Astronomical Discovery

red upon his work under conditions of this kind, it being the opinion of experienced astronomers who had looked at the facts that there was nothing of interest to be got by watching sun-spots. In the

apers which he contributed to the Astronomical Journal on the subject in the years 1891-94, but it may help in the understanding

itu

th the phenomenon of the earth's rotation in this way: the axis about which it is rotating points to the centre of that little circle, and any change in the position of the axis can therefore be determined by observing these motions of the Pole Star. Such changes may be of two kinds: firstly, we might find that the size of the circle increased or diminished, and this would mean that the earth's axis was pointing farther away from the Pole Star o

of la

d not have any appreciable effect on climate, and the question has long been before them whether, putting aside large movements, there were any minute variations in position of the North Pole.Twenty years ago disbelieved. Twenty years ago the answer to this question would have been given decidedly in the negative; it was considered as certain that the North Pole did not move at all within the limits of our most refined astronomical observations. Accepted theory seemed to indicate that any movements must in any case recur after a period of ten months, and carefu

er's p

he Variation of Latitude"-I say courageously, because at that time it was believed that the latitude did not vary, and Mr. Chandler himself was only in possession of a small portion of

igns of

m November 1884 to April 1885 being about four-tenths of a second. There was no known or imaginable instrumental or personal cause for this phenomenon, yet the only alternative seemed to be an inference that the latitude had actually changed. This seemed at the time too bold an inference to place upon record, and I therefore le

enting them with the clearness which is so well marked a feature of the w

verified by this discussion of more abundant material. The presumption t

med in

rt to those which I had pointed out in 1885. The verification afforded by the recent parallel determinations at Berlin, Prague, Potsdam, and Pulkowa, which show a most surprising and satisfactory accordance, as to the character of th

and opens with the following brief state

ays'

ionally, for the purpose of statement, that this is a motion of the north pole of the principal axis of inertia about that of the axis of rotation, the direction of the former from the latter lay towards the Greenwich meridian about the beginning of the year 1890. This, with the period of 427 days, will serve to fix approximately t

atured by a thorough examination of observational evidence. The only period in which the earth's pole could revolve was believed to be ten mouths; and here was Mr. Chandler proclaiming, apparently without any idea that he was contradicting the laws of dynamics, that it was revolving in fourteen months! The radius of its path had been found to be insensible by careful discussion of observations, and now he proclaimed a sensible

w fact is added-when the Cambridge (U.S.A.) latitudes were the smallest those of Berlin were the largest, and vice versa, as would clearly be the case if the phenomenon was due to a motion of the earth's pole; for if it moved nearer America it must move further from Europe.Pulkowa puzzle solved, He then examines a long series of observations made in the years 1864-1873 at Pulkowa, near St. Petersburg, and again

Washi

rate determinations of declination ever made at the Naval Observatory. The probable error of a declination from a single transit was ±0″.141, and judging from the accidental errors, the series ought to give trustworthy results. Upon reducing them, however, it was found that some abnormal source of error existed, which resulted in anomalous values of the aberration-constant in the different years, and a negative parallax in all. A careful verification of the processes of reduction failed to discover the cause of the tro

llence as these presumably were, and, as I hope satisfactorily to show, actually are. When this variation is taken into account the observations will unqu

aper.Direction of revolution of Pole. After discussing the Washington results, and amply fulfilling the promise made in the preceding extract, Mr. Chandler compares them with the Pulkowa results, and shows that the Earth's Pole must be revolving from west to east, and not from east to west. And then he writes down a simple formula representing this motion, and compares his formula with the observations. He gives the results in seconds of arc, but for the bene

hin

ion of

served.

28 - 28 fee

r. 19 -

1 +1

11 +22

9 +1

13 - 1

lk

ion of

served.

