935 



follows from the above equation ((() for //; or also, since 5;" approaches 

 x^» = a = ^1-"+^ : f>'k, and /? = b'k ■ 



xh—h k 



Now X — h\ = Vï ^''"0 (^' — ^0)' hence : 



x]c— b'k 1 



(-» Q ul, ^U , 



xk v — v^ 

 or also 



xl 



Since (/^^ — b,) : {V — z;„) = {{bk — b,) : (b — />„)) X ((^ - f>o) ■ (^ - Vo)) = 



= é-' X ^v 



With assumption of (30) the value of b'\ is therefore always =0, 

 since d approaches to 0. The final course of the curve b=f{v) is 

 therefore straight, the coefficient of direction being indicated by 



V 



b\ = |/a. 



That for v =: go, in consequence of v — v„ in the numerator oï x, 

 both b\, and b",f become =: 0, is self-evident. 



Let us now examine the values of a and n for different values 

 of bk — />o or of 7. 



When we substitute in 71 = {1 — ivk) : {xk — b'h) the values of ,rA: and 

 b'k, we get: 



bk-b. 



1 



Vk—Vo 



vk— Vg bk vie 



or also, taking the relations (22) into account, i. e. />/,• : b^ = 2/, 

 Vk ■v, = 2 (I + y), in which b, = v,: 



2y-1\ ^2y-l (2y-lV 



71 = \ \ 



27+1; V^r+1 4y(y4-.l)^ 

 i. e. 



n :=^ 87(y + 1) : (2y-l) [4y{y + 1) - (2y -j- 1) (2y-l)] , 



or 



8y(y+l) 2bkvk 



(31) 



(2y-l)(4y+l) (bk-b,) {2bk -\- b,) 



So the exponent n ranges from 375 (when y := 1) to x (when 

 y = 7ii)- For ordinary substances (y^ü,9) n becomes =46:171=: 

 = 3,72 ; for Argon (y = 0,75) n = 5,25. 



