Metals undergo when in contact with cold Material. 303 



risen in the time t. Let B/, Q/ be the horizontal and vertical 

 components of the pressure upon the rocker at the point at 

 the time t. Then the equations of motion are 



d*x 



The geometrical relations are 



% = a cos 6—b sin 0, 



\y = 5 cos + « sin + h. 

 From these equations we obtain 



dW f . d*K 



F 



dW ( d Ll h\ 



dVi\ 



~ a [? + w) very near1 ^ 



Integrating and noticing that when t — §, i-=&)'jWe have 



Integrating again and noticing that when £=0, ^ = 0, and 

 0= — -, we have 



W-. 0=- ^ -ah + k*co ! t+F. 5.. 

 2 2a 



Now, just before the next impact will have risen to a height 

 H, and ! will have sunk down to its original position. There- 

 fore the values of 6 and — will be respectively — — and — <w. 

 at (Ca 



Hence, if it be the period of the vibration, we have 



k 2 . H ag7r 2 . TT 1Q , 



- = -%-+«. H — /cVtt; 



a & 



,_ aV.7r 2 + 2H ( ft 2 - /c 2 ) 



From (7) we have 



dh 

 dt 



(8) 



k*{co + co ! )=a<}Tr + a~> (0) 