25 - 18 fee

9 + 3

22 +26

eb. 22

4 - 11

17 - 1

it is a difficult thing to deduce, even from the most refined observations, the position of the earth's pole to within a

nds up his seco

he same conclusion as that already drawn from the simultaneous series at Berlin and Cambridge, 1884-1885. The

d various other series of observations, after which the results of all will be brought

's obse

made to ascribe the discordance to changes in the instrument, but Mr. Chandler shows that such changes, setting aside the fact that Bradley would almost certainly have discovered them, will not fit in with the facts.Latitude varied in twelve months then. The facts, when analysed with the skill to which we have become accustomed, are that there is a periodic swing in the results with a period of about a year, and not fourteen months, as before, "a result so curious," as he admits, that "if we found no further support, it might lead us to distrust the above reasoning, and throw u

ley's observations may be put

g.

r and summer. It could not be due to the parallax of the stars for which Bradley began his search, for stars in different quarters of the heavens would then be differently affected, and this was not the case. "There rema

f the polar rotation at that epoch appears to have been probably somewhat over a year, and certainly shorter by about two months than it is at the present ti

y's gr

ighly appreciated as it has been, has still been hitherto obscured by the presence of this unsuspected phenomenon. When divested of its effects, the wonderful accuracy of this work must appear in a finer light, and our admiration must be raised to higher pitch. Going back to it after one hundred and sixty years seems indeed like advancing into an era of practical astronomy more refined than that from which we

completion. These include Bessel's observations at K?nigsberg, 1820-24, with the Reichenbach circle, and in 1842-44 with the Repsold circle; the latitudes derived from the polar-point determinations of Struve and M?dler with the Dorpat circle, 1822-38; Struve's observations for the determination of the aberration; Peters' observations of Polaris, 1841-43, with the vertical-circle; the results obtained from the reflex zenith-tube at Greenwich, 1837-75, whose singular anomalies can be referred in large part to our present phenomenon, complicated with instrumental error, to which until now they have been exclusively attributed; the Greenwich transit-circle results, 1851-65, in which case, however, a similar complicat

l nature o

expressible in a numerical formula. Indeed, the general impression produced by a study of these changes in the length of the period is that the cause which produces them operates capriciously to a certain degree, although the average effect for a century has been to diminish the velocity of the revolution of the pole. How far this impression is due to the uncertainty of the observations, and to the complication of the phenomenon wi

the shorter periods being apparently associated with the larger coefficients for the latter. The verification of these surmises awaits a closer comparative scrutiny, the opportunity for which will come when the computatio

on of d

credulity which found their way into print, especially in Germany. But the first note of welcome came from Simon Newcomb, in the same number of the Astronomical Journal as the pap

was disposed to doubt its possibility. But I am now able to point out a vera causa which affords a complete explanation of this period.Newcomb's explanation. Up to the present time the treatment of this subject has been this: The ratio of the moment of inertia of the earth around its principal axis to the m

d that of figure, in a period of 306 days, and in a direction from west toward east. The attempts to determine the value of these constants have seemed to show that both are zero, or that the axes of rotation and figure are coincident. Several years since, Sir William Tho

otten as

lso the elasticity of the earth. The combined effect of this fluidity and elasticity is that if the axis of rotation is displaced by a certain amount, the axis of figure will, by the changed action of the centrifugal force, be moved toward coincidence with the new axis of rotation. The result is, that the motion of the latter will be diminished in a corresp

n some new fact seems to challenge our conclusions. It might further be expected that this discovery of the way in which theory had been defective would as a secondary consequenceBut Chandler's work still mistrusted. inspire confidence in the other conclusions which Mr. Chandler had arrived at in apparent contradiction to theory; or at least suggest the suspension of judgment. But Professor New

e been established beyond reasonable doubt by the observations collected by Mr. Chandler. But two of h

of the inequality is

inequality has remained consta

, which are too technical in character to reproduce here. But

tion of the period is in such direct conflict with the laws of dynamics that we are entitled to pronounce it impossible. But we know that t

considers that in this case the other must go.Chandler's reply. Mr. Chandler's answer will speak for itself. It was delayed a little

ises the work of seventeen observatories (four of them in the southern hemisphere) with twenty-one different instruments, and by nine distinct methods of observation. Only three of the series (XXI., XXV., and XXXV.), and these among t

r I have studiously sought to compress the form of statement without omitting anything essential for searching criticism. That it was important to do this is manifest, since the conclusions, if established, overthrow the existing theory of the earth's rotation, as I have pointed out on p. 21. I am neither surprised nor disconcerted, therefore, that Professo

