26 



GANESH PRASAD, 



The initial temperafures, (0), T^(Qi), . . . T^(0), of tlie assemblages J„ A^, . . . A^ 

 heing giren, find fJieir subsequent temper aüir es. 



Approximate analytical representation of the conditions 

 of the phenomenon. 



26. The conditions of the phenomenon are the same in the present theory 

 as in the theory expounded in the previous part ; but an exact analytical repre- 

 sentation of these conditions, in terms of the temperatures of the assemblages, 

 is impossible because the precise circumstances of the phenomenon are not known. 

 For example , even if the exact law according to which the molecules oscillate 

 were known, the fact of the conservation of the energy in the volume, initially 

 occupied by a molecule, wovild still be incapable of exact analytical represen- 

 tation, as such a representation would involve considerations regarding the inter- 

 nal Constitution of the molecule and the distribution of the energy inside it; 

 and these considerations are essentially foreign to the theory. Thus it is an 

 essential feature of the theory that an exact Solution of the p)rohlem is impossible. 



27. The following three hypotheses suffice for an approximate analytical re- 

 presentation of the principle of the conservation of energy ; in formulating them 

 I will detail , for the sake of clearness , certain unimportant points which are 

 easily distinguishable : 



i. The resultant efFect of the molecular radiations, in A^, A^, in any inter- 

 val {t, t + r) is the flow of a quantity of heat equal to 



f^'\TAt')-TAt')\R.dt' 



from A^ to A^ along the line which joins the centres of A^ and A^ at time 



^ + • Here B^^ is a finite and positive function of the positions of the centres 



of A^ and A^, when the distance between them is less than a certain length 

 2Aj, and vanishes when the distance equals or exceeds 2^^ ; further, the greatest 

 values of 



ö 



and 



dx, 



B, 



are less than ^ whatever q and q' may be, a;^ , and x,,, , being the ic-coordinates 



of the centres of A^^ and A^, respectively, at time t. 



ii. Conduction is wholly due to molecular radiations. 



iß.) 



üi. The quantity of heat absorbed by A in any interval (t, t + t) is equal to 



cO^{t+j)\T,{t + r)-T^{t)\, 



