1268 



we multiply by <9— ^,, this factor becomes greater for the negative 

 interval than for the positive, so that: 



ic{o){ü—t^)(W<iO when »- (<J > 0. 



'i 

 In llie same way appears of course: 



t 



io{0){0—t,)dOyO when io{t^)<^0. 



ti 



t 



ƒ■ 



It is true that the course of wi^)" ' can be more intricate than I 

 have assumed heie. Instead of one there may take place more reversals 



of sign. Not improbably n^f' is represented by a damped periodic 

 function, or at least it has a course closely resembling it. But in any case 

 equation (11) must hold for not too small values of t, and in this 



the values of ?"(<9)" ' which agree in sign with iv{t^), will undoubtedly 

 have smaller abscissa than those that dilTer in sign from it, which 

 warrants the validity of (5c). 



Remark IV. I pointed out on p. 1260 that the obtained result for 

 A^ probably amounts only to half or about half the true value. It 

 is natural to try to bring a correction in this by the assumption 

 of another value for the measurable velocity. We defined the quantity 



— as "measurable velocity". But it is the question whether this is 



I; 



really the quantity that is to be multiplied by Qjr^a in order to 



A 



find Stokes's force of friction. We might, of course, define — as 



t 



the time-average of the measurable velocity of a particle that travels 



over a path A in the time t. And when a force of viscosity opposes 



this displacement, it is the question whether this force may be taken 



proportional to the time average. It is to be expected that the 



measurable movement is not uniform. When we divide the interval 



t into sub-intervals, it is to be expected that the displacements obtained 



in the tirst of these sub-intervals will have less influence on the 



force of viscosity that prevails at the end of the interval i than the 



displacements obtained in the later sub-intervals. And this force of 



friction at the end of the interval was the quantity that we had 



in view when executing our computation. 



