300 



Mr. A. S. Davis on the Vibrations which Heated 



and the contraction of the copper is 



1-2 x 0000017 x '0475 x -23 x T, x \/t 

 = -000000223 xT,xv//. 



Therefore the copper is raised in time t through a space 

 •000000623 TV7 decimetre, 



or 



•000062T A A millimetre. 



Let us now consider the case in which the area of the surfaces 

 in contact is very small, which will be the case applicable to the 

 rocker and block. 



If the heat which flows out of the hot metal and into the cold 

 metal were wholly confined to those parts which are vertically 

 above and below the surfaces in contact, then the height to which 

 the surfaces would rise would be given by the expression already 

 found. But in general a certain portion of the heat will flow 

 laterally ; and consequently the height to which the surfaces rise 

 will in general be less than the expression already found. The 

 proportion of heat which escapes laterally will be greater the 

 greater the depth to which the heat has flowed. 



Thus let a a be the 

 part of the surfaces in 

 contact. When the 

 heat has flowed to the 

 depth q' q ! , the whole 

 amount of heat which 

 has escaped laterally 

 bears a larger propor- 

 tion to the heat which 

 has flowed directly 

 downwards than it 

 does when the heat 

 has only flowed to the 

 depth q q. It will be 

 seen also that the pro- 

 portion of heat which escapes laterally depends upon the ratio 

 of the diameter of the surface in contact to the depth to which 

 the heat has flowed. 



Assuming, as a probable value, *2 millim. for the diameter of 

 the surface in contact, and supposing that the vibrations are 

 taking place at the rate of 225 per second, let us inquire what, 

 under these circumstances, will be the proportion of heat which 

 flows laterally. It will be seen from the figure that only a small 

 part of the heat which has flowed into the lead has penetrated to 



