424 



KNOWLEDGE 



[Maiicii 17, ]882. 



passage would Iiavo shown that the tidal action of the moon 

 alonr would Ih- lliirty tiiiirs greater tliaii the n-al action of 

 tli<" sun and moon togetlicr. In rfality, tlin did'crfncc? of 

 ccntrifiipil ti'iidciicics thus iiiin^^imd lias no exist<-nce — a 

 circiinistancr which no one would have recognised more 

 readily than Professor Nowcondi, had he thought of 

 examining the matter carefully. The motion of tlu; earth 

 around the lomnion centre of gravity of th<! earth ami 

 moon may he thus illustrated :• - Conceive a hall S in. in 

 dianu'ter .suspended hy a long thread, and not rotating ; 

 then imagine the j oiiit of suspension carried steadily round 

 in a horizontal circle in. in dianuster. Tims the centre of 

 the ball will be carried round, and so will ('very point in 

 the ball, in a horizontal cirdi^ of the same dianiet<jr. 

 Neglecting the earth's rotation on her axis, which 

 is an independent movement, her motion round 

 the centre of grax ity of her own mass and the 

 moon's takes place in this manner, each jioint in the 

 earth (whose diameter is about 7,900 miles) describing, 

 once in a lunar month, a nearly circular orbit about 6,000 

 miles in diameter. Professor Newcomb's mistake consists 

 in supposing that the motion is of a v<'ry different kind, 

 such, for instance, as our illu-strativo ball would possess, if 

 it were twirled round on a knitting-needle thrust through 

 it at a distance of .'Sin. from the centre, and held in an un- 

 changed upright position while rotated, carrying the ball 

 with it. In this case, points near the needle would 7nove 

 in small circles, wliile points farther away would travel in 

 large circles, tho.se furthest off travelling in a circle 14in. 

 in diameter. Tlius there would be different centrifugal 

 tendencies in the different parts of the ball. If the 

 earth moved in this way round .the centre of her 

 monthly orbit, while also rotating on her axis once 

 a day, and round the sun once a year, we should 

 have the state of things imagined by Professor New- 

 comb. But our opportunities for observing the result 

 would be precarious ; for the tidal waves would be of por- 

 tentous magnitude, and at least half the present land 

 surface of tlie eartli would be uninhabitable. It is strange 

 tliat it should not liave occurred to Professor Newconib 

 that, if his explanation of the lunar tides were correct, the 

 solar tides explained on the same principle would be 

 utterly insignificant compared with the lunar ones, in- 

 stead of bearing to these about the proportion of 2 to ."). 

 His mistake in this matter is a curious illustration of the 

 errors into which even the profoundest mathen)aticians 

 may fall in careless moods. It can only be compared 

 with one which Lord Brougham is said to have made in 

 one of the earliest publications of the Society for Dif- 

 fusing Useful Knowledge. Professor Tait, in a lecture 

 delivered before the British Association at Glasgow, stated 

 that in such a treatise, quickly withdrawn from publica- 

 tion. Brougham explained that a man carries a load more 

 readily over his shoulder than suspended from his hand, 

 because in the former case it is furtlier from the centre of 

 tlie earth, and gravitj' diminishes as the square of the dis- 

 tance from the earth's centre increases. The story seems 

 incredible, but it is scarcely more remarkable than that a 

 mathematician like Newcomb should employ reasoning as 

 unsound in reality as that of those who deny the moon's 

 rotation. In fact, Newcomb's paradox is \ery similar in 

 character to that of Messrs. Jellinger Symons and H. 

 Perigal, though not quite so obviously erroneous. 



It is in some i-espects even more remarkable that Pro- 

 fessor Newcoudi should ha\e given an equally erroneous 

 explanation of the precession of the exquinoxes, or rather 

 of the motion to which precession is due — the reeling of 

 the earth like a mighty top, each reel lasting forthe 

 long period of 25,890 years. The subject is, indeed, far 



more difficult to explain to the non-mathematical student 

 than the tide.s. I!ut for that very reason wc should have 

 expected t^> lind our author on his guard again-st miKtakes. 

