134 LAMBERT: CONSTITUTIOX OF THE EARTH 



the point of demonstrating the reahty of Euler's motion, only to 

 be disappointed each time as the obsen'ations that had looked 

 so promising ended by negativing the period sought. Finally 

 S. C. Chandler'-^ undertook the study of old obser\'ations with 

 no presupposition as to the period, and found evidence of an 

 annual period and of another period of about 14 months. The 

 reality of these periods was proved by observations made speciall}^ 

 for the purpose, and the matter is now being studied at a series 

 of special observ-atories, the functioning of which has been some- 

 what affected by the war. The annual period-- is naturally 

 explained by seasonal changes in the distribution of matter, 

 such as the unsymmetrical growi:h of the load of ice and snow in 

 the polar regions. The reason for the 14-month period was for a 

 while a puzzle. The idea of the earth's elasticity was compara- 

 tively novel then, and astronomers did not realize the natural 

 consequence of that elasticity in prolonging the ic-month Eulerian 

 period. Newcomb-^ appears to have been the first to suggest 

 the idea, and further examination confirmed it. The rigidity 

 required was rather higher than previous estimates had given, 

 greater than that of steel by a third to a half. 



I have been talking rather loosely of the elasticity of the earth. 

 What I \vish now to bring out is that what we get directly from 

 tidal obser\'ations — and with these I include observations of the 

 zero of a pendulum — and from the prolonging of the Eulerian 

 period is not the modulus of rigidity or of compressibility of the 

 earth as a whole or of any part of it,, but simply two numbers — 

 pure dimensionless ratios — which I shall call Ji and k, following 

 a certain amount of precedent. To deduce from these numbers 

 the elastic constants of the earth, we must make hypothesis as 

 to the law of density within the earth, and as to the relation 

 of the elastic moduli to each other and their law of variation 

 within the earth. The theory of the numbers h and k is quite 

 simple ; their interpretation so as to deduce from them the elastic 



21 Chandler's work runs through several 3'earsof the Astronomical Journal, 11-22. 

 1 892-1 902. The 14-month period is announced in 11, No. 249. 

 2* The annual period proper, not the "Kimura term." 

 23 Monthly Notices Royal Astron. Soc. 52: 1892. Astron. Journ. 11, No. 251. 



