59 5 1 - 65

8 1 24 47- 8

60 35 3 - 85 90 0 0

a : 29 24 56- 15=CP 60

Tozfind

- — PB (PC (b) 8 _ cos cos Cos 0' cos d) ° ’ - = - 9 1654516 ¢=C as found above 81 2l 14 01

9- 7899399 29 24 56 - 15

- — - 18 9553915 (qt PC) 5 1 56 17 86 9 1770486

9- 7783429 Whence 6 40 - 1

T ' O fin d PC find P C . B. To B

’ ' Sine PCB sine PB Sine P CB sine P B ’ Sine CP B sin e

9- 9952973 9 9954014

9- 3627240 93 404676

19- 3580213 19 3358690

9- 9029822 9- 9029822

9- 4550391 9- 4328868

° ’ ° ’ " 16 33 15 43 l 4 - 6 PCB= 163 26 180 ’ = P C,8 164 16

find u To ann al angle at C. P’ CB ’ ’ ° ’ ” P CB 164 16 45 - 4 3044 - 7 PCB 163 26 0 - 7 75 years

’ POP 0 50 44 - 7

Wh - 5 6 ence 9 .

fin d u l r To ann al motion of pole on smal ci cle . ’ - A. 1 0 CP Log A. 6 84832 Logsine OP 9- 6912060

M = - - A. . I 9 93835 1 2996892 61

TO fin d u d ration of cycle . 6 1 126050 3600 1296000 Cycle 1 -6084832 4 5041218

C =31924 - 33 ycle years .

To find CE and zero year from above results and from i u 1840 obl q ities of (Sir G. Airy) and 1895 (Nautical

Almanac) .

’ ° ’ Given CP =CP 29 24 56 - 15

EP 23 27 36 - 5

’ EP 23 27 10 - 41

’ ” POP = 40 - 596 x 55 years ’ ” - 37 12 - 7

’ Fir find PP Short . rede C st on great circle ( , ase II . )

’ Cos PCP 9- 9999746

Tan PC 9- 7511480 Cos P0 9- 9400581 ’ ' ’ ’ Tan P C 9- 75 11480 Cos P O 9- 9400581

- — Log as 1 5022706 Log (cH l ) 0 1198776

’ 0- 317885366 Cos PP 99 999938

1 - 317885366 From 0° To 0 (Say) PP ’ on great circle=0

’ S ort fin EPP . h Next d ( rede Case I . )

’ Cos EP 9- 9625528

Sec EP 00374709 Co tan EP 10- 3625249 ’ ’ See PP 0- 0000062 Co tan EP 12 - 2722394

- — - Log a; 00000299 Log (c 1) 5 8388491

’ a; 1 -000069 Cos EPP 8 - 4736134

' ° ’ c —l 0- 000069 EPP z ' 88 17 62

’ Next find OPP and OPE.

’ ° ’ ” OP 29 24 56 - 15

OP 29 24 56 - 15 Cosec 0- 3087940 0 18 22 Cosec 2 - 2722456

59 8 14 - 3

29 34 7 - 15 Sine 9- 6932573

29 24 56 - 15

0 9 11 - 0 Sine 7- 4267259

19- 7010228

9- 8505 114

° ’ 44 51 51 - 4

’ OPP 89 43 42 . 8

’ EPP 88 17 40 - 93

OPE 1 26 l - 87

C . find OE . Shortrede To ( , ase II )

Cos OPE 9- 9998640

Tan OP 9- 7511480 Cos OP 9- 9400581 Tan EP 9 6374751 Cos EP 9- 9625291

Log 2; 1 - 3884871 Log (a+1) 00950358

n; 02 4461722 Cos OE 9- 9976230

— - (aH l ) 1 24461722

OE=5° 59’ 21

find POE =POZ P D . 1840. To ( ) when is at A . foregoing Diagram .

