EFFICIENCY OF PLUG-COCK FOG CHAMBER. 3 



approximation in the isolated chamber. Finally, when the chambers 

 are put in communication, the variables (No. 6) are the same in both. 

 This account of the phenomena may seem prolix, but it is essential 

 to a just appreciation of the efficiency of the plug-cock fog chamber. 

 Quantities in table i referring to a given chamber may be connected at 

 a given time by Boyle's law, as for instance, (p n)=Rpr. This gives 

 eleven equations, some of which may be simplified. Corresponding 

 quantities in groups i and 2, as, for instance, r/r l , may be connected 

 by the law for adiabatic expansion, giving two equations. In addition 

 to this, an equation stating that a given mass of air is distributed in fog 

 and vacuum chambers (volumes v and V, respectively) is available; or 



All the quantities TT are supposed to be given by the corresponding r, 

 though at high exhaustions the lower limit of known data, n = f(r), is 

 often exceeded, at least in case of vapors other than water vapor. 



3. Approximate computation of p t and p 2 . It will first be necessary 

 to compute p 2 , the pressure which would be found in the fog chamber 

 when it has again reached room temperature r, if there were no further 

 transfer of air from fog chamber to vacuum chamber, due to the con- 

 densation of water vapor in the former after adiabatic cooling. 



For the purpose of obtaining more nearly symmetric equations it 

 seemed to be expedient to write 



-/* and r/r' 



at the outset, in correspondence with Boyle's law, and thereafter to 

 correct for the temporary introduction of TT into the adiabatic equation. 

 Believing that the completed equations would be much more com- 

 plicated by contrast than they actually are, I made many of the com- 

 putations, where a mere guidance as to the conditions involved is aimed 

 at, with these symmetrical equations. The constants for use will be 

 computed by the more rigorous forms of sections 4, 5, 8, and 9. Mean- 

 while the comparison of both groups of equations will make it easier to 

 pass from the equations with p re, wherever they were used in my 

 work, to the correct forms of the next paragraph. It is for this reason 

 that the equations now to be given were retained. 



The pressure p 2 is given by the gages of the piston apparatus, since 

 there is but a single chamber, and in this respect the plug-cock appara- 

 tus differs from it because the corresponding gage-reading is essentially 

 even less than p 2 . (Sections 5 and 9.) 



The solution when the air in both chambers is continually saturated 

 leads to transcendental equations for the adiabatic pressures p l =p' l , 



