1055 



•n 



(2r 



l):(2y + -l), x^{J>~h;):{i.-v, 



4y' — 1 fh -b^2>y-\-l\'' 

 h—b,. ~ " 



1 



2y— 1 



4yrr + l)V'^-ï'o 2y— 1 



1 



4y* — 1 



4^-fï) 



111 this equation h — />„ occurs botli in the first and in tlie second 

 member, and cannot be solved from it (in consequence of ??•'' power). 

 We are tlierefore obbged to sohe v — i\ for the calculation, and 

 then we lind after some reductions (?'„ =: A„) : 



2y+16-^>„ 



■ ■■ (38) 



in which ?i=8y(y+l) : r2y— l)(4y-|--J), 2y— 1 being = 0,038 l/7\ 



In order to get an idea about the actual course of the curve l/=f{v) 

 according to formula (38), I have taken the (rouble — also with a view 

 to testing the calculated values by those which the equation of state 

 will yield for Argon e.g. — to calculate the corresponding values 

 of [h — h^)-J)^ and {v— v„) : y„ for different values of y, i.e. of T. 



The limiting value J>,, for v = oo is evidently found by putting 

 the denominator of (38) = 0, from which follows : 



hn — h. ^ j "/4y(y4-l) 



(2y - 1) 1/ 4^;V , . • . (38a) 



K. ' ' ' y 4v+i 



agreeing with (34). 



And with regard to the limiting value (/> — h^\{v — vj for h-=:b , 



,. ib-b,) 



Lim =: x^ 



("— '^u) 



i^'/.vk 2y— 1 I "/4y(y+l) 



follows immediately from f30/v) of I, when instead of yk quite 

 generally again y is written. 



a. y = 0,9. {T= ± 450 absolute;. 



For n we find 171 : 46 : 3,7174, so that (38) etc. passes into 



3, 



V — I' h — 6„ 

 ^=3,5 " 



i'n b,. 



171 115 



.'i,T 



5 h-K 



4 b, 



3,7 



\1 



(b,-b,^) : />„ = 0,8 1/171 : 1 15 ; x,^ = "/. \/\l\ : 56 

 This yields I he following survey (when for n not the shortened 



\cdue 3,7, bul 3,7174 is taken). 

 Prof'.et'diDgs Royal Acad. Amsterdam. Vol. XVI. 



üy 