all teaching

entangled condition of the whole subject required that it should be examined afresh by processes unfettered by any preconceived notions whatever. The problem which I therefore proposed to myself was to see whether it would not be possible to lay the numerous ghosts-in the shape of numerous discordant residual phenomena pertaining to determinations of aberration, parallaxes,

not di

the 427-day period was propounded, it was as inconsistent with known dynamic law as the variation of it now appears to be. Professor Newcomb's own happy explanation has already set aside the first di

ay's

about these words. Let us compare the

ances; have no favourite hypothesis; be of no school; and in doctrine have no master. He should not be a respecter of persons, but of things. T

ticism,His ultimate satisfactory solution. he was able to announce that he had found the key to the new puzzle, and that "theory and observation were again brought into complete accord." We will as before listen to the account of this new step in his own words, but a slight preliminary explanation may help those unaccustomed to the terminology. The polar motion was found to be compounded of two independent motions, both periodic, but having different periods. Now, the general results of such a composition are well known in several different branches of physics, especially in the theory of sound.Interference of two waves. If two notes of nearly the same pitch be struck at the same time, we hear the resultant sound alternately swell an

g.

2 3 4 3 2 1 2 3 4 3 2 1

2 1 2 3 4 4 3 2 1 2 3 4

5 3 3 5 7 7 6 4 4 4 6 6

sturbanc

3 4 3 2 1 2 3 4 3 2 1 2

3 4 4 3 2 1 2 3 4 4 3 2

3 5 7 8 6 4 2 4 6 8 7 5

distur

e 42nd term. Now those unfamiliar with the subject may not be prepared for the addition of one physical wave to another, as though they were numbers, but the analogy is perfect.Illustration from ocean travel. Travellers by some of the fast twin-screw steamers have had unpleasant occasion to notice this phenomenon, when the engineer does not run the two screws precisely at the same speed; there come times when the ship vibrates violently, separated by periods of comparative stillness. Instances from other walks of life may recur to the memory whe

's final

inally, by a discussion of these quantities, to establish the general character of the law of the rotation of the pole. It is now requisite to analyse the observations in a different way, and discover whether the deviations from the general provisional law, in the last column of Table

he second has an annual period with a range variable between 0″.04 and 0″.20 during the last half-century. During the middle portion of this interval, roughly characterised as between 1860 and 1880, the value represented by the lower limit has prevailed, but be

le of seven years' duration, resulting from the commensurability of the two terms. According as they conspire or interfere, the to

ds increased to near 440 days, and very recently fell to somewhat below 400 days. The general course of these fluctuations is quite faithfully represented by the law of eq. (3), (No. 267), and accurately, even down to the minor oscillations of individual periods, by the law of eq. (15), hereafte

less catch the general purport-that the difficulties felt by Professor N

nsecutive values of T in Table XII., namely, that there has been no discontinuity in the revolution, such as Professor Newcomb regarded as so pr

if it will not

stworthiness of the latter, and, at the same time, of the theory that demands an invariable rate of motion; providing a perfectly fitting key to the riddle by showing that another cause has intervened to produce the variability of the period. I feel confident that Professor Newcomb will agree with

menced just two years before. His work was by no means done; rather was it only beginning, for the torch he had lit illuminated many dark corners. But he rightly regarded his discovery as now so firmly established that the series of papers dealing with it as still under consideration might be terminated. In this final paper he first devotes the most careful attention to one point of detail. He had shown earli

y to decide. I cannot think so. One of the most salient results of these articles has been the proof of the fact that theory has been a blind guide with regard to the velocity of the Polar rotation, obscuring truth and misleading investigators for a half a century. And even if we were certain, which we are not, that the fourteen months' te

