LAMBERT: CONSTITUTION OF THE EARTH 1 33 



method, depending on the interference of Hght. We can assert 

 of the short-period tides of this artificial body of water, or of 

 their mathematical analogue, the zero of the pendulum, what we 

 cannot assert of the tides in the ocean, namely, that the water — 

 or the direction of the vertical — adjusts itself to the forces almost 

 immediately, so that we can predict even for these short-period 

 motions of the water and the vertical what they should be for a 

 rigid earth. Just as before, the observed movement is interme- 

 diate between the zero to be expected for a plastic earth and the 

 full theoretical amount for a rigid earth. Interpreted in terms 

 of the elastic constants of the earth, the short-period tides, the 

 pendulum, and Prof. Michelson's pipe tides give about the same 

 rigidity as the long-period tides of the ocean, or a rigidity a little 

 higher. ^"^ 



We get information about the rigidity of the earth also from 

 the phenomenon of the variation of latitude. The history of this 

 question is interesting. It was shown by Euler^'^ that if by chance 

 the axis of rotation of the earth should not coincide with the axis 

 of maximum inertia, the former would shift its position, its pole 

 describing a circle about the pole of the axis of inertia in a period 

 of some 305 days, say lo months, the exact period depending on 

 the principal moments of inertia, which can be found with con- 

 siderable accuracy from the phenomenon of the precession.^'-* 

 The astronomical latitude and longitude are dependent on the 

 position of the instantaneous axis of rotation, and if it shifts, 

 they change. x\stronomers naturally tried to test the invaria- 

 bility of these latitudes by observation, but they looked either for 

 a secular change or for a variation with Euler's period. -'' They 

 did not find the secular change, but several times they seemed on 



'' The rigidity deduced in the article cited in the preceding footnote should be 

 interpreted in the light of the later correction, and also with reference to what is 

 said hereinafter in regard to the assumptions necessarily underlying a statement 

 about the rigidity of the earth. 



1* Theoria motus corponun solidanim sen rigidonim. Greifswald, 1765. 



''' The number of sidereal days in the Eulerian period is the reciprocal of {C—A)/C, 

 A and'C being, as before, principal moments of inertia of the earth. 



-^ See Helmert, Hdhere Geodasie, 2: 394. 



