No. 530] SHORTER ARTICLES AND DISCUSSION 125 



of the table in getting the sum S(ry) we shall get .just one half 

 the sum we should get by using the whole table: the sum for the 

 whole table would therefore he obtained simply by doubling this 

 half-sum. Now, if in place of making a symmetrical table we 

 enter always the larger member of each pair in the vertical 

 columns, the smaller in the horizontal rows. we shall get a table 

 that is precisely one of tin se duplicate halves of the symmetrical 

 table; this will be seen by comparing 'fables I and II. The 

 quantity 8(xy) from such a table will then be just half that 

 from the symmetrical table; it may then be doubled, and the 

 further computation will be identical with that for the symmet- 



30,316 32533,343 3 5,36,3,7 38, 39, 40,41 4 42 5 43 <i 44, 45„ 



the dividend in obtaining the coefficient of correlation, may be 

 divided by a number half as great as in the symmetrical tables, 



It will further be seen that if in place of entering all pairs in 

 the same way— the larger members in the columns, the smaller 

 in the rows— we enter some or all of them differently, this will 

 make no difference in the result. If in Table [I, for example, 

 the pair showing measurements 44 by 34 were entered in the 

 reverse way, it would fall, no longer in the right upper quad- 



