Then I have sought to form with our visual sensations a physical continuum equivalent to space; that certainly is easy and this example is particularly appropriate for the discussion of the number of dimensions; this discussion has enabled us to see in what measure it is allowable to say that 'visual space' has three dimensions. Only this solution is incomplete and artificial. I have explained why, and it is not on visual space but on motor space that it is necessary to bring our efforts to bear. I have then recalled what is the origin of the distinction we make between changes of position and changes of state. Among the changes which occur in our impressions, we distinguish, first the _internal_ changes, voluntary and accompanied by muscular sensations, and the _external_ changes, having opposite characteristics. We ascertain that it may happen that an external change may be _corrected_ by an internal change which reestablishes the primitive sensations. The external changes, capable of being corrected by an internal change are called _changes of position_, those not capable of it are called _changes of state_. The internal changes capable of correcting an external change are called _displacements of the whole body_; the others are called _changes of attitude_. Now let [alpha] and [beta] be two external changes, [alpha]' and [beta]' two internal changes. Suppose that a may be corrected either by [alpha]' or by [beta]', and that [alpha]' can correct either [alpha] or [beta]; experience tells us then that [beta]' can likewise correct [beta]. In this case we say that [alpha] and [beta] correspond to the _same_ displacement and also that [alpha]' and [beta]' correspond to the _same_ displacement. That postulated, we can imagine a physical continuum which we shall call _the continuum or group of displacements_ and which we shall define in the following manner. The elements of this continuum shall be the internal changes capable of correcting an external change. Two of these internal changes [alpha]' and [beta]' shall be regarded as indistinguishable: (1) if they are so naturally, that is, if they are too close to one another; (2) if [alpha]' is capable of correcting the same external change as a third internal change naturally indistinguishable from [beta]'. In this second case, they will be, so to speak, indistinguishable by convention, I mean by agreeing to disregard circumstances which might distinguish them.