° ’ PE 23 27 36 - 5

PC 29 24 56 - 15 Cosec 0- 3087940 CE 5 59 21 Cosec 09 815474

58 51 53 - 65

29 25 56 - 82 9 6914326

23 27 36 - 5

5 58 20 - 32 9- 0172330

19- 9990070

Cosine 9- 9495035

64

' T d P . To find P . o fin

' OE cosine P OE Tan ct tan OE cosin e P OE Tan 9 02082 96 9 - 0208296

99 97962 3 9 - 998415 1

9 01 87919 9 - 019244 7

° ' " -02 q; - 8 5 58 3

- 29 24 56 . 15 29 24 56 05

- 23 2715 - 35 23 26 53 13

tan POE sine 4) Tan P Tan P sine (OP rt) 8 9872 148 9 01 64369

18 00365 1 7

9 - 5999015

8 - 4037502

° ' ” 1 2 7 4 - 96

° ' ” P in 1834 : 1 2 7 4 - 96

' P in 16 5 1 - 68

5 10 13 - 2 8 =in tim e 40 - 885

3 im e in 18 2 : 4 - 885 Whence error of t 9 0 .

AN SWERs To PROB LEM WORK ED B Y B ORI ONI s To FIND

’ DRAY SON S D ATA

° ' ' OP radi us of second rotation 29 24 56 - 15 OE pole Of ecliptic to centre of second

rotation .

M. Annu al motion of pole (A. ) Annu al angle at centre of second rota tion (AA ) Z A Of O 5 . ero year . lignment and E and year of minimum Obliqui ty Duration of complete cycle year Accumulated difference or error of sidereal time from 1834 to 1892 409 -885 65

It should be clearly un derstood that the foregoing results ’ not O Dra son s bu t f are btained from y data , are merely rom ’ my attempt to prove the su bstantial correctness of Drayson s system by officially recorded Observations . It should also be remem bered that (for the reason before ed ul u stat ) my res ts in the above calc lations, and those given

e mi u ur . in the foregoing table, have no pret nce to n te acc acy ur Of i For the p pose comparison , I append the correspond ng ’ results obtained from Drayson s data . ~ 29° 25' 47 w 6° 0’ O”

" w20 - 0529

” e 40 - 81143

- m 2294 75 A . D .

a 31755 - 814

fl 415 - 283 S E C T I O N I X

THE TEMPERATE AND GLACIAL EPOCHS

z rsz z

I 8 E .G. 35 3

6 B . C . 5 44

u the the above cycle of abo t years, I have termed two halves of the cycle respectively the Temperate and the E u u w Glacial pochs, and nder s ch denomination it ill be seen that

1 . The last glacial epoch may be said to have commenced

u B . C . . u abo t viz abo t years ago , when the ° ’ obliquity of the ecliptic was 29 25 47

mi - d u B . C . . 2 . The last glacial epoch was abo t viz

u O ui m m u abo t years ago , when the bliq ty was at its axi m of 35° 25 ’ 47

3 . The last glacial epoch terminated and the temperate

m B . C . 5644 . u 7500 epoch com enced , viz abo t years ago, ° ’ When the obliquity was 29 25 67

- 4 . mi d The next temperate epoch , which we are now 22 5 z A . D . 9 vi u 385 closely approaching , will be in , . abo t years ° ’ O u w m hence, when the bliq ity ill be at its inimum of 23 25 47 ° ’ " As the Obliquity of the ecliptic will have been 35 25 47 at

mid - i Ar the glacial period, it will be ev dent that the ctic and ° A u 54 ntarctic circles came down to abo t 4 at that period, and thu s reached respectively abou t the latitudes of Durham and i C . C C ape Horn Sim larly, the tropics of ancer and apricorn ° w l e u 35 u i l have reced d to a distance of abo t 5 from the eq ator, (say) to about the latitu des of the Straits of Gibraltar in the C u . north, and to that of the ape of Good Hope in the so th In order to give a more graphic representation of the changes in Obliquity which have caused the alternation of temperate u i and glacial periods , I have constr cted a d agram, which I ui u have called the obliq ty c rve, for the period of a whole cycle .

ur This c ve may be of interest, as it shows at a glance how the glacial and temperate epochs have been determined by Dray son to have been cau sed simply by the increase and decrease i u Of the Obliquity . The d agram also shows that altho gh the alteration in the Obliquity is cau sed by the regular and un " u 20 - 0529 changeable motion of the pole, amo nting to per u u i annum , the ann al rate of alteration of obliq ity is var able m for instance, at the present ti e when approaching the mid " temperate epoch the rate of diminution is only about 0 - 4 l m i per annum, and is stil a di in shing rate whereas , at the ui u beginning of the glacial period, when the obliq ty was abo t " u 11 n u 29 the annu al rate of increase was abo t per an m .

