Metals undergo when in contact with cold Material. 297 



tact. Faraday *, Seebeck f, and Tyndall J have adopted this expla- 

 nation ; and they have shown that most of the facts which they 

 and others have ascertained respecting these vibrations are easily 

 explained upon this view of their cause, supposing only that the 

 expansion is sufficiently great to produce any sensible effect. 



Professor James Forbes §, on the other hand, after an extensive 

 series of experiments, was led to reject Sir John Leslie's expla- 

 nation, one of his principal reasons for doing so being the im- 

 possibility, as it appeared to him, that the expansion occasioned 

 by so slow a process as the conduction of heat could produce any 

 sensible mechanical effect. He says, " Even at first sight it does 

 appear very difficult to conceive how, when the vibrations are 

 increased to 500 or more in a second, a process depending upon 

 so slow an operation as the conduction of heat should cause the 

 metal to expand and contract successively by a finite quantity. 

 The effect has every appearance of being one of active and almost 

 instantaneous repulsion, and bears no resemblance whatever to 

 the slow mechanical elevation of the surface by the process of 

 expansion.'" After remarking that such inferences are often erro- 

 neous, he enters into a closer consideration of the phenomenon, 

 but finds no reason for altering the opinion expressed in the 

 passage just quoted. 



It thus appears to be an interesting problem to determine by 

 calculation the amount of expansion produced in the block in 

 any given time, and to find whether it is sufficiently great to 

 cause the vibrations in question. This is what I have attempted 

 to do in the present paper ; and the conclusion at which I have 

 arrived confirms the truth of Sir J. Leslie's explanation. 



I. To find the expansion produced in any given time. 



It will be convenient to consider in the first place the follow- 

 ing problem : — A large heated piece of metal is laid upon a large 

 cold piece of the same kind of metal, the surfaces in contact being 

 horizontal planes. To find the height through which the sur- 

 face of the cold metal has been raised in any given short time. 



The time being short, the depth to which the heat will have 

 penetrated will be small ; and the pieces of metal may therefore 

 be considered infinite in extent. We have, then, for determining 

 the temperature v at any depth % after the time t 3 the following 

 equation, 



2vr 



2 *lkt 



-£2 



z \dz, . . . . (1) 



* Proc. of Roy. Inst. vol. ii. p. 119. f Pogg. Ann. vol. li. 



% Proc. of Roy. Inst. 1854. See also 'Heat as a mode of Motion/ 

 p. 127. 



§ Phil. Mag. vol. iv. 