jectors of eminence who still lingere

answ

hat it is not sufficient to show that the observed variations, attributed to the unsteadiness of the Earth's Pole, are near the limit of precision attainable in linear differential measures, and in the indication of the direction of gravity by means of the air bubble of the level; or to show that there are known variations in divided circles and in levels, dependent on temperature and seasons. Nor need we require of objectors the difficult, although essential, task-which they have not distinctly attempted-of showing that these errors are not eliminated, as they appear to be, by the modes in which astronomers use their instruments. Neither need we even urge the fact that a large portion of the data which have been utilised in the present researches on the latitude were derived by methods which dispense with levels, or with circles, a part of them indeed with both, and yet that the results of all are harmonious. On the contrary, let us admit, although merely for argument's sake, that all the known means of determining the direction of gravity-including the plumb-line, the level, and a fluid at rest, whether used for a reflecting surface or as a support for a floating instrument-are subject to a common law of periodical error which vitiates the result of astronomical observation, obtained by whatever methods, and in precisely the same manner. Now, the observed law of latitude variation includes two terms, with periods

ed by the explanation of anomalies in series of observations which had been put aside as inexplicable. We have seen how the observations made in Russia, or in Washington, or at Greenwich, in all of which there was some puzzling error, were immediately straightened out when Chandler applied his new rule to them.Suspected observers acquitted. We in England have special cause to be grateful to Chandler; not only has he demonstrated more clearly than ever the greatness of Bradley, but he has rehabilitated Pond, the Astronomer Royal of the beginning of the

f Aberrati

s not obtained, and Chandler has been able to show one reason why, and to remove some of the more troublesome differences. It is impossible to give here an idea of the far-reaching consequences which such work as this may have; so long as there are differences of this kind we cannot trust any part of the chain of evidence, and there is in prospect the enormous labour of examining each separate link until the error is found. The velocity of light, for instance, may be mea

Variati

ation, which I have compared to the vibrations felt by passengers on an imperfectly engineered twin-screw steamer. A more sensational effect is that apparently earthquakes are more numerous at the time when the vibration is greatest.Earthquakes. We remarked that the vibration waxes and wanes, much as that of the steamer waxes and wanes if the twin-screws are not running quite together. Now the passengers on the steamer would be prepared to find that breakages would be more numerous during the times of vigorous oscillation; and it seems p

caution you may not be by any means the right one. We are accustomed to think of this great earth as being sufficiently constant in shape; if asked, for instance, whether its centre of gravity remains constantly in the same place inside it, we should almost certainly answer in the affirmative, just as only twenty years ago we thought that the North Pole remained in the same place. But it seems possible that the centre of gravity moves a few feet backwards and forwards each year-this would at any rate explain certain curious features in the observations to which Mr. Kimura has drawn attention. Whatever the explanation of them may be, or to settle whether this explanation is correct, we want more observations, especially observations in the Souther

seems to have become tedious and unprofitable (as in the search for minor planets) than we are confronted with the possibility that by such simple devotion to the day's work we may be losing a great opportunity, as Challis did. We can scarcely go wrong in following up the study of residual phenomena in the wake of Bradley; but there is the important difficulty that we may be wholly unable to find a clue for the arrangement of our residuals, as is at present largely the case in

detection, until at last it encounters an alert Herschel, who suspects, tests, and verifies, and even then announces a comet-so little did he realise the whole truth. Fifteen years of unrequited labour before Astr?a was found, nineteen years of observation before the discovery of nutation could be ann

ll the would-be discoverer. The situation has been well summarised by Jevons in his chapter on Induc

of experience. He must entertain the feeblest analogies, and the merest guesses at truth, and yet he must hold them as worthless till they are verified in experiment. When there ar

N

111, 112, 117, 118, 1

iscovery, 15

, 12,

luti

32, 40

ers,

ghen

ntar,

used for

T. C., 8, 142,

elm,

llo

on,

nsio

on, forg

, 22,

c chart, 12

cal Journ

he Nachrich

ophi

ers

Sir

l Coll

, Sir

E. E.,

1, 183, 18

r-map, 45,

sel

na, 2

ngham

(in transit

ss,

rs of Greenwich

11, 14

13, 38, 43, 45,

deau

, 40, 42, 4

120, 188-192, 21

y, Joh

men

ow, 87

ggs

kley

Associ

now,

forn

(Mass.), 1

ry, 23, 42, 49, 52,

University

vatory, 12

ds,

ni II

nia,

s, 1

orna

-54, 63-68,

S. C., 1

n's "H

ago,

osphe

e, C.