- Of Again, at the mid glacial period the rate of increase u 0 Obliquity will have been red ced to , and at the end of the glacial period the rate of decrease of obliquity will have again ” u 11 u i s vi increased to abo t per ann m , as e dent by the steep ness of the cu rve at the periods of change from temperate to glacial epochs . 68

' T HE O BL I QUIT Y CURVE DU RIN G A CY CLE OF Y EARS.

’ the c mm ment dura tion an d termination of last Glacial Perio d. Shewi ng o ence , , 69

FACTS CONNE CTED WITH ASTRONOMY AN D GEOLOGY

In 1896 Drayson wrote Upon examining the writings i u R of the older geologists it w ll be fo nd that amsey, Lyall, Bu l A Mur i ck and, gassiz, Darwin , Forbes, ch son, and others give abu ndance of facts proving that this great change of climate occurred and produced what they termed a glacial ” period . M odern geologists , among whom may be mentioned P W U W B K . E . rofessors arren , pham, right, . merson, J P E. A dr restwich, Dr . n ews, and many others, not only corroborate the evidence of former writers as to su ch a glacial i but ffi v period having ex sted, they a rm that the e idence is v con incing, that this great change of climate ceased not u 7000 u longer than abo t years ago , and had lasted abo t

years . Sir Joseph Prestwich has long expressed his Opinion that these dates as to the dur ation and termination ’ of the glacial periods are proved by undeniable evidence . ’ u ul Dra son s S ch, then, are the facts res ting from y system, n mi u ni and granti g, as ad tted by geologists , and, indeed, versall ff m y , that a glacial epoch a ecting both he ispheres has u u occ rred in the past, the alteration in the obliq ity of the ecliptic as described by Drayson appears to be the only mi hi un ad ssible theory w ch can acco t, and that with the

u u . tmost simplicity, for s ch glacial epoch having taken place From the foregoing it will be seen that among the results Of ’ Drayson s di scovery is the geometrical proof that the glacial u period lasted only abo t years or years, and i u 500 term nated abo t 7 years ago .

- u The before mentioned cycle of abo t years, and the m dates of the com encement and ending of the glacial epoch, can only be considered as correct for future ages on the su pposition that the produ cin g causes will remain u nchanged . ’ u fir a r It wo ld, however, Drayson af med, be a f tal e ror to assume that because the second axis of rotation is now inclined ° ’ to the axis of daily rotation at an angle of about 29 25 it ur must always have been so, and hence that d ing all past u s time there must have been s cce sive glacial periods, is as 70 reckless as to assert that the earth ’ s axis has always been fixed at a permanent angle of 66° 32 ’ to the plane of the du e l . As v ec iptic the centre of gra ity of the earth varied, u to the elevation and depression of lands , and the conseq ent

u r mi i transferal of h nd eds of ll ons of tons of ocean waters , so u vi m st the centre of gra ty of the earth have varied, and consequently the angle formed between the poles of daily l ur and second rotation, and hence the c imatic changes d ing ’ each second rotation . The announ cem ent that the glacial period terminated abou t 7500 years ago was so entirely in opposition to the theories u w then believed in by geological a thorities , ho , instead of 7000 e m un dr us s m y ars, clai ed h eds of tho and and even illions ’ G Dra son s ur of years, that eneral y acc ate geometrical proofs

nl but m u were not o y ignored, the dates he gave beca e a s bject u for ridi cule . D ring many years General Drayson had to submit to thi s treatm ent becau se he positively stated the above dates for the glacial period . Of late years nearly all geologists in America and England have from geological evidence found that the dates given by General Drayson about thirty years ago were absolu tely

