* THEORY OF STATISTICS. 
with a unit divergence of the other, and to obtain some idea as to 
the closeness with which this relation is usually fulfilled. 
8. Suppose a diagram (fig. 32) to be drawn representing the 
values of means of arrays. Let OX, OY be the scales of the two 
variables, v.e. the scales at the head and side of the table, 01, 12, 
etc., being successive class-intervals. Let J/; be the mean value 
of X, and M, the mean value of ¥. If the two variables be 
absolutely independent, the distributions of frequency in all 
parallel arrays are similar (Chap. V. § 13), and the means of arrays 
must lie on the vertical and horizontal lines JM, M,M, the 
fx : 2 hoa 5 6X 
Fig. 32. 
small circles denoting means of rows and the small crosses means 
of columns. (In any actual case, of course, the means would not 
lie so regularly, but, if the independence were almost complete, 
would only fluctuate slightly to the one side and the other of the 
two lines.) 
The cases with which the experimentalist, e.g. the chemist or 
physicist, has to deal, where the observations are all crowded 
closely round a single line, lie at the opposite extreme from 
independence. The entries fall into a few compartments only of 
each array, and the means of rows and of columns lie approximately 
on one and the same curve, like the line ZR of fig. 33. 
The ordinary cases of statistics are intermediate between these 
two extremes, the lines of means being neither at right angles as 
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