PRACTICAL STANDARDS FOR ELECTRICAL MEASUREMENTS. 211 



where () is the cooling eflfect and t temperature on the ordinary centigrade 

 scale, represents the experimental values rather more accurately than the 

 inverse-square formula. The values of a and yS calculated by him for air, 

 carbonic acid gas, and liydrogen, the change of pressure being represented 

 by 100 inches of mercury, are as follows : — 



Air . , 



Carbonic Acid 



Hydrogen . . . 



To apply equation (1) to the discussion of the gas-thermometer, we 

 may begin (like Joule and Kelvin) by expressing the work civ, required 

 to restore the gas to its initial condition, in terms of the observed cooling 

 effect, and may write 



"«=JC9=Jc(^ + /3), 



where J is the mechanical equivalent of heat and C the specific heat of 

 the gas under constant pressure. If we remember that J may be written 

 J^W/??if:(', where Wis the work that must be spent to raise the tempera- 

 ture of a mass m of water by the amount 0', we see that the thermometric 

 scale on which d and ti' are expressed is of no consequence, provided it is 

 the same for both. 



Putting IT for the change of pressure producing a cooling effect 0, we 

 may write equation (1) thus, taking reciprocals of both sides : 



^ce-"--rr{T+^^j (') 



or, dividing throughout by T- and integrating between limits T and 

 infinity — 



(V\ _V_JCfa l3\ 



With I'egard to the first term on the right, it may be remarked that 

 all gases appear to approximate more and more nearly as temperature 



rises to agreement with the equation ^^ =R (a constant). Applying this 

 to (3), we get 



2? T n V2T2"''tA 



or. 



HT JG p f a . r, \ ... 



^^=^-n--i(2f-^^ j ... (4) 



Neglecting, provisionally, the Joule-Kelvin effect, we have, as a first 

 approximation, 



RT 



and we may take this value as accurate enough for use in the small tei'm 

 containing p on the right-hand side of (4). 



r 2 