ur . fi acc ate The position , therefore, which scienti c societies u u u w u i s bseq ently occ pied as that, altho gh th rty years ago a proof was given them of the exact date and dur ation i of the glacial period, they ignored or fa led to comprehend

u . A the proof, and rejected the dates as abs rd fter long years of research they foun d the dates formerly given by

ur Drayson to be acc ate, and appear to have claimed that ul di this res t is a modern scovery of their own . The accurate determin ation of the date and dur ation of he t glacial period, which has been described as a brilliant ’ r i du e fl mode n d scovery to geologists, is a mere tri e in com ’ G Dra son s B parison to other portions of eneral y work . efore Drayson could so accurately give these dates he had dis u of covered the ca se the glacial period, and had proved, by hi u w ul the most exact and therto nkno n calc ations , that the u fi ca se was correctly de ned . Having som e eighteen years ago set to work to examine

72

u which several others have made , I may say that s ch asser tions as that competent authorities do not agree with Drayson that he is co ntradicted by the theories of La ’

P e G etc . n lac , Le range, that he is merely giving a other ’

to . etc . name that which everybody knew before , etc , are e to reasonin gs not worthy of consideration . With all r spect u s the able astronomers above q oted, it is not rea onable to say that their kn owledge was incontrovertible for all fu ture e fi time . For instance, the great st scientists might, fty years u u ago , have prono nced that it was impossible witho t tele graphic wires to hold conversations with persons hun dr eds or di u thousands of miles stant, and yet s ch pronoun cement would in these days have been held invalid in the fa ce of the us s Of M marvello di coveries arconi and other wireless scientists . When we see the soun d scientific base of these and similar ul fin d t o calc ations, and that the fac s of astronomy and geol gy a t are explained, and how ex c ly the two tell the same tale, it seems astoun ding that men claiming to love science for its

own sake should ignore these facts . Every wild and baseless speculation to account for the glacial period has been put n di u fi forward and solem ly sc ssed before scienti c meetings, but after a very short time each of these has been foun d

inadequ ate to explain the facts . di hi h Here, however, we have a scovery w c not only explains ct but u the fa s , gave the acc rate dates of these facts thirty i i years before geologists , and in add t on enables an average m athematician to make calculations hitherto un known to

astronomers . That such an important matter should have been neglected hi u but during t rty years is bad eno gh, when one small portion

Of C i it is laimed as a recent d scovery by geologists, it is really

u out the d ty of every honest man to speak .

It is interesting to note that Drayson, when writing to me Ma 1901 : hi a 26th y , said T rty ye rs ago I sent the formula for

u B . Ai finding the Obliq ity to Sir G . ry (the then Astronomer

R . oyal), and asked him to test it He replied that it worked but correctly, that he had tried in vain to discover how I had ’ framed it . 73

When General Drayson announ ced that the hitherto accepted movement of the pole was a geometrical im possi bilit u y, that the tr e movement was a circle with a radi u s 29° 25’ 47 23° 28’ i of and not as had h therto been stated, ° that the centre of this circle was 6 from the pole Of the 18 ur s ecliptic and had a right ascension of ho s, it is not ur a Of prising that he raised storm indignation which , had the x ul ui old laws e isted, wo d have placed him in the Inq sition , us him M and th have proved wrong . ore especially would this have been his fate becau se he boldly told geologists that their dates for the glacial epoch were utterly wrong . That u instead of this epoch having, as they imagined, lasted h ndreds us n of tho ands of years and termi ated years ago, it u lasted only years and terminated abo t 7000years ago . G u di fus eological a thorities were in gnant , and re ed even to listen to su ch heresy . Hence the leaders in both astronomy and geology refused to permit any fur ther investigation Of the m m facts, and even had the te erity to state that the atter had min r been fully exa ed and had been proved inco rect . ’ N ot only has no proof ever been given against General ’ ’ Drayson s system which was worth even half an hou r s i but exam nation , proof after proof has been given of its

u . Wh accuracy . There o ght to be no popery in science en , find nl Of hi however , we that the o y portion t s system, viz . i A e the most simple, giv ng the date of the Ice g , is at last

un us un - E comprehended, it is j t and nglish for men to be given credit for discovering that which Drayson told them thirty years previously . u When, many years ago, Drayson s bmitted a paper to the

