SECT. II.] GENEKAL TEMPERATURE-VALUES. 235 



1 sin 3it sin 2u -^versm.* 



n v sin u 



sin 3w sin 2w - ^^ 



+ c, 



sm 

 sin 3*&quot; 



sin 

 &c., 



255. To determine the constants a, b, c, &amp;lt;#...&c., we must 

 consider the initial state of the system. In fact, when the time 

 is nothing, the values of a, /3, 7, &c. must be equal to a, 6, c, &c.; 

 we have then n similar equations to determine the n constants. 

 The quantities 



sinw sinOw, sin2w sinw, sin3w sin2w, ... , sin nu sin (n 1) u, 

 may be indicated in this manner, 



A sin OM, A sin w, A sin 2w, A sin ou, ... A sin (?i 1) u ; 



the equations proper for the determination of the constants are, 

 if the initial mean temperature be represented by C, 



a = (7+ a + b t + q + &c. 



, v A sin u A sin u A sin u&quot; 



