V.—MANIFOLD CLASSIFICATION, 
(1768)2/1169 26739 
(946)%/1303 686-8 
(115)2%/357 37-0 
(807)2/1088 5986 
(1387)%/1212 1587-3 
(438)%/332 577-8 
(189)2/506 706 
(746)%/563 988-5 
(288)%/154 5386 
(47)%/48°0 46-0 
53)%/534 526 
16)2/14-6 17-5 
Total= = 78752 
I. 6800 
-—- = 1075-2 
i 10752 EEE (1. 
The squares in such work may conveniently be taken from 
Barlow’s Zables of Squares, Cubes, etc. (see list of tables on 
P- iy or opi a9 be used throughout—five figure 
ogarithms are quite sufficient. 
9. While such a coefficient of contingency, in some form or 
other, is a great convenience in many fields of work, its use 
should not lead to a neglect of those details which a treatment by 
the elementary methods of § 4 would have revealed. Whether 
the coefficient be calculated or no, every table should always be 
examined with care to see if it exhibit any apparently significant 
peculiarities in the distribution of frequency, e.g. in the associa- 
tions subsisting between 4,, and B, in limited universes. A good 
deal of caution must be used in order not to be misled by casual 
irregularities due to paucity of observations in some compartments 
of the table, but important points that would otherwise be over- 
looked will often be revealed by such a detailed examination. 
10. Suppose, for example, that any four adjacent frequencies, 
say— 
(4,.B.,) (Ams Bn) 
I. (441Bns1) 
are extracted from the general contingency table. Considering 
these as a table exhibiting the association between 4, and 2B, in 
a universe limited to. 4.4.41 BoB alone, the association is 
positive, negative, or zero according as (4,,8,)/(4d,,+1B,) is greater 
67