34 



NATURE 



[May 8, 1879 



peculiar interest. The author says : "The theory was 

 next propounded that the earth was an ellipsoid of three 

 axes, but the proposition was not fully supported by the 

 evidence." Upon this Col. Clarke remarks : " This is 

 scarcely correct ; the figure of three unequal axes agrees 

 better with the observations than does the spheroid 

 of revolution. But there is a necessity for this, 

 and the ellipsoidal figure cannot be regarded as esta- 

 blished." 



I venture to think that this note ought to be printed in 

 capital letters. It condenses, especially in the words, 

 " but there is a necessity for this," the following impor- 

 tant paragraph in the preamble to Col. Clarke's well- 

 known paper in the Memoirs of the Royal Astronomical 

 Society, 1861 : — 



" Whatever the real figure of the earth may be, if in 

 he investigation we suppose it an ellipsoid, it is quite 

 :lear that the arithmetical process must bring it out an 

 ellipsoid of some kind or other, which ellipsoid will agree 

 uetter with all the- observed latitudes, as a whole, than 

 any spheroid of revolution will. Nevertheless it would 

 scarcely, I conceive, be correct to say we had proved the 

 earth not to be a solid of revolution. To prove this 

 would require data which we are not in possession of at 

 present, which must include several arcs of longitude. 

 In the meantime it is interesting to ascertain what ellip- 

 soid does actually best represent the existing measure- 

 ments." 



It may seem superfluous, so far as the main point is 

 concerned, to add anything to these quotations ; but of 

 the three which have been given, I have very little doubt 

 fiat the first was by way of a protest against the fallacy 

 which, in spite of the last, has gained such a remarkable 

 currency. Am I mistaken in thinking that it ts a too- 

 prevalent opinion that the equatorial section has been 

 shown to be elliptical ? It may be so ; but I conceive it 

 to be so noxious an error, when it does exist, that it is 

 better to give too much than too little currency to every 

 authoritative corrective of such an error. 



It is very much to be regretted when investigations 

 which are essentially tentative, and which are carefully 

 guarded as such by sentences which are to be found if 

 looked for, obtain through no fault of their own the 

 character of demonstrations. I think Col. Clarke has 

 run the risk of giving to the above fallacy a stronger 

 hold by neglecting to emphasise with sufficient force, in 

 his more recent calculations, their true character ; and 

 perhaps still more by seeming to entertain something of 

 an expectation that the arithmetical result will be sub- 

 stantiated by increased data. Writing of the later result 

 —as to which we may properly note that the equatorial 

 .najor axis occupies a position diflfering from that of the 

 tormer by 24" of longitude— he says : " But too much 

 confidence must not be placed in it : as yet it is merely 

 indicated by the existing observations, and the amount 

 of the eccentricity of the equator shown is really very 

 minute." 



I am unwilling to seem to differ from so high an 

 authority, especially on a point which I wish to have 

 "reserved:" I therefore refrain from inquiring whether 

 any such expectation is really entertained, preferring to 

 a idu:e some arguments which tell the other way. 



Whatever the real figure of the earth may be, it is as 

 certain that, if we knew it exactly in every part— instead 

 ot only very uncertainly in a very few— a triaxial ellip- 

 soid could be found which would fit it better than any 

 other triaxial ellipsoid, as it is that a biaxial ellipsoid 

 could be found which would fit a given egg better than 

 my other biaxial ellipsoid. But we happen to know that 

 eggs are generally egg-shaped, and not elliptical. So 

 also we know— I hope it is not necessary to stop to prove 

 If '*r' u^' ^^^ ^^^""''^ '* earth-shaped, and not ellipsoidal, 

 ij j?^' possible ellipsoid were fitted to it, the two 

 would disagree everywhere more or less. It is not, 



therefore, as regards the present argument, a question of 

 more data. If the figure were conformable to any 

 ellipsoid, the existing data would suffice. Their in- 

 sufficiency proves the non -conformity, and additional 

 data cannot disprove it. 



What additional data may be expected to do is to 

 modify the approximate ellipsoid until the ellipticity of 

 its equator disappears — in other words, until it becomes 

 an elliptic spheroid. 



Can I give any ground for this expectation ? It would 

 be fair to ask in return. Can any ground be shown for 

 expecting a body, believed to have acquired its spheroidal 

 form by rotation, to have an equator not circular? I 

 will answer the latter inquiry first, myself. The same, or 

 similar, causes which distributed land and sea irregularly 

 have probably produced an equator which is not circular. 

 But I know nothing to lead me to expect that the form of 

 the equator has any better claim to be considered 

 elliptical than circular, than this — an ellipse can generally 

 be found which will fit an irregular area better than a 

 circle. This argument can be turned against me, but 

 only by admitting the irregularity. If the irregularity is 

 admitted, I concede an eUiptic equator for the approxi- 

 mate or mean figure. And the question is now reduced 

 to one of degree. 



The difference of equatorial semi-axes in Clarke's earlier 

 investigations was 5,308 feet (1861), and subsequently 

 6,378 (1866). It is now 1,524 feet. 



We are here, to go no further, within the limit of 

 inequality assignable to the larger disturbances of sea- 

 level; that is to say, to one kind only, of local irregularity. 



In short, while I recognise with the most unreserved 

 respect and admiration the labours which have resulted 

 from the first attempt to ascertain whether a tri-axial 

 ellipsoid was sufficiently indicated to be i robable, I pre- 

 sume to think that Colonel Clarke's words of caution 

 demand the utmost attention, and that the results at 

 which he hasl arrived should be construed rather as 

 disproving than as proving the reality of a sensibly elliptic 

 equator. 



I should extend this article too far if I did more than 

 indicate one other ground for caution in describing the 

 figure of the earth. Our knowledge on that head, as 

 derived from arc-measures, is deceptive in proportion as 

 we lose sight of the significance of the fundamental 

 assumption that the figure is a regular one. Gross 

 assumptions which suit an early stage of an inquiry may 

 have to be abandoned later. The forms of the surfaces 

 whose curvatures arc-measurements determine, are in 

 any case local and particular ; and so soon as local cha- 

 racter appears, further consideration of the assumption 

 is demanded. This, no doubt, is the reasoning out of 

 which the tri-axial ellipsoid grew. It must not stop 

 there. The tri-axial ellipsoid is not the only next step. 

 Forced by the rigour of observation to abandon the ellip- 

 tic spheroid as a final definition, and to admit irregu- 

 larities as coming now within the range of more particular 

 inquiry, the prob'em has in effect changed its face. To 

 cling to the old assumption is to delay the recognition of 

 the new phase. To look for additional data as means of 

 substantiating or modifying an empirical modification of 

 it is to halt in the presence of the larger problem which 

 is opening before us. 



Will it not be wiser to change the mode of attack ? To 

 bestow increased attention on the causes of irregularities 

 and the probable magnitude of their effects ? To theorise 

 and calculate in this direction, on the one hand, and to 

 extend experiment on the other, where such reasoning 

 shall point the way ? If we do this, the ultimate inade- 

 quacy of arc-measurements must receive recognition 

 The most obvious of all the causes of irregularity — the 

 fluidity of the ocean and its obedience to the attraction 

 of the land masses, must, one would think, invalidate 

 their evidence materially. If, further, we consider the 



