EQUATIONS OF FOG CHAMBER. 63 



easier to compute the water precipitated per cubic centimeter (without 

 stopping to compute the other pressures) with a degree of accuracy 

 more than sufficient when the other measurements depend on the size of 

 coronas. 



To prove this, let d, L, and n refer to the density, latent heat of 

 evaporization, and pressure of water (or other) vapor; let p, k, c, t, 

 denote the density, specific heat at constant pressure, specific heat at 

 constant volume and temperature of the air, the water vapor contained 

 being disregarded apart from the occurrence of condensation. Let the 

 variables, if primed, refer to the vacuum chamber, otherwise to the fog 

 chamber. When used without subscripts, let them refer to isothermal 

 conditions or to room temperature. Let the subscript x refer to the 

 adiabatic conditions on exhaustion; the subscript 2 to isothermal con- 

 ditions, if the chambers could be isolated immediately after exhaustion 

 and allowed to heat and cool from the adiabatic state independently. 

 This case is in fact realized in the piston apparatus. Let the subscript 3 , 

 finally, refer to the isothermal conditions which prevail if the cham- 

 bers are put in communication at a room temperature after exhaustion. 

 Then the usual equations for heat evolved in the condensation of vapor 

 lead easily to 



rf = [ t i 1 ]-p 2 C(7-/ 1 )/L (1) 



where d is the density of saturated vapor at t, where t is the tempera- 

 ture to which the wet air is heated from its adiabatic temperature t A , 

 in consequence of the condensation of water vapor, where [rfj is the 

 density of water vapor if cooled as a gas, i. c, without condensation, 

 from / to t v Moreover 



[d 1 ]d = m (2) 



the mass of water precipitated per cubic centimeter by condensation or 

 the quantities sought. 



If Boyle's law is assumed to hold both for the gaseous water vapor 

 [d t ], and for the wet air, it is convenient to reduce equation (i) to room 

 temperature (isothermal state) and it becomes 



.*., ir c p 2 ir ~ . . . 



d = d V^ rLp^-V-h) (3) 



If the vapor density of saturated water vapor is known at a temperature 

 as low as t, 



d=f (*) (4) 



so that t, the only unknown quantity in equation (3), since the equation 

 of adiabatic expansion determines t lt is found from the intersection of 

 the curves (3) and (4). This is the method of Wilson and of Thomson. 



