HYDROSTATICS. 337 



at atmospheric density : prove that, for small vertical oscillations, 

 the distances of the piston and of the top of the cylinder from 

 their n-spi-ctive positions of equilibrium, at a time t, are of the 

 form 



A sin (AJ + a) + B sin (jit + /?), 

 A, /A being the positive roots of the equation 



and mm . The weight of the air in the cylinder and 

 en 



the resistance of the fluid may be neglected. 



W. 22 



