Prof. Potter on some properties of the Air Thermometer. 265 



extremity of the liquid column will rest when the equilibrium is 

 restored, and OA=#, AB = Z>. 



If P is the position of the extremity of the column at any 

 time tj let OP=#. 



Let a = perpendicular section of the tube, 



p = density of the liquid in the cistern and tube, 



then the mass in motion at the time t is pa x BP 



z=pa(a-rb — a?). 



The moving force on the column B P is the difference of the 

 pressures on its ends at B and P, of which that at B is constant, 

 whilst that at P is variable and given by Boyle's law whilst we 

 neglect considerations of heat or cold developed, and the adhe- 

 sion of the liquid to the tube. 



Let V be the volume of the receiver and tube up to the point 

 0; then the volume to the point P is V-f «#, and 



the elastic force of contained air in volume PO V -f ax 



. — — . . - - - ■ . ■ . — t ' — . . - ■ » 



the elastic force of contained air in volume FP V 



Let p = constant pressure on a unit of area of the atmosphere 

 and the liquid in the cistern at B, and therefore pa = pressure 

 on the surface of the end of the column at B as well as at A, 

 and when there is equilibrium. We have the moving force on 

 the column when the surface is at P 



=pa— pressure due to the elastic force of the contained air 

 on the surface at P, 



V 



pax 



which varies as x very nearly, since ax is very small compared 



with V. 



Prom these we have the accelerating force acting upon the 



d x 

 column of liquid BP= j-% 



the difference of the pressures at B and P 

 mass of the liquid in the column BP 

 pax 



"~ (V + az)pa{a + b — x)' 



7J X 



= -y • . _ very nearly, since ax is very small compared 



with V. 

 Phil Mag. S. 4. Vol. 24. No. 161. Oct, 186.2. T 



