314 



Dr. Gladstone on the Relations between the 



u itur 



If we glance at this list we notice some peculiarities, but no 

 very striking ones. We might ask, for instance, Why should 

 there be so many elements congregated about No. 28; and, 

 again, about 52 ? Why should there be only one atomic weight 

 between 80 and 99, and then a group of four ? 



The following letter, kindly sent me by Professor De Morgan, 

 will give the data for calculating the probabilities of this. I 

 introduce it on account of its applicability, not only to this par- 

 ticular case, but to others which will occur in these observations. 



"Univ. Coll., Lond.,Dec. 18,' 1862. 



"Dear Sir, — The following, though but an imperfect view 

 of the whole question, will be enough, I think, for your pur- 

 pose. I send formula and all, that who likes may verify it. 



" If there be n numbers, each of which may be drawn at any 

 trial, and all equally likely, and if the following denominations 

 be used, 



R: 



m- 



m— 



»n-2 1 



S=»i 





m— I m— 2 

 "2 3~ 



