138 Mr. J. Rose-Innes on the Practical Attainment of 



readings of the constant-volume thermometer into tempera- 

 tures on the thermodynamic scale. 

 We start with the equation 



pv 



-^ Rr «i a.-> ) 



As before, let the suffix applied to p and t refer to the 

 freezing-point, and let the suffix 1 refer to the boiling-point. 

 Then 



„ r r «i «2 "i 



p v=Rt - - ^a f + - + — J>, 

 _, R f , , a l ■ a 2 "1 



Multiply the first of these equations by t^ — t^ the second 

 by £ — fi, the third by t — t, and add 



v{p(h- 1 ) +p (t - h) + Pl (t -t)} 



_ Ra 2 fh-tp ^i *o-q. 



~3i; L t t t x J 



Hence 

 p(t 1 -t )+p Q {t-t 1 )+ Pl (t -t) 



= /Ra a r (t l -t )t 1 t +(t--t 1 )tt l + (t o -t)t o t\ 

 3v 2 \ tt t l J 



(p-l^)(h-to)-(Pi-Po)(t-to) 



= __ R«2 fa-g )ft-gft-fj 



Divide by^ — p and transpose 



_ P~P° ( t t) \ G2 ft~*o)ft~*i ) 



We see from this equation that the expression 

 «2 ft-*o)ft— *i) 



'6V ttyti 



gives us the required corrections to the readings of the 

 constant-volume gas-thermometer. We notice also that in 

 order to calculate this term we require to know the value of 

 t, a quantity not accurately known. Sufficiently accurate, 



