64 VAPOR NUCLEI AND IONS. 



In the piston apparatus p 2 as well as p may be read off by the gages; 

 but, as stated above, this is not true when the fog chamber communicates 

 directly with the vacuum chamber. In this case, however, p x is nearly 

 given by p 3 . Consequently it is expedient to reduce equation (i) to 

 the adiabatic conditions, whence (if r refers to absolute temperature), 



d-d (t=*y>-gsy<>$- td (s) 



f P\ Vi\(k-c)/k 



i = t U-=^r; (6) 



m = 



_ PC/ pj-ir Ac/k- 



L\p 



ir,\c/ . . . 



ZiV V-ti) (7) 



Here it lt the vapor pressure at t v is usually negligible (about 0.5) as com- 

 pared with p v and p x may, in practice, where great accuracy is not 

 demanded, be replaced by p 3 , which, like p, is read off while n holds 

 at /, which is also read off. 



In illustration I will give a numerical example taken from table 216 

 where 



=76 cm. 3 = 45.5 cm. tj =- 17.8 C. 



ir = 1.7 cm. 1 = 46.1 cm. t =5.25 C. 



P =0.00118 ,, = 54.7011. *' 1 =24.iC. 

 '=43.5 cm. 



If equation (3) is taken 



w== 5-36Xio -6 grams per cubic centimeter 



If equation (5) is taken 



w=5-35Xio- 

 If equation (5) is taken and p x replaced by p 3 



m== 5-3Xio -6 



the error being 1 per cent of the true value, which is quite near enough 

 in practice and admits of easy correction. 



Finally one may compute p 2j the pressure which would be observed 

 at the fog chamber instead of p 2 if allowance is made for the water pre- 

 cipitated in the fog chamber, whereby additional air escapes into the 

 vacuum chamber, since the former is heated from T,to Ti. The chambers 

 are supposed to be separated (cock closed) immediately after conden- 

 sation and no further loss of air is to take place from fog chamber to 

 vacuum chamber while the absolute temperature of the fog chamber 

 passes from r t to atmospheric x. Without giving the full discussion for 

 which there is no room, I will merely add that 



p2n == p 1 -($2n) 



