EFFICIENCY OF PLUG-COCK FOG CHAMBER. 9 



Assuming the law of adiabatic expansion to hold both for gaseous 

 water vapor and for wet air in the absence of condensation, it is con- 

 venient in a plug-cock apparatus of fog and vacuum chamber (where 

 p l is nearly given by p 3 ] to reduce to adiabatic conditions; whence 



d=d 



where m is the quantity of water precipitated per cubic centimeter of 

 the exhausted fog chamber. Finally d, the density of saturated water 

 vapor, must be known as far as r, so that an equation d=/(r) is addition- 

 ally given. Here n l the vapor pressure at T t , is usually negligible (about 

 0.5 cm.) as compared with p^, and p l may in practice (where great 

 accuracy is not demanded) be replaced by p 3 , which like p is read off, 

 while TT holds at T, which is also read off. In the next section I 

 give a numerical example, taken from table 2, for p' : =43-5 c m - 



If the original equation (isothermal) is taken, m = 5.36Xio~' 8 grams 

 per cubic centimeter. If the above equation is taken, w = 5.35Xio~ 6 . 

 If the same equation is taken and p l replaced by p 3 , w = 5.3oXio~ 6 , 

 the error being i per cent of the true value, which is near enough in 

 practice or admits of easy correction. 



7. Approximate computation of p 2 . Since the plug stopcock can 

 not be closed before the water condenses in the fog chamber after 

 sudden exhaustion, the pressure observed in the fog chamber when the 

 room temperature reappears is smaller than p 2 . An excess of air has 

 passed to the vacuum chamber, so that the pressure within the fog 

 chamber is eventually p 2 , or less. The equation for p l and p\ remains 

 as in section 3, or better, as in section 4. 



The new quantities are 



PI 



Pi 



where ( o t is the density of air at r t . The ratio pj p l may be found when 

 r t is known as 



where ~r\ and T\, n\ and n\, p l and p\ are nearly the same. The last 

 equation may usually be written 



