( 121 ) 



\!lj =: -f 366,25 X 10-' ^^l'^ = + 366,25 X 10-' 



)S^ — — 471,614 X 10-' ^\ = + 662,387 X lO-« 



(s^ =: -f 233,300 X 10 " ^\ — — 355,774 X 10-'^ 



T)^ = _ 360,485 X 10-" ^\ = + 780,380 X 10-" 



(f^ = _|_ 683,07 X 10-'' ^\ = + 346,72 X 10 " 



%^ = — 90,14 X lO-'' T^\ = — 698,82 X 10-" 



If further we put ;i=0,00i02 (calcuUited froui 7^^=304,45, yy/,=72,y 

 and ?'yt=:0,0()424, we find at the critical point: 



V\„^ 0,98833, v\n-=0,10305, v\o=-0,16831, p,„ = - 5,30648, 



p,„^75,79292, Poi = 7,34410, p„=:-9,99986, v\,= 27,76382, etc. 



The vahies of v\n' ^\n ^ï^^I v\o ought to be equal to 1, and 

 respectively ; the tolerably large deviation of tlie two last derivatives 

 proves that the series used do not represent the shape of the iso- 

 thermals in tlie neighbourhood of the critical point so accuratel}'' as 

 we might wish ^). Hence it follows that the values of the other 

 derivatives calculated here cannot be very precise, and jn-ohably this 

 uncertainty increases ^vith the order of the derivative. 



I take as approximate values of the reduced differential quotients 

 at the critical point : 



V3„ r= - 5,3, v\o ^ 76, Po, = 7,3, \\, = - 10, r,, = 28, wliile C- 3,6. ") 

 According to van dek Waals' original (reduced) (Mjualioii of state: 



_ 8r 3 



we should have 



P30 =- - ^ , W. = 126 , p„, = 4 , p„ = - 6 , p,, = 18. (\-^l-= 2.7; ») 



and according to tiiis modified equation: 



_ 8 f 3e^-t 



^' — 3 tZIï ^ ■ 



Pso = - 9 , v\„ == 126 , x\, = 7 , p„ = - 12 , p,, = 36 , C, = 2,7. 

 Finally I substitute tiie numerical values of the derivatives obtained 



1) On the cause of that inaccuracy and the possibility ot improving upon it 

 a new communication by Kamerlingh Onnes is to be expected. (Gomp. Conun. 

 n'\ 74, p. 15). 



-) Keesom gives (Gomm. n"*. 75, p. 9 and 10) ('4 = 8,45, p, i = 7, i)n = ~9.3. 



3) It will be seen that these values agree tolerably well with the former ; it is 

 thus not remarkable that so close a resemblance exists between the forms of 

 the boundaries found by KouTF.wEf; and by me, which indeed is based on van der 

 Waals' original equation. 



