936 



For the value of a, i. e. the limiting value .r,, of (/; — h^ : [v — vj 

 for V = i\, h := J\, we find fVoni ./■„" = a = ,r//'4-i : ///^. (see 30^) 

 the value : 





(32) 



iji wliicli li possesses tiie value given hy (3J). This limiting valne 



j'j,, which is at the same time = //j, (see above) assumes for y=i 



the valne : 



1 . 3'V 8 



: \!^ X 1>*^59 = 0,453; foi- y = 0,9 the value 



7. X 1 >'^'^0 = 0,38(5 ; for y = 0.75 the vahu 



è y 3 



0,8 ,3,:-j/G 84 



2,8 



2 24 



0,5 , •^Vi/ó,-.!5 ^ ^ 



oT X , .,r = V5 X J .314 = 0,263 ; while for 7 = 0,5 it properly op- 



proaches (/> — />„ then namely has become continually =0). For x/'yXk-.b' k) 

 then approaches unity, the factor (2y— 1) : (2y4-l) approaching to 0. 



Accordingly for all "ordinary substances", where y is about 0,9, 

 the line h=^f{v\ will approach the point of convergency v^Ji^ at 

 an angle of about 21° [tg <p = 0,39). 



In conclusion we will still discuss the value of /a/ : hi- according 

 to (30''), viz. 



bk — b. 



n—b'k 



The limiting value of this for y =1 isevidentlv 



31/ 



'A:(73-V,s) 



1,(3= 1,158, whu-h with />/, : /k = '2 leads to />;, -. bk =r 1,079. 



For ordinary substances (y = 0,9) we find 



3,72 



7::(7r-7ss,5) 



^171,: 115) = 1,113, leading with />/,:/>„ = 1,8 to h,,:bi, 

 = 1,050, i. e. the normal value. For Argon (y =z 0,75) the second 



' s : (/A - 7.0 



member becomes 



(21 -.16) = 1,053, 



which with A/, : />„ = 1,5 for />,; : /;/, yields the value 1,018. Finally 

 for an ideal substance bf, : bk = 1- 



Equation (30) found by us, therefore, yields good results in every 

 respect, from r =r x to v =^ r„, and that for all values of b/c — //, 

 or of y. In addition it may once more be stated, that when b 1= b^ 

 in the first member, the second member too must be = 0, hejice 

 .(jk = b'ic{'Vo : a-i:)", in consequence of which a-^.Tj* assumes the value 



