446 Prof. S. D. Wicksell on the Normal Correlation 



The experiments of Franck and Hertz show that in some 

 cases, for example, argon and nitrogen, an electron may 

 collide with a very large number of atoms without losing 

 energy, and in cases where the electrons cannot make many 

 collisions before being captured and attached to an atom, the 

 effects seem to be reconcilable with the view that such 

 collisions as occur are elastic, and that the alternatives are 

 capture or escape with undiminished energy. 



Since the frequency of vibrations of an electron is pro- 

 portional to the magnetic force it is evident that it would 

 be affected by an external magnetic field ; it would also be 

 affected by an external electric field, since this would 

 displace the position of equilibrium. The consideration of 

 these effects must, however, be left for another occasion. 



XXXVII. A General Formula for the Moments of the 

 Normal Correlation Function of any Number of Variates. 

 By S. D. Wicksell, Lund, Sweden* . 



IF £ 19 ,v 2 , .... x n be n variates reckoned from their 

 respective means and expressed in their respective 

 dispersions as units, and r pq is the coefficient of correlation 

 of x p and x q , the normal correlation function is given by 



where 



S = 



and 



«o = 



~^a 'S'S.SpqXpXq 



•JH 



(27T) n/: VS 



''11, ?'l2, 

 ^21? r 225 



'In 



r 2n 



r„i, r»s 



*** " -dr 



M 



(i) 



= r 



m 



The function <j>(x u x 2 , x n ) may also be written in 



the form of a certain multiple integral which will be 



* Communicated by the Author. 



