. On the Theory of Consistence of Logical Class-Frequencies, and Its Geometrical Representation. Fig. 15. 126 ME. G. UDNY YULE ON THE TllEOEY OF CONSISTENCE The Limits to Associations given by Conditions of Consistence. § 32-^-§ 37. § 32. The general conditions of consistence give limits to the frequencies of any-one aggregate in terms of the frequencies of two or more given aggregates of thesame congruence. Hence they give limits also to the possible associations betweenattributes in the unknown aggregate. Thus, to take an imaginary example, suppose we have (AC)(Ay) (aC)( (AB) 11 (A^) 22 («B)

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. On the Theory of Consistence of Logical Class-Frequencies, and Its Geometrical Representation. Fig. 15. 126 ME. G. UDNY YULE ON THE TllEOEY OF CONSISTENCE The Limits to Associations given by Conditions of Consistence. § 32-^-§ 37. § 32. The general conditions of consistence give limits to the frequencies of any-one aggregate in terms of the frequencies of two or more given aggregates of thesame congruence. Hence they give limits also to the possible associations betweenattributes in the unknown aggregate. Thus, to take an imaginary example, suppose we have (AC)(Ay) (aC)( (AB) 11 (A^) 22 («B) 39 (a/B) 28 5215 100 100. Required the limiting values of the BC aggregate. From the conditions of con-sistence, § 5, we have (BC) < 33 -f 50 + 60 — 100 -- (1 -- 8 < 24 < 11 + 8 — 33 60 + 11 — 8 > 63 > 50 ~ 11 + 8 > 47. Therefore the limiting values to (BC) are 24 and 47. But we know (B) —? 50, (C)?= 60, (U) = 100, therefore the limiting values to the frequencies of the aggregate aie (BC) 24 47 (/3r) 26 3 (^C) 36 M m 14 o r7 100 100. Hence

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