Geological Society, in which he gave those very dates for the hi un u glacial period w ch are now fo d to be acc rate , the Society W be u pronoun ced that these were wrong . hen s bmitted the astronomical portion of hi s discovery to the Royal Astro vi u nomical Society and in ted a disc ssion , his paper was suppressed . C O N C L U S I O N

I N u i m concl d ng this treatise, I feel that so e apology may be due for what might be deem ed too mu ch self- assertion on my Al u m i so part. tho gh a lifeti e at sea w th , to speak, a sextant u n in my hand, m st have given me considerable k owledge of m N u As m that s all branch of astronomy termed a tical trono y, it should be un derstood that I make no pretence to knowledge of that great science, or to being in any respect a scientist, but I do claim to have soun d reasoning powers and to have fur done my best to exercise them . Let me ther express the

u n profo nd respect I have for astronomy, a science some k ow

Oi w i r lli bu t u ledge h ch is not only enth a ng, leads its st dents to a more j ust idea and appreciation of the marvellou s works Of Al fu the mighty, works so wonder l as to be far beyond the

m an c onception of . m e u It has grieved to notice how little s pport, or even tolera t f fi ion , Drayson has received rom the scienti c world, and I ’ f so Dra son s eel that , if little acceptance of y system has been ’ him l u m accorded to after half a ifetime s st dy of astrono y, I c annot expect mu ch attention to my poor endeavours to e hi s xplain and make system known . I have written with sm l Of m a l hope engaging the attention of great astrono ers , but u un w I do hope to ind ce the yo ger generation , hose pro fessional advancement is not dependent on blind adherence

o - s t text book , and who may take an interest in fully examining ’ Dra son s m and proving or disproving y syste , to bear in mind t u d fif hat the astronomy of a h n red and ty years ago , and its

- parrot like repetition, is not necessarily perfect for all time . ’ The direct proof Of Drayson s system is Obviou sly di fficult bu t u u to establish , as in criminal j rispr dence circu mstantial — e vidence is in many cases more reliable because un like a 75

— ’ it Of D witness cannot lie , so in the case rayson s system l u ut w there is the fo lowing circ mstantial evidence to p for ard, evidence which any person of ordi nary mathematical ability can test for himself . The system enables such persons to u ul ascertain by calc lation the following res ts for any year , fu u u past, present, or t re, witho t reference to the Nautical Alman ac of the year required

l - l The O ui bliq ty of the ecliptic . w fi The right ascension of any xed star . o b Of fi The declination any xed star . h s ui The precession of the eq noxes . fi The right ascension of a star from its apparent an nual i in if precess on in decl ation known .

6 . An d o n u c nversely, the apparent a n al precession in li sc s dec nation from its right a en ion . ’ a ul Dra son s The bove calc ations are, by y system, as I have wi hi said, t n the competence of any person possessing su ch l mi n of l ul i ted k owledge mathematics as myse f, and the res ts Of u u w l s ch calc lations can be tested, as they il be found to agree precisely with the amounts stated in the Nautical Al O manac, which have been btained by years Of innum erable i Observations at Greenwich . I th nk I may claim that no r u ast onomer, however able , can prod ce the above results ’ u Dra son s h or witho t acceptance of y t e y and data . In con firmation vi us whereof, as I have pre o ly stated, so great and n ui G ir disti g shed an astronomer as the late Sir eorge A y, ’ hil mi ti e Dra son s u w st ad t ng the correctn ss of y form la, told e i m him that he had tri d in vain to d scover how he had fra ed it . Let me urge young students in search Of the truth to test for themselves the accuracy of my claim on behalf Of Drayson u n ua ul Of um to r witho t reference to an l rate or r e th b, and bea ’ — in mind a saying of Drayson s in which I believe there is

— u - mu ch truth that in st dying astronomy, old text books had been hi s greatest obstacles . ’ m Finally, I should add that in my eighteen years exa ination ’ Dra son s fir of y system, I have from the st taken nothing for u i granted. Similarly, I ask those who favo r me by read ng but these words also to take nothing I have said for granted,