814 



simple, the more so as there occurs only one quanlity, viz. /"', in it. 

 For ƒ'=:ƒ= 4 we have ,3' ^. = 0, as we should have. 



4. If we may really put X^ : 1^ = 1, .v is perfectly determined 



by /' through the relation fy), and only one quantity either s or ƒ' 



suffices. Then we have only to put : 



8/' 8. 



01' ./ = Ö — 



8+/' 



everywhere in the above. Further in (3) rs simply becomes = 8 

 and in (4) ƒ ' will become = 8 : (r — 1). 



Hence if we express everything in ƒ', we have: 



\7f'"- I 



= I 4- T., ; ^- = ^r., —. 



, (7) 



8f_ =^±11^X4-^ A=— 5^^— 



3+/' ' ' ƒ' ^f' ' ■ (/'_l)(8+/')^ 



16(/'— 1) „ /■'— 4 



/'(8+/') ^ ƒ' 



by the side of which we mention a few more earlier relations in 



the new form : 



27 27 1 

 rs = S ; f'{r—l) = S ; ^ (ƒ ' — 1) =: — == — .s^ 



' y V / ' vy '' r^ 64 , (8) 



r — 3 : l/A (ƒ' — 1) : 3 ; s = V, V^X (ƒ' — 1) : 3 I 



when ;.i = A.^ is represented by A. We once more point out. that all 

 the foregoing relations hold quite generally and perfectly accurately, 

 but that the relations (7) and (8) will be dependent on the assumption 

 AjiA, = 1. But this latter relation may be considered as perfectly 



accurate. 

 Now 



8 a 1 , a 



27 bk ^ 27 bk'' 



is simply found for RTk and pk, so that we can calculate the quan- 

 tities a and bk very accurately from the observed critical pressure 

 and temperature. 



As for the quantity ;., it is =r 49 : 50 = 0,98 for f = 7 ; for 

 ƒ = 6 we find 243 : 245 = 0,992 ; for / :=: 5 we have ;. = 

 675: 676 = 0,9985, and for/ =:4the value 1 is found. So whereas 

 Aj : A^ is pretty accurately =1, Arr^Aj^/^ will in the utmost case 

 only deviate 2 7o fi'om unity, and will approach more and more to 

 1 for substances with lower values for ƒ'. 



Let us now proceed to give the new relation and at the same 

 time introduce the reduced coetllicient of direction of the straight 

 diameter y. 



