Page:ScienceAndHypothesis1905.djvu/95

 To sum up:

1. In the first place, we distinguish two categories of phenomena:—The first involuntary, unaccompanied by muscular sensations, and attributed to external objects—they are external changes; the second, of opposite character and attributed to the movements of our own body, are internal changes.

2. We notice that certain changes of each in these categories may be corrected by a correlative change of the other category.

3. We distinguish among external changes those that have a correlative in the other category—which we call displacements; and in the same way we distinguish among the internal changes those which have a correlative in the first category.

Thus by means of this reciprocity is defined a particular class of phenomena called displacements. The laws of these phenomena are the object of geometry.

Law of Homogeneity.—The first of these laws is the law of homogeneity. Suppose that by an external change we pass from the aggregate of impressions A to the aggregate B, and that then this change &alpha; is corrected by a correlative voluntary movement &beta;, so that we are brought back to the aggregate A. Suppose now that another external change &alpha;′ brings us again from the aggregate A to the aggregate B. Experiment then shows us that this change &alpha;′, like the change &alpha;, may be corrected by a voluntary correlative movement &beta;′, and that this movement &beta;′