815 



5. A new relation. 



1 found, namely, that remarkably enough, there always exists a 

 simple relation between the quantities r = Vk : hk and z = />/; -. Vg. 

 Not the approximate equality of s and s' =-• vj^ : i\, brought forward 

 by VAN DER Waals, but another accurate relation. For though .? 

 differs little from s' , yet the difference can amount to Vs o^ the 

 value, whereas the relation found by me seems perfectly accurate ; 

 the value of.y: 5' can be calculated from it for every value of the 

 chosen independent parameter. 



We know that according to the property of the "straight diameter" 



i {d, + d,)~l 



1 — ?n 



when d^ and d^ represent the reduced densities of liquid and vapour. 

 When d^ may be neglected with respect to d^, we have simply: 



id,=^l 4. y(l_„,), 

 which for m = would pass into ^ d^^l -\- y or 



d, = —=2{l+r). 



Here v^ is therefore the fictitious extrapolated liquid volume at 

 the absolute zero-point ; this volume can of course not be realized 

 for liquids, but in this ideal limiting case we may write ^o for it — 

 by bg we must, therefore, understand the same thing as is understood 

 by Vq, i.e. the smallest volume that a number of molecules lying 

 closely together, so that they are all in contact with each otliei-, 

 can occupy. 



So if in futui-e we represent the relation v^ : v^ by s\ and the 

 relation bk : ^0 by z, we have : 



^A: , „ ,, , , bk s' 2 (1 -f 7) 



- = .' = 2(1+;/); -=z=- = ^ ^ , . . (9) 



6„ 60 r r 



because r=:vk-bk. So far these equations do not contain anything 

 new; the last may serve to calculate z, when y and r are known, 

 in which r may be calculated from one of tha equations (7), viz. 

 r = I -j- (8 : ƒ'). Thus z = 1,8 e.g. for an ordinary substance (/ =0,9, 

 r = 2,12); z = l,5 for argon (;- == 0,75, r=: 2,33); 2 = 1 for an 

 ideal substance (/ = 0,5, r = 3). 

 But now I found that always: 



' = -^ (10) 



for the most different substances. In this form the relation was first 

 discovered by me. Thus among others: 



