TEMPERATURE AND THE PROPERTIES OF GASES 3 7 



coincide at the critical point. Without going through the 

 process it follows from this that 



(7) (* + |) (30-0 = 80 



is the reduced equation. 



On the other hand equation (6) can only be put into the 

 reduced form by making some general assumption with regard 

 to the relations of the critical data. One which is very nearly 

 true in a large number of cases, and may be found to be strictly 



true in some, is that s— — = a constant = A, say, and then the 



equation will appear as 



(8) . . . . \v(f> = A' + B'/0\ + C'A£ ! X 2 + D'/<£ 4 \* + etc. 



in which A' B' etc., are functions of the reduced temperature 6 

 of the form 



(9) B' = 6x6 -{■ b 2 + 6J6 + b t J6* + b>!6\ 



In using this equation it is not necessary to give a value 

 to \ if, as is very useful, the values of pv/T at given values 

 of p, v and t are wanted, for we get X ir^\d = A" + B"/(f)\ + 



C'7<£ 2 \ 2 + etc., and hence /z//T = A"+ BvQf) + C'W 2 ^) 2 + etc; 



where B" etc. = b y + b 2 /0 + b 3 /6~ + b x \8' + b b j6\ The value of Tcjpc 

 is much more accurately known than \ and is usually between 

 2 and 4 (see, however, Table III.). For general deductions a 

 value of A, can be taken and the reduced form ir<f> obtained 

 for some special values of cf> and 6. 



Either from (7) or (8) or any other reduced equation it is 

 hence possible to calculate relations between ir, 4> and 6 which 

 apply, at any rate up to the practical limits of these, to a fair 

 approximation for any given substance, when the values of the 

 critical constants are inserted. 



In fig. 1 the system of values obtained from equation (7) 

 by plotting irfyjd against 1/$ = 8 as rectangular co-ordinates is 

 shown, but it must be clearly understood that the numerical 

 values can only be taken as an approximation to the results of 

 experiment, although the main principles are correct. 



It will be noticed that there are two clearly defined limits, 

 where § = 3 and at high temperatures. As far as the first is 

 concerned, Amagat found at his highest pressures values of 



