1060 



the sign is certainly negative. But if, as is not excluded, /y(/') changes 

 its sign more than once, (3) is not sufficient to lead rigorously to 

 the negative sign. Possibly this may be shown by the aid of an 

 analysis according to Foukier, but it is simpler to derive this from 

 fig. B, where a course of the curve has been drawn which does 

 satisfy (3), and yet yields a positive value of Q. Nol)ody will, 

 however, assume a course like that. If the curve presents more 

 than one change of sign, it will probably be lepresented by a 

 strongly damped oscillating line of the type of fig. 6', in which (he 

 fact that it ends with a positive part at 7v{t) and satisfies condition 

 (3), renders the negative sign very probable for Q. 



III. One of the principal objections of 0. and B. lefers to the 

 fact that Miss Snkthlagk and 1 repeatedly make use of the three 

 equations which must be considered in connection with each other, viz. : 



~^^ = ~,it = -P^^iO^<i(') ..... (4) 

 m at dV 



1 -^^MO 

 p=^ — -==r ^ constant (5) 



Wi m' {t) 



«lOf (0 == .... ^ .... (6) 



0. and B. assert that it follows from this that m" cannot be con- 

 slant. When we now examine these equations, we see that (4) means 



d^u , . • 1 111 



onlv that we take — foi- a detiuile particle, and add nu to it 

 ^ ill' 



{p =^ 'd positive constant that has been left undetermined for the 



present). As u is a function of /, this sum will also be so, and we 



can represent it by q{t). Taken in this way this equation does not 



hold only for a definite moment ^ = 0, as Ornstkin asserts, but of 



course for any moment. It is an ordinary differential equation and 



it can be integrated without difficulty, though neither from the 



equation itself nor from the integral anything can be derived when 



it is not considered in connection with (5) and (6), which are derived 



as follows. We differentiate u-{t) = constant twice with respect to 



t and get then : 



"<'>-^ [-^J -" ''> 



As we can differentiate at any moment, also this equation holds, 

 of course, for every value of t '). 



If we now multiply (4) by u{t) (not by n{0)\}, if we then average, 



1) Ornstein has repeatedly asserted that these equations do not hold for every 

 value of i, that (4) is no differential equation, and that it may not be integrated. 

 He has, however, never adduced any proof for these assertions. Ornstein and 



