90 THEORY OF HEAT. [CHAP. IT. 



two consecutive sources of heat, are represented by the terms of 

 a recurring series whose scale of relation is composed of two terms 

 q and 1. 



Experiments have fully confirmed this result. We have ex 

 posed a metallic ring to the permanent and simultaneous action 

 of different sources of heat, and we have observed the stationary 

 temperatures of several points separated by constant intervals; we 

 always found that the temperatures of any three consecutive 

 points, not separated by a source of heat, were connected by the 

 relation in question. Even if the sources of heat be multiplied, 

 and in whatever manner they be disposed, no change can be 



v ~\~ v 

 effected in the numerical value of the quotient - 1 - 3 ; it depends 



only on the dimensions or on the nature of the ring, and not on 

 the manner in which that solid is heated. 



110. When we have found, by observation, the value of the 

 constant quotient q or 1 ^ 3 , the value of a x may be derived 



from it by means of the equation a A + of A = q. One of the roots 

 is a\ and other root is a~\ This quantity being determined, 



we may derive from it the value of the ratio ^, which is 



J\. 

 o 



j (log a) 2 . Denoting a x by co, we shall have o&amp;gt; 2 qw + 1 = 0. Thus 

 I 



nr 



the ratio of the two conducibilities is found by multiplying 



L 



by the square of the hyperbolic logarithm of one of the roots of 

 the equation o&amp;gt; 2 qa&amp;gt; + 1 = 0, and dividing the product by X 2 . 



SECTION II. 



Equation of the varied movement of heat in a solid sphere. 



111. A solid homogeneous mass, of the form of a sphere, 

 having been immersed for an infinite time in a medium main 

 tained at a permanent temperature 1, is then exposed to air which 

 is kept at temperature 0, and displaced with constant velocity : 

 it is required to determine the successive states of the body during 

 the whole time of the cooling. 



