SECT. II.] EQUAL PRISMATIC MASSES IN CIRCLE. 239 



the same temperatures after the time t has elapsed. Each of the 

 quantities a is evidently a function of the time t and of all the 

 initial values a lf a z , a 3 ...a n : it is required to determine the 

 functions a. 



260. We shall represent the infinitely small mass of the layer 

 which is carried from one body to the other by a). We may 

 remark, in the first place, that when the layers have been separated 

 from the masses of which they have formed part, and placed re 

 spectively in contact with the masses situated towards the right, 

 the quantities of heat contained in the different bodies become 

 (ra G&amp;gt;) a t + a&amp;gt;a n , (m CD) 2 -f a&amp;gt;z v (in o&amp;gt;) a 3 + coy 2 , . . ., (m a&amp;gt;) a n 

 + w^n-i &amp;gt; dividing each of these quantities of heat by the mass m, 

 we have for the new values of the temperatures 



a * + (**-t ~ Gi ) * and a + ( a -l ~ a ) ; 



// V i/V 



that is to say, to find the new state of the temperature after the 

 first contact, we must add to the value which it had formerly the 



product of by the excess of the temperature of the body 



from which the layer has been separated over that of the body to 

 which it has been joined. By the same rule it is found that the 

 temperatures, after the second contact, are 





The time being divided into equal instants, denote by dt the 

 duration of the instant, and suppose o&amp;gt; to be contained in k 

 units of mass as many times as dt is contained in the units of 

 time, we thus have a&amp;gt; = kdt. Calling Ja,, da 2 , (fa 3 ...da.,...cfa H the 



