818 

 r^^^ (14) 



r 



Then trom (3), viz. rs = 8 X 0^, ■ '^■,), when A^ : A, = 1 is put, 



8y 



1+r 



follows for s, whereas from s'^2{l-\-y), (see (9)), follows: 



s' (i+yr- 



- = ^^ (16) 



8 

 From ƒ' = 8ó' : (8 — s) (see a little above (7)), or also from/' = ■ 



r — 1 



according to (4) we derive : 



/ = 8y> (IV) 



an exceedingly simple relation, which states that the critical coeffi- 

 cient of pressure f' ^) will always be equal to eight times the reduced 

 coefficient of direction of the straight diameter. 

 From (7} follows for y: 



27 y* 



A = (18) 



(l+y)^(8y-l) ^ ^ 



Further according to (7) we have 



8y — 1 



l-h'k = -^ ; b\ 



4y(l+y) 



Then also according to v7) 



1 7' - ^^-iL K' - (^y-^)\ ^v- _ (2y-i)- .,^. 



^-''-^^yY ''-4y(H-y)' l-h'k" 8y-l " ^'^^ 



vkb"i. f' — 4 2y— 1 

 l—bjc ƒ 2y 



Thus we arrive, substituting bk : b^ for 2y according to (12), at 

 the exceedingly simple relations at the critical point: 



(bk—b,y , bk—b, 



b/cVk bk 



From this we can already get an insight into the probable values 

 of b' and p" also outside the critical point, and try to derive the 

 relation b=f{v) by integration. But this will be discussed later. 



If we now finally summarize what has been found, in a table 

 in which some principal types of known substances have been 

 inserted, we get the following instructive summary, from which it 

 may be seen how the ivhole behaviour of the substance can be 

 deduced from one fundamental quantity — here the quantity y (also 

 =zy^(bk-b,)), the reduced coefficient of direction of the straight dia- 

 meter according to 7^ id^ -{-d^) — 1 = y (1 — in). We may further 

 avail ourselves of the following table for the prediction of still un- 



1) In which f' is properly speaking =ƒ:(! + :?), see (5). But f' always differs 

 exceedingly little from f. 



