1192 



u is exceedingly small, the time in which the very first part of 

 the path close to the neutral point M is passed over will be very 

 great, in spite of the attractive action (which will then, 

 however, be still very small). We shall presently see that it is this 

 circumstance which leads to the essential element of Planck's 



1 



relation viz. to the logarithmical approach (in direct ratio to 1 : log —) 



to of ii' (i.e. of T), when u,^ (i. e E— E,) approaches to 0. The 



time integral lu*dt remains namely finite (in consequence of the 



attractive action the exceedingly slight value of u,* increases to a 

 finite value), notwithstanding t itself approaches (logarithmically) to 

 infinite. 



Further we now find for t^ with 



1 / 2^ - 



y=:(;r — (/-5)) 1/ / 2f 



= ly v ^^3 *'" y\ .— 

 y m m 



+ etc)) 

 But in consequence of the relation 



2/ 2b 



m' = „ » + -^ {i-sy {s-s'Y = 



m m 



at the culminating point of the collision (see equation {h)), the quan- 

 tity under Bg sin will be exactly = 1, so that: 



'■ = >"|X^£ <») 



the known expression for the time of vibration under the influence 

 of the quasi-elastic repulsive , action, proportional to the deviation 

 from the state of equilibrium. (That here \\ :x occurs instead of 2 rr, 

 is owing to this that only a fourth part of the entire oscillation is 

 considered, (see above)). 



We shall now compute the value of z<* according to (r/). The first 

 integi'al within [ ] gives: 



