72 Mr. HOPKINS, ON THE MOTION OF GLACIERS, 



when n is even ; 



TT w + 1 

 = when n is odd. 

 Consequently when n is even 



u + — ^ - e <■ "" COS (2 n-< + - - - V'TT - 6) 



+ i- _£_.e-f^^cos(4^<--\/2^-^,) 

 D, l.S.TT a 



A Stt ^ 2 n ^ 



+ &c. 



24. If II denote the temperature which would exist at any point within the sphere at the 

 depth w beneath its surface, if the external temperature were always equal zero, we have 

 (,r being small compared with the radius of the sphere) 



" = "o + V'''' 



where v^ is the superficial temperature of the sphere, and y the rate at which the temperature 

 depending on the original heat of the sphere, increases with the depth. 



Let n denote the temperature of the sphere at the depth x, as depending both on the 

 original heat, and the variable external temperature ; then 



u = V + u, 

 or 



V C b /2V C\ .'-^ ,c * -^ ■'' /- ^s 



U = Hfu + 'V''' + -^ e " cos(2'n-r + v/ ir - d) 



27r ' D Kit 21 2 a 



+ — -. e ""'""cosCiTr* \/2 7r-6,) 



Z), 1 . 3 . TT « 



+ &c {3) 



the complete expression for the temperature required. 



25. I am not aware of any experiments for the determination of a and b for ice. Poisson 

 has given their values for the case of the earth, deduced from observations made at Paris on the 

 annual variations of temperature at different depths. They are 



6 = 1,05719 r 

 He also gives 



«o = O°,0265 ) ^ . ^ ^ 

 7 = 0",0281 j ('^^t'g^ade). 



Substituting the above values in the expressions for D, D,, &c. we obtain 



a = 5,11655 , . 



• in metres. 



