230 THEORY OF HEAT. [CHAP. IV. 



followed by a term equal to ay. We have then, as formerly, on 

 substituting kdt for &&amp;gt;, the following equations : 







252. To integrate these equations, we assume, according to 

 the known method, 



Ajjflj, 2 , 3 , ... , being constant quantities which must be deter 

 mined. The substitutions being made, we have the following 

 equations : 



k 



ift = -(-i)&amp;gt; 



J A = -{(s- a )-(a 8 -a 1 )}, 



k 



- 



If we regard a t as a known quantity, we find the expression 

 for a 2 in terms of a v and A, then that of a z in a 2 and h ; the same 

 is the case with all the other unknowns, a 4 , a 5 , &c. The first and 

 last equations may be written under the form 



m 



and ^ = (K +1 - &amp;lt;O - K - Ol- 



