Page:ScienceAndHypothesis1905.djvu/92

 changes, otherwise mutually independent, may be reciprocally corrected? A mind already familiar with geometry would reason as follows:—If there is to be compensation, the different parts of the external object on the one hand, and the different organs of our senses on the other, must be in the same relative position after the double change. And for that to be the case, the different parts of the external body on the one hand, and the different organs of our senses on the other, must have the same relative position to each other after the double change; and so with the different parts of our body with respect to each other. In other words, the external object in the first change must be displaced as an invariable solid would be displaced, and it must also be so with the whole of our body in the second change, which is to correct the first. Under these conditions compensation may be produced. But we who as yet know nothing of geometry, whose ideas of space are not yet formed, we cannot reason in this way—we cannot predict à priori if compensation is possible. But experiment shows us that it sometimes does take place, and we start from this experimental fact in order to distinguish changes of state from changes of position.

Solid Bodies and Geometry.—Among surrounding objects there are some which frequently experience displacements that may be thus corrected by a correlative movement of our own body—namely, solid bodies. The other objects, whose form is