Prof. Potter on some properties of the Air Thermometer. 267 



Let F be the ball or receiver of the thermo- 

 meter furnished with a pipe and stopcock Gr, by 

 which a portion of the air may be suddenly re- 

 moved and the stopcock closed. 



Let E B be the vertical tube of the gauge dip- 

 ping into the cistern CD which contains the 

 liquid of the gauge. 



Let A be the level of the liquid inside the tube 

 in equilibrium before the portion of the air is 

 removed through G, and the new position of 

 equilibrium after that removal; and the volume 

 of the contained air then V. 



Let P be the surface of the column of the liquid 

 PB at any time t, and OP = #, OA = «, AB = 5. 

 The upper surface of the liquid will oscillate about 

 0, and may attain some maximum height OA', 

 when the velocity will be again nothing. 



Let r be the radius of the tube, and a its per- 

 pendicular section, or Tr?^=u; let p = density of the liquid of 

 the gauge. Then, as in the former case, 



the mass of the column PB = p«(«-f & — x), 



the elastic force of the air in the receiver and pipe to P V 



the elastic force of the air in the receiver and pipe to " V + ox' 



If p is the pressure of the atmosphere on a unit of area when 

 the height of the barometer formed of the liquid is h } then the 

 elastic force of the air filling the receiver and tube to 



-p—gp.OA. 



=gp{h-a), 



V 



and the elastic force in the volume to 'P = gp(h — a)^ F • 



•^ 'Y + ux 



The moving force acting on the column PB = pressure of the 



atmosphere on the area a — the weight of the column PA of the 



liquid — the elastic force of the air contained in the receiver and 



the tube to P, acting on the area «, 



= c/pu ^h -(a-x)- (h - a) ^— -J* 





Let V now =«//, where h' will be very large in the experiments 

 compared with a and x, and we may put 



a{h — a) u(h — a) h—a h 

 V + ax ah' + ux h' + X " h 1 

 nearly when a and x are small. 



T2 



