IL.—CONSISTENCE. J 
consistent with one another. They conform with one another, 
and do not in any way conflict. 
The conditions of consistence are some of them simple, but 
others are by no means of an intuitive character. Suppose, for 
instance, the data are given— 
: 1000 (4D) 42 
(4) 525 (AC) 147 
(5) 312 (BO) 86 
(C) 470 (4BC) 25 
—there is nothing obviously wrong with the figures. Yet they 
are certainly inconsistent. They might have been observed at 
different times, in different places or on different material, but 
they cannot have been observed in one and the same universe. 
They imply, in fact, a negative value for (afy)— 
(aBy)=1000 — 525 — 312 — 470 +42 + 147 + 86 — 25. 
=1009 - 1307 + 275 - 25. 
= — 57. 
Clearly no class-frequency can be negative. If the figures, 
consequently, are alleged to be the result of an actual inquiry in 
a definite universe, there must have been some miscount or 
misprint. 
6. Generally, then, we may say that any given class-frequencies 
are inconsistent if they imply negative values for any of the 
unstated frequencies. Otherwise they are consistent. To test the 
consistence of any set of 2" algebraically independent frequencies, 
for the case of = attributes, we should accordingly calculate 
the values of all the unstated frequencies, and so verify the fact 
that they are positive. This procedure may, however, be limited 
by a simple consideration. If the ultimate class-frequencies are 
positive, all others must be so, being derived from the ultimate 
frequencies by simple addition. Hence we need only calculate 
the values of the ultimate class-frequencies in terms of those 
given, and verify the fact that they exceed zero. 
7. As we saw in the last chapter, there arc two sets of 2° 
algebraically independent frequencies of practical importance, viz. 
(1) the ultimate, (2) the positive class-frequencies. 
It follows from what we have just said that there is only one 
condition of consistence for the ultimate frequencies, viz. that 
they must all exceed zero. Apart from this, any one frequency of 
the set may vary anywhere between 0 and co without becoming 
inconsistent with the others. 
For the positive class-frequencies, the conditions may be 
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