Consider any two aggregates of sensations. Either we can discriminate them one from another, or we can not, just as in Fechner's experiments a weight of 10 grams can be distinguished from a weight of 12 grams, but not from a weight of 11 grams. This is all that is required to construct the continuum of several dimensions. Let us call one of these aggregates of sensations an _element_. That will be something analogous to the _point_ of the mathematicians; it will not be altogether the same thing however. We can not say our element is without extension, since we can not distinguish it from neighboring elements and it is thus surrounded by a sort of haze. If the astronomical comparison may be allowed, our 'elements' would be like nebulae, whereas the mathematical points would be like stars. That being granted, a system of elements will form a _continuum_ if we can pass from any one of them to any other, by a series of consecutive elements such that each is indistinguishable from the preceding. This _linear_ series is to the _line_ of the mathematician what an isolated _element_ was to the point. Before going farther, I must explain what is meant by a _cut_. Consider a continuum _C_ and remove from it certain of its elements which for an instant we shall regard as no longer belonging to this continuum. The aggregate of the elements so removed will be called a cut. It may happen that, thanks to this cut, _C_ may be _subdivided_ into several distinct continua, the aggregate of the remaining elements ceasing to form a unique continuum. There will then be on _C_ two elements, _A_ and _B_, that must be regarded as belonging to two distinct continua, and this will be recognized because it will be impossible to find a linear series of consecutive elements of _C_, each of these elements indistinguishable from the preceding, the first being _A_ and the last _B_, _without one of the elements of this series being indistinguishable from one of the elements of the cut_. On the contrary, it may happen that