62 VAPOR NUCLEI AND IONS. 



The case is illustrated graphically for p f = 4$ cm. in the notched 

 curves of fig. 27c in a way easily understood. It seems probable that 

 whereas the smaller fog chamber has more than returned to isothermal 

 conditions (p 2 ), the large vacuum chamber is about a millimeter short 

 of it when the cock is again closed. The constancy of this difference 

 is in all probability referable to the systematic method of investigation, 

 though the effect of precipitated moisture has not yet been considered. 



Anomalous relations in the data for the fog chamber (as in the case 

 of p , = S9-5 cm -) are direct errors of observation. On the other hand, 

 however, since within the ranges of observation and very nearly 



p =a 



p 2 = a 2 + b 2 p' 

 p 3 = a 3 + b 3 p' 

 ip-p2)/(p-p*) = (A 3 + B 3 p')/(A 2 + B 2 p')=A+Bp' (nearly), 



where a,b, A, B, etc., are constant. Frequently B is negligible, so that 



(P ~ Pi) I(P~Pz)=A = const. , 



in which case the graph for {p 2 -p 3 ) / '(p-p 3 ) = i-A also passes through 

 the origin as in the two cases (fig. 30). There is no need of this and it is 

 at best an approximation which facilitates computing. 



Some remarks may here find place on the moisture precipitated in the 

 fog chamber per cubic centimeter, and on the absolute temperature t x 

 to which this precipitation heats the chamber above the adiabatic 

 temperature t v I have shown above that the combination of fog 

 chamber with a large vacuum chamber and a sufficiently wide passage- 

 way, though affording superior practical advantages, and little if any 

 inferiority in efficiency to the piston apparatus within the range of 

 measurable coronas, nevertheless does not give the volume expansion 

 of the air within the fog chamber either under adiabatic or under iso- 

 thermal conditions. It makes no difference how rapidly the stopcock 

 is manually closed. The conditions of the vacuum chamber are always 

 impressed upon the fog chamber. The adiabatic and isothermal data 

 may, however, be computed if the volume ratio of the fog and vacuum 

 chambers and the pressures before exhaustion (when the chambers are 

 isothermally separated) and after exhaustion (when the chambers are 

 isothermally in communication) are known; and these computations are 

 simple because the reductions are practically linear. 



When the vacuum chamber is large, moreover, its pressures vary but 

 slightly, and therefore the pressure observed at the vacuum chamber 

 after exhaustion, when the two chambers are in communication, is very 

 nearly the adiabatic pressure of the fog chamber. This result makes it 



