360 THEORY OF HEAT, [CHAP. IX. 



366. If H be made nothing, we have 



This equation represents the propagation of heat in an infinite 

 bar, all points of which were first at temperature 0, except those at 

 the extremity which is maintained at the constant temperature 1. 

 We suppose that heat cannot escape through the external surface 

 of the bar ; or, which is the same thing, that the thickness of the 

 bar is infinitely great. This value of v indicates therefore the law 

 according to which heat is propagated in a solid, terminated by 

 an infinite plane, supposing that this infinitely thick wall has first 

 at all parts a constant initial temperature 0, and that the surface is 

 submitted to a constant temperature 1. It will not be quite 

 useless to point out several results of this solution. 



Denoting by (7?) the integral ^ \dre~ r * taken from r = to 



JTTJ 



r = 7?, we have, when R is a positive quantity, 



hence 



(- 5) ^&amp;gt; (JR) = 20 CR) and t? = l-20/ ~ 



~CD, 

 developing the integral (R) we have 



Paris, 1826. 4to. pp. 5201. Table of the values of the integral Jdx (log IV*. 



The first part for values of Hog - j from 0-00 to 0-50; the second part for values 

 of x from 0-80 to $-00. 



Encke. Astronomisches Jahrbuchfvr 1834. Berlin, 1832, 8vo. Table I. at the 



2 ft 

 end gives the values of - / e~ tz dt from f = 0-00 to t = 2 QO. [A. F.] 



