Mathematical and Physical Papers. 208 



have been examined are peculiar in that they manifest the period- 

 icity quite uniformly and distinctly for a number of years, then for 

 k while irregularly and obscurely. 



Simon Newcomb, one of the greatest of living astronomers, in 

 his discussion of Chandler's theory, writes as follows : 



" Mr. Chandler's remarkable discovery, that the apparent varia- 

 tions in terrestrial latitudes may be accounted for by supposing a 

 revolution of the axis of rotation of the earth around that of figure, 

 in a period of 427 days, is in such disaccord with the received theory 

 of the earth's rotation that at first I was disposed to doubt its pos- 

 sibility. But I am now able to point out a vera causa which af- 

 fords a complete explanation of this period. 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 

 mean of the other two principal moments admits of very accurate 

 determination from the amount of precision and nutation. This 

 ratio involves what we might call, in a general way, the solid ellip- 

 ticity of the earth, or the ellipticity of a homogeneous spheroid 

 having the same moments of inertia as the earth. 



"The question now arises whether Mr. Chandler's result can be 

 reconciled with dynamic theory, I answer that it can, because the 

 theory which assigns 306 days as the time of revolution is based on 

 the hypothesis that the earth is an absolutely rigid body. But, as 

 a matter of fact, the fluidity of the ocean plays an important part in 

 the phenomenon, as does also the elasticity of the earth. The 

 combined efPect of this fluidity and elasticity is that if the axis of 

 rotation is displaced by a certain amount, the axis of figure will, by 

 changed action of the centrifugal force, be moved toward coinci- 

 dence with the new axis of rotation. The result is, that the motion 

 of the latter will be diminished in a corresponding ratio, and thus 

 the time of revolution will be lengthened. I think the result of in- 

 vestigation will be that the rigidity derived from Mr. Chandler's 

 period is as great as that claimed by Lord Kelvin from the phe- 

 nomena of the tides." 



Mr, Chandler himself says: "It is unnecessary for the purpose 

 of disposing of objections to insist that it is not sufiicient 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, depend- 

 ent on temperature and seasons. Nor need we even urge the fact 