osta

mbus

88, 108, 1

on, plan

A. A.,

e Ren

tock

Astrograph

icus,

ba, 1

u, 2

a, 17

Humboldt

mbre

on of P

eptune, 4

f Uran

pat

hotographi

is, γ,

nis,

ssen

plat

lin

quake

Pole,

ricity

ses,

burg

ard

ria

mion

hyla

26, 28,

an, 20

lyn

times of

ul?

day,

ed, 39,

g, Mrs

ra,

s, Mar

cademy,

eo, 9

, 45, 47,

aris

(railw

s, 1

orum,

III.,

rgia

Sidus,

D., 32,

lis

ha,

ld,

am,

law of, 38, 4

ves,

, 88, 89, 114-117, 130, 160-

ry, 9

. E., 1

A., 18

-92, 108,

en,

ness

wig,

Observatory, 1

be

el,

lberg

eter,

ium

ngfor

2, 23, 64

rothers

Sir John,

William, 2-11,

(Uranus

2, 23,

e, 9

ard,

oldt

Rev. T.

eia

ata

stri

borg

at Greenwi

22, 23

son

ons

, M., 1

9, 2

, 28, 43,

ites,

, 1-3

4, 112,

Lord,

r, 95

, 96, 1

l,

ura

sberg

, 118,

7, 11,

eia

lac

lata

ion, 99, 100, 1

er, 39,

ier, 12

uss

servato

le's Jo

longitud

, 23,

g,

ude, 9

Bisho

α, 18

ld, Earl o

ler

ervations, 1

de equa

kre

28, 32, 3

er,

t of plate

ue Céle

rne, 1

dum (Ad

cur

sie

orit

(Novem

s, 2

eter,

y Wa

erv

planet

ets tables

kes,

amuel, 94-9

Vide

tables

minor pla

yth,

al Alma

, 124,

11, 12, 3

lege La

81, 183, 184,

rs, 121

, 84, 90-9

k, long

ina

hlea

mberla

norum, 14

sei, 143

00, 110, 115, 1

ory (mag

lo,

rs,

c game

ani

ment

rsity, 87-89

ervatory, 121, 130, 1

Observato

isa

s, 9,

4, 91, 95-9

is,

st, J.

heno

e, 73

ulum

us, 8

ation, 31, 1

th,

Uranus, 12, 42, 5

s, 18

tusa

pher, 2

al Transact

graph

ethods, 24, 33

s, 12

s of sun,

i, 13

g, E. C.

burgh

na,

y distan

ssion

erin

by photo

laris), 177,

, 19

am, 1

rs., 104

James, 89-

gue

sion,

mno

seu

rich

, 181-1

at Green

ium

or, 52-58,

gh, Lo

efore dis

or, 93,

nith tube

n, 96, 10

tor, 9

eau

mena, 108-110,

. P., 87,

e,

schi

Society, 40, 47, 68

ety, 4, 9,

R. A.,

ernan

iago

ho,

, 43, 61,

, Sir

fessorship,

Julius,

ter,

155-163

ian The

bour

lipse, 2

eliograph

s, 45, 6

-trap

compara

, E.

184, 1

istance

ots, 1

Observa

Observa

pes, 92

s Riv

stocl

ia Mo

d observa

Sir W.,

es,

ius

Observa

ahé, 95,

4, 25, 38-8

le sta

itude, 99, 100,

s, 9

ter o

of, 28

a, 2

, 22, 25

Zach

ace,

4, 104, 110,

d,

rvatory, 184-18

sun-spots,

er,

esid

Mrs. E.,

revolutio

ecke

Dr. Ma

Rudo

Sir

ry, 145, 146, 15

ss,

, 64,

E

Ballantyne,

rgh &

WARD A

ST

and Techn

sistant Physician to the London Hospital and to the Hospital for Sick Children, G

