240 THEORY OF HEAT. [CHAP. IV. 



infinitely small increments which the temperatures a 15 2 ,...a 4 ...a n 

 receive during the instant dt, we have the following differential 

 equations : 



Ja 2 = -dt 



k 

 d*i = -dt 



^-i = -^( a - 2 - 2 Vi + &amp;lt;&amp;gt;&amp;gt; 



Illi 



&amp;lt;fe.^ ~ &amp;lt;&(&amp;lt;.._, -2*. 4 a,). 



261. To solve these equations, we suppose in the first place, 

 according to the known method, 



The quantities 6 t , 6 2 , & 3 , ... & are undetermined constants, as 

 also is the exponent li. It is easy to see that the values of 

 cij, ff 2 ,... B satisfy the differential equations if they are subject to 

 the following conditions : 



(6 -26, 



7/i 



Let = -v- , we have, beginning at the last equation, 



. = 6.-, (2 + 2 ) - J 



