J04i> 



the artit'lc in the Arcli. Tcyler (2) IX, 3'' [)Hr(io: •'(^)uel(HiC8 Rcmar- 

 ques snr l'équation d'état"). 



This is therefore exactly the same as van der Waals continued 

 years later'), quite independently of the above investigations, and 

 in which he found several remarkable approximate relations. These 

 were afterwards bronglit to a more accurate form by me, throngh 

 the introduction of the (juantities P.j and P..^ into the expressions for 

 ET]c and p]^, in which it appeared that ).^ =: ).^ for ordinary sub- 

 stances amounts to about 0,98, and approaches to 1 as the substances 

 approach more and more to so-called "ideal" substances with J) 

 little variable or invariable. (See also I). 



Thus all the quantities were expressed in ƒ and s. But in con- 

 sequence of the equalization of -^i and /, all of them could also 

 be expressed in the one quantity ƒ (or rather f' = /: (1 -j- ^/) — 

 see I p. 811 and p. 814). This further step was followed by a still 

 more decisive one in consequence of a new relation being found 

 (See 1, p 815 et seq.), on account of which everything could be 

 expressed in the one quantity y")-, the reduced coefficient of direction 

 of the straight diameter*). For h]^:ir^ appeared to be = 2y (p. 816 

 loc. cit.). Of special importance is ihe simple relation /'=8y (p. 818). 



The table on p. 819 was the result of these new considerations. 



And now that we have also an idea of the course of the function 

 b = f{v) — though of course the found relation (30) or (29) is not 

 the only one that satisfies all the imposed conditions, but certainly 

 one of the simplest relations that can be put — now the temperature- 

 influence neglected np to now, forces itself upon our attention. For 

 the found expression (29) only holds for one temperature, viz. for the 

 critical. Here too we shall have to be satisfied for the present with 

 an em{)irical relation, leaving it to futui-e investigation to give the 

 found equations h =z f {v) and h =i f [T) a theoretical foundation, in 

 which then the relations, found in I between hu and ?'„ (/>„), and 

 those for //^ and />"/., will find a natural explanation. 



14. Tlie variabiliti/ ivitli respect to T. 



In the expression (30) the quantities bk ■ Z^, c^'^c' ^'^• • ^'o occur besides 

 in the first member also in the second member because of x/c and 

 b'l^ and the exponent n. In this bk ■ b^ =z 2y and rk : v^> = 2(y -(-J). 



1) These Proc. XIH, p. 118, 1216 el seq. 



3) These Proc. XIV, p. 771 et seq. 



^) And througli which some approximate relations of v. d. W. (These Proc. 

 XV. p 'J03,. 971 and 1131) which were based on tlie approximate equality of s 

 and s' (which quantities can, however, diller more than 12%) could be replaced 

 by more accurate ones. 