Demonstrator of Physiology, St. Bartholomew's Hospital; Leonard Hill, M.B., F.R.S., Lecturer on Physiology, London Hospital Medical School; J. J. R

turer on Anatomy at the London Hospital Medical College. With 300 Illu

M.D. Edin., F.R.C.P., Assistant Physician to the London H

M. S. Pembrey, M.A., M.D., Lecturer on Physiology in Guy's Hospital Medical Sch

lated by J. H. Sequeira, M.D. With I

ll-pox-II. Light as an Irritant-III. Treatment

Hill, M.B., F.R.S. With 173 Illustrations

IOLOGY. By Leona

lated by Dr. R. A. Lehfeldt. In three volumes. Illustrated. Demy 8vo., 28s. net; or obtainable separately, as follows: Vol. I.-Chem

lleges. By W. A. Shenstone, Lecturer in Chemistry at Clifton C

'A Laboratory Companion for Use with Shenstone's Inorganic C

t, Professor of Physics at the East London Technical Co

OMPOUNDS. By Professor Raphael Meldola, F.R.S., of the City and Guilds of London T

ions of Physics to Physiology and Medicine. By Dr. R.

a Preface by J. H. Van 'T Hoff. Translated by Dr. R. A. Lehfeldt,

nest H. Cook, D.Sc., F.I.C., Principal of the Clifton Laborato

d, F.I.C., Lecturer on Agricultural Chemistry in the County Technical Laborat

ith 90 Illustrations. 350 pages. Crown 8vo., cloth, 3s. Also obtain

y C. E. Ashford, M.A., Headmaster of the Roy

termination of Physical Quantities. By W. R. Kelsey, B.Sc., A.I.E.E., L

and electro-chemists. By Dr. Karl Elbs, Professor of Chemistry at the Unive

the Sorbonne. Authorized English Edition. Translated by A. T. de M

E., Professor of Electrical Engineering in the Siemen

of the Osborne Royal Naval College, late Senior Science Master

s, Descriptive and Experimental. By J. Paley Yorke, of the Northern

essor of Mechanical Engineering and Applied Mathematics in the City and Guilds of

ring, Royal University of Ireland, Fellow of the Royal Indian Engineering College, a

M.A., A.R.S.M., F.I.C., F.G.S., etc., Professor of Mining and Lecturer on Surveying, Du

F.R.S., Professor of Mechanics and Mathematics in the

Head of the Electrical Engineering Department in the University

Schuster, Ph.D., F.R.S., Professor of Physics at the Universi

an Professor of Astronomy in the University of

the Central Technical College By Professor O. Henrici, F.R.S. Edi

., Head of the Engineering Department of the Northern Po

Lecturer on Mathematics at King's College, London. For use in Schoo

Lond., late Scholar St. John's College, Cambridge, Lecturer on Pure and Appl

B.A., Demonstrator of Mechanical Engineering and Applied Mathemat

.Sc., Head of the Mathematics and Physics Department of the West H

sity of Freiburg-im-Breisgau. Translated by Professor J. Arthur Thomson. Wit

ismann has from time to time during the last quarter of a century frankly altered some of his positions, this deliberate summing up of his mature conclusions is very valuable. In the second place, as

University College Bristol, author of 'Animal Life and Intellige

.D., F.R.S. With Photogravure Frontispiece

at the London School of Medicine for Women, and the Polytechnic Institute, Re

Assistant Master at Tonbridge School. With numerous I

., and A. J. Maslen, F.L.S., Lecturer on Botany at the Woolwic

y the Hon. R. J. Strutt, Fellow of Trinity College

DUSTRIES. By Charles G. Matthews, F.I.C., F.C.S., et

lications of the Timbers of Commerce. By G. S. Boulger,

Lloyd Morgan, LL.D., F.R.S. xii

.S. viii + 312 pages, with 52 Illustrations (ma

RNOLD, 41 & 43 M

tno

s comes closer, but is not v

Rigaud, and published by the Oxford University Press in 1832 as

n to Saturn and back again to the earth, th

he Royal Astronomical So

ould be Cam

lacement, but only the displacement towards Washi

riber'

the middle of a paragraph

he original text, but the links navigate to the page numbe

s been correct

ormation, inconsistencies in spelling and hyp

in this text by the transcriber.