By Professor Pell. 7 



approximations the condition s = o when j5 = is preserved 

 tnrougliout. The last term is not made use of in the final applica- 

 tion of the result, but is required in the course of the approxima- 

 tions. 



The temperature may be assumed to be proportional to the 

 average vis viva, or to 

 27r 



'dz 





cm 

 which, neglecting higher powers of p 



. -2^! (1 - 2^ . 8f ) 



lliis is proportional to t, the absolute temperature, so that we 

 may put 



p^ (1 - 2^ + ^~:^) = ^r 



where X is some constant. If M be the mass of an atom, H the 

 quantity of heat to each atom, J the mechanical equivalent of 

 heat, 



2 

 where u is the velocity when z = 0. It may be easily shewn 

 that 



u^ = m'hy (1 - 2i? + ^) 



and approximately, 



f (1 - 2i^ + -f ) = AT + -^^ 



' H M ni''¥ Kt , 2J_Xt 

 ^ 2Jg ^^ 16 i 



If s be the specific heat at the temperature t, or the quantity 

 of heat necessary to raise a unit of mass through one degree, 



/Hx _ m'¥K.^ 21 Kt) 



