The fourth dimension

106 THE FOURTH DIMENSION

Americans.” And this method is what is called the ‘quantification of the predicate.”

The laws of formal logic are coincident with the conclusions which can be drawn about regions of space, which overlap one another in the various possible ways. It is not difficult so to state the relations or to obtain a symmetrical poiograph. But to enter into this branch of geometry is beside our present purpose, which is to show the application of the poiograph in a finite and limited region, without any of those complexities which attend its use in regard to natural objects.

If we take the latter—plants, for instance—and, without assuming fixed directions in space as representative of definite variations, arrange the representative points in such a manner as to correspond to the similarities of the objects, we obtain configuration of singular interest ; and perhaps in this way, in the making of shapes of shapes, bodies with bodies omitted, some insight into the structure of the species and genera might be obtained.