928 



in which within [ ] J has been omilted bv the side of the infinitelj 

 ]arge value of the exponential quantity. But now the tirst menibei' 

 of this equation =1, the second member.becominji; = X ^°^' 1^^"^'^ 

 approaching go. Not until vk — i\ should be of the order bi- — h„, 

 hy which the exponential quantit\ could be made of the order 

 hkVk--{bk — b^Y, could the above equation be satisfied. But then i\ 

 would get into the neighbourhood of Vk, when bk — b^ approaches to 

 0, i.e. when y appi-oaches to 7-2' ^"^ ^^^^^ '•'' i"ipossible. 



It is easy to see from the graphical representation that the indicated 

 /(y) intersects the r-axis already soon after vk, in consequence of 

 which b passes to negative values, so that there can be no question 

 of a convergency to the point i\, b^. 



And it is easy to see that this cannot be changed by changes in 

 the form of the chosen exponential function. Nor can Kamerlingh 

 Onnes" function satisfy. For this function, viz. 

 b = b,, — (bg — b,)e-'-''"-^-o) , 



leading after substitution of Vk and bk, through which v„ and b^ are 

 eliminated, to 



b = b, - [b, - bk)e-'-'^'^'k), 



is identical with {b). when e "/,s is substituted for /{v), (« satisfy 

 is then = ^3),. For it would inevitably lead to the rejected 

 equation (25). 



And if this and suchlike functions are made to satisfy at i\, b^ 

 — they will necessarily not satisfy at Vk, b/,, i.e. the values b'k 

 and b"k will then entirely differ from the theoretic^,! \alues indicated 

 by (24). 



Second example. 





As ,? will disappear here, an exponent 6 must still be added to 

 satisfy the conditions (24), which exponent can then again be deter- 

 mined from (c), b,j being given by ((/). 



We now find : 



and hence for {— f {vi^f '• f" {vl) the value 



In consequence of this {e) becomes : 



