Tsothermals of Tsopentane. 77 



with isopentane upon this formula is fully considered by 

 Prof. Young in his paper. Accepting the formula, and 

 writing it as 



p = bT-a, 



where b and a are functions of the volume only, the values of 

 b and a for a large number of volumes are given in the paper 

 (loc. cit. pp. 650-655), and they are sufficiently numerous to 

 enable us to fully test any algebraic expression that endeavours 

 to represent them. I spent a considerable amount of time 

 examining the values of a and b, testing the formulae that 

 have been proposed by various physicists, as well as others of 

 my own devising, without arriving at any that gave complete 

 satisfaction ; and it occurred to me afterwards that possibly 

 more definite results could be secured by examining some 

 physical quantity which depended upon both a and b than by 

 examining h and a separately by themselves. Thus if we accept 

 Ramsay and Young's linear law, there will be one and only 

 one temperature for each volume at which the gas has its 

 pressure equal to that given by the laws of a perfect gas. 

 In effect, if we put 



p = bT — a 



as giving the actual pressure, we may also write 

 RT /, R> 



P=— +(b )T 



V \ V / 



RT 

 and this shows that p= — if we take T= , ", . (Jul] 



v b — R/t 



the temperature so found t; the values of t have been calcu- 

 lated and are given in the following table (p. 78) ; the results 

 above vol. 400 are not included, as they vary within such wide 

 limits owing to experimental errors. 



In calculating this table, the value of R was taken = — . 



. -001158 



An examination of the table shows that the temperature in 

 question is very much the same for all large volumes down to 

 about vol. 8. Of course the actual numbers obtained vary a 

 good deal, but these variations are without method, sometimes 

 in one direction and sometimes in another, and when the 

 numbers are plotted against iH it appears to me impossible 

 to tell from an inspection of the diagram whether the value 

 above vol. 8 is on the whole increasing or decreasing. These 

 variations may therefore be attributed to experimental error ; 

 and they may be to a large extent got rid of by employing 

 "smoothed" values of b and a, as was done in Ramsav and 



