1256 



LoRENTZ in her Thesis for the Doctorale, e(|iiation (3) is first iiitegi'ated 

 over a small time r, so small that the velocity chanyes not much 

 during r. We then get: 



m (.r, ■'■,) ^ — 6 .T ? a (./•, — .c,) {- | X dt . 





 And now it is not assumed that the equation Xx = holds for 



any moment, but that .(;, | A'(/^ is zero on an average. As x does 







not differ much from .r, during t, the difference between the two 



suppositions is not great. But whereas A'.c :=: Ü excludes the perfor- 

 mance of work by the force A — at least o( a, work [\ni mean value 

 of which differs from — this is not the case wiih the supposition 



T 



.i;^ I A(/^ = 0. Here the possibility exists that A on an average performs 







positive work of such an amount that it compensates the loss of 

 kinetic energy by the viscosity. 



Yet it seems to me that when has once it been seen thai the splitting 

 up of the force inro a "force of viscosity" and "irregidar forces" 

 is untenable, also the si)litting up of the force into two terms, as it 

 has been applied by Mrs. dk Haas, becomes |)roblematical. At bottom 

 also this splitting up is after all based on the idea of a friction against 

 the thermal movement of the particles. 



Miss Snkthlagk and 1 ') have therefore thought we had to take 

 another course to arrive at an equation for ^^ We started for this 

 purpose from the postidate that: 



;5{.^• = . . . (A) 



When this equation is differentiated with respect to t, it yields: 



im . 1 — 



--..v + -~iV = . (B) 



at jn 



This is satisfied in the simplest way by putting: 



= ^-fx^q {€) ^) 



dt 



in which q will be a function of t that repeatedly changes its sign 



1) These Proc. Vol. XVI fl, p. 1322. 



^) See for the justification of this equation the exposition in Remark 1 at the end 

 of this paper. 



