1054 



For every value of y we may calculate the corresponding value 

 of (^2;'' — 1) : (2/— 1) from (34), bearing in mind that 7iz=8y {y-\-l) : 

 . (2y — 1)(47 + J). We shall then find the mean value 1.08 for that 

 ratio, so that the factor of I T will get an average value of 0,038 

 (which also represents a mean value) Xl>^8 = 0,041. 



In this it will no (lonl)t follow from the nature of the thing that 

 the factor 0,041 in the formula for />,, — A„ is the same for all the 

 substances, luit the factor 0,038 in the formula for hi- — /\, varies 

 somewhat with ditferent substances, dependent on the value of the 

 ratio {b,, — f\,) ■ {h — f'„)- For />,, is, so to say, a natiiyal point in 

 the series of values between the final points />« and h,j — but bk 

 onlv an accidental point, dependent on the situation of the critical 

 point. It follows, however, from this that now, for Helium e.g., the 

 factor for {hjc- b^,) -. />„ will become greater than 0,038, viz. 0,041 : 

 : 1,004=0,041, because for He the value of (A,;— Aj : (/^jr.— />J=1,004. 

 But this does not i)resent any difficulty, for He can very well have 

 a somewhat greater value of the factor. With 0,041 '2yi,. — l would 

 namely become zn 0,093J ; so 7^: = 0,547, oidy little higher therefore 

 than 0,543, and still smaller ihau 0,56. 



For the sake of completeness I shall just give the corrected values 

 of yk (calculated) for the other substances mentioned in the table. 

 For H3 Yk would become = 0,615. (Here the reduction factor 

 Ö ==(/;,-/>„) :(/>/,— A,) = 1,0Ü). P^or Argon we find n- = 0,739 (with 

 <^ = 1,053): for Xenon with <9 = 1,077 we find the value 0,824 — 

 both almost identical with the values in the original table. CjH, 

 yields yjt = 0,832 with ^ = 1,084; Isopentane yk = 0,8^7 with 

 ^>==1,11; Fluorbenzene finally gives 7;^. = 0,933 with ^ = 1,12. The 

 last value of yk is now also equal to the "found" value of 7^-. 



16. Calculation of the theoretical b-values. 



The values of b can now be calculated from the reduced equation 

 of state in the form [see I, p. 812, equation (c)] : 



[n — i^) = sm . . . . . . (87) 



In this ii represents b : vk- The values found thus can then be 

 compared with those which we can calculate from (30) and (35). 

 For equation (30) we may write: 



h — bo bjc — hg\" xk \xk 



b, ' b„ J i - b'k : xk 



I e. with (A,. — 60) : b, = 2y — 1, b'k = (2 7 — Ij^ : 4 7 (7 + 1). 



