Denoting the areas of the three strips by A, B, and C, and introducing the middle ordinate **ug**, we can express A + B; B -{- C; A + B -FC; and B in terms of uo, u 1, u 2; u 1, u2, u3; uo, u, u 3; and u 1, **ug**, u 2 respectively.

The breadth of the trapezette being mh, it may be shown that its area is 2 2 N 4 4 iv I mh **ug** m + 24 m h u gm + 1920 m h u g m + 322560 no/tourgm -}- m3l1gu i„?

(i) If m is even, **ug** m will be onejof the given ordinates, and we can express h 2 u, m, 4 u" m, ...

Denote 2 (**ug** 'm _ z + **ug** m+ g), ?

The general formulae of § 54 (p being replaced (i) by 2m) may in the same way be applied to obtain formulae giving the area of the trapezette in terms of the mid-ordinates of the strips, the series being taken up to b 2f ul m or /th 2J **ug** m at least, where u is of degree 2f or 2f + I in x.

24) we owe the triple distinction into inference from particular to particular (irapf16ecy i **ug**, example, or what we call " analogy "), inference from particular to universal (i raywy17, induction), and inference from universal to particular (ouXXoyco-Os, syllogism, or deduction).

Thus we get two expressions for A + B -}- C, from which we can eliminate **ug**.

., where l aug m, µ6 2 **ug** m,.

In short, the Ainu suggest much closer affinity with Europeans than does any other of the types that go to make **ug** the population of Japan.