Metals undergo when in contact with cold Material, 301 



a depth greater than 2\/kt, and that two thirds of the whole 

 amount is confined to a depth less than vkt. Hence, in the case 

 under consideration, only a small part of the heat has penetrated 

 •44 millim. into the lead, and two thirds of the whole amount 

 has not penetrated '22 millim. In the same way it will be 

 found that but little heat has flowed out of the copper from a 

 depth greater than '63 millim., and that two thirds of the whole 

 amount has come from a depth less than '32 millim. If, then, 

 we draw the figure so that aa, aq, a q', ar, ar 1 are proportional 

 respectively to the numbers 20, 22, 44, 32, 63, we may, by con- 

 sidering the proportions which the masses of heated and cooled 

 metal vertically above and below the surfaces in contact bear to 

 the whole masses of heated and cooled metals respectively, form 

 a rough estimate of the proportion of heat which is available in 

 raising the rocker. 



Taking one fifth of the heat which flows into the lead as 

 available in raising the rocker, and one tenth of that which 

 flows out of the copper as available in diminishing the height to 

 which the rocker is raised, the height through which the rocker 

 is raised will be 



•0000147x^x^7 millim.*, . . . (4) 



when t has a value about % l- 5 -. 



II. Taking this as the correct expression for the height 

 through which the rocker is raised, I now proceed to determine 

 the difference of temperature between the copper and lead neces- 

 sary to produce continuous vibrations at a given rate in a rocker 

 of given shape. 



Let the rocker be a rectangular parallelopiped with two pa- 

 rallel ridges on its underside. Let the point of support which 

 rests upon the table be so far removed from the body of the 



O R 



* I here assume that the total flow of heat into the lead is the same as 

 if there were no lateral flow of heat. The fact that a lateral flow of heat 

 occurs will probably increase the total flow, and will also probably have 

 the effect of diminishing the depth to which the heat flows in a given time. 

 For each of these reasons the value found above would be too small. 



