14 Rev. 0. Fisher on the Surjace Elevations and other 

 3a* 



3 Aid 

 = r—y — = r—mt } suppose. 



Hence the depth of this level from the surface is 

 _3 4id_Sa* 

 ' — 2 r ~ 2 r ' 



6 id 

 This agrees with Prof. Darwin's value, — ; but it docs not 



agree with Mr. Davison's law that the depth varies as the 

 square root of the time, m is very small, being ooyooS* 



j- is the rate at which the temperature at the level 



of no strain is falling at the time t. Let Z be the position of 



10 

 a shell under compression between Z and the surface ; -j 



the rate at which the temperature of Z is falling. the 

 centre of the sphere. 



Now the property of the level of no strain gives that the 

 mean contraction of OZ in the interval dt is the same as that 

 of the circumference at Z , because, on contracting, the shell 

 is neither stretched nor compressed. 



Hence, OAving to the change in position of that level in the 

 time dt, OZ is diminished by mdt ; and, moreover, by the 

 contraction of the radius according to the property just men- 

 tioned, it also diminished by e(r — mt)-j-dt. 



For like reasons, Z Z is increased by mdt and diminished 

 by [ Z ef t dtdz. 



The mdt' s cancel ; and if we take z' as the value of z before 

 the interval dt, we shall have 



z f = z + e(r-mt) ( ^-dt + e V jdtdz. 



Now the contribution to the superficial elevations from the 

 shell at Z, caused by compression during the interval dt 

 arising from want of room, would be, if the shell did not 

 contract horizontally, 



(iTrz't-lTTzyiz, 



where it is to be observed that z 7 cont ains dt. 



But, owing to the horizontal contraction of the shell, this 



