923 



which in physics is an impossible result. 



If we square (2) and determine the average according to (a), we 



obtain 



- 







a result which, as is immediately obvious, is opposed to the theorem 

 of equiparlition, as the average of the second member is essentially 

 positive, so that if e.g. a\* is more than the equipartition-value, 



this would also be the case with x*. If we determine the average 

 of the square of (2) in the supposition (6) we tind 



r 







And as now a'/ in this case has the equipartition-value, .^' would 

 be essentially more than this value, which contains a contradiction, 

 as the average square of the velocity must be equal for all particles, 

 at any moment. 



Van der Waals has made use of the second integral of (1) viz. 



t 



X = x, -\- x,t + (w{») {t—») d» 







to arrive at his theory. In the same way as above we can demon- 

 strate that this combined with his supposition A\iü{t) = leads to 

 incorrect results, contrary to theory and observation. Foi' if we make 

 up X' — .1', = A', supposition (a) yields 



A' = X,' <• + j Civi») it—») d» . 







And as the average in the second member is positive the highest 

 power of t which occurs in A' will as least be 2, consequently 

 V. D. Waals' supposition comes into conflict with the formula A' = bt, 

 which he applies himself (p. 1257 I.e.). If we determine the average 

 according to (b) the only difference is that .r,' must be replaced by 

 the equipartition value of the velocity-square, so that also in deter- 

 mining the average according to van dkk Waals the formula used 

 by him combined with his supposition .u^iu(t) = leads to an incor- 