 Th<r ablest mathematician may trip in explaining offhand 

 an easy subject, precisely as the ablest gymnast may fail 

 when lightly essaying some simple feat. But in dealing 

 with such a subjcsct as the precession of the equinoxes, 

 even the ablest mathematician girds up his loins as for a 

 task of ditliculty. Yet Newcomb's explaiation of the 

 phenomenon is altogether erroneous, though his statements 

 respecting the nature of the phenomena aie, of course, 

 entirely correct. '^ 



The explanation of the peculiarities which theory indi- 

 cates as aH'ecting the figure of the moon, thongi observation 

 has not yet demonstrated their actual exist-nce, is also 

 erroneous. It brings our author so close to tht ]>aradox of 

 Jellinger Symons (earlier jiropounded by Beitley), that 

 one cannot but wonder how he failed to notice the mistake 

 which underlies his reasoning. 



The account of the llarton Colliery expriment for 

 determining the mass of the earth is incorret, and the 

 princij)les on which tJie experiment depends a-e not pro- 

 perly stated. Professor Newcomb says that if lie density 

 of the earth increases as we approach the <-ntre, the 

 diminution of the force of gravity will be less rf)id as we 

 descend. But in reality the actual increase )f density 

 towards the earth's centre causes gravity to incrase as the 

 depth I lelow the surface increases. This increase continues 

 to a depth hundreds of times greater than can b reached 

 by man. Our author goes on to say that " a detfmination 

 of the density of the earth by the diminution of jravity in 

 a mine was made by Professor Airy at the Harto Colliery 

 in 18.t5." But in this experiment Airy fourl gravity- 

 greater at the bottom of the mine than at the toj Owing 

 to this increase in the force of gravity, the periulum at 

 a depth of 1,260 ft. gained 2| seconds per da; as com- 

 pared with its indications at the mouth of the nine. It 

 is, by the way, worth noticing, though so far aswe know 

 the point is not mentioned in any of our tratises on 

 astronomy, that even if the density of the erth were 

 uniform, gravity at the bottom of a deep openinpvould be 

 greater or less than at the surface, according tcthe sliape 

 of the opening. It can be shown that if the earn were at 

 uniform density, the action of gravity on a bdy at the 

 bottom of an opening would be equal to the ittraction 

 which a mass equal in all respects to the remoed matter 

 would exert on that body (only this attractio must be 

 regarded as acting towards the earth's centre), ided to the 

 attraction due to the body's distance fronj le centre. 

 The latter portion is less than gravity at theurface, in 

 just the same degree that the distance of th^iody from 

 the earth's centre is less than the earth's radis ; but the 



* Some one in America, criticising the a.stronomic articles in 

 the "American Cyc!opa;tlia" (Applcton), which wcrcovised, and 

 in {;rcat pai-t re-written, by me, was kind cnoiigli to jut ont that 

 my cxjilaiiation of the precession of the equinoxes waiot new. It 

 was not mine, but was left by nic almost untonch, being well 

 written, and correct. I left, for a like reason, the itter relating: 

 to ]>recossion in the " KncycIopa;dia Britannicn " alrst untouched 

 when the article on astronomy was entrusted to » for revision 

 and rc-writing. Possibly, if I had endeavoured to :d an entirely 

 new explanation, 1 might, like Professor Xewcomb, Vc come upon 

 one which, tliough new, was not true. At any rate, icre so skilful 

 a mathematician went astray, none need be ashned to err. 1 

 believe that in a later edition of Professor Newcib's book, the 

 errors jiointed out above, and in my earlier revv in the Coh- 

 lempnyartj, have been corrcded. Tlicy wore, at an;ate, corrected 

 in American journals. Professor Xewcomb is one ithosc who are 

 strong enough to be able and willing frankly to aJit and correct 

 such niistakos as all active thinkers are bound to iko from time 

 to time. — Ed.] 



