CHAP. VI.] CORRESPONDING CONTINUED FRACTION. 301 



whence we derive, denoting the functions 



% tfy tfy o, 



dO W dO&quot; 



by y\ y&quot;&amp;gt; y &quot;&amp;gt; &c., 



-y =y + 0y&quot; or g. = 



_ __ 



1-2-3-4-5- &c/ 



&c.; 



whence we conclude 



Thus the value of the function &amp;gt; , x - which enters into the 



7W) 



definite equation, when expressed as an infinite continued 

 fraction, is 



_0_ _ _0_ _0_ 6 

 1-2-3-4- 5-&C.&quot; 



314. We shall now state the results at which we have up to | 

 this point arrived. 



If the variable radius of the cylindrical layer be denoted by x, 

 and the temperature of the layer by v, a function of a? and the 

 time t ; the required function v must satisfy the partial differential 

 equation 



dv _ , (d?v 1 dv 

 + 



for v we may assume the following value 



v = ue~ mt ; 

 u is a function of a?, which satisfies the equation 



m d?u 1 du 

 T w + -r-a-h- j- = 0. 

 K ax x ax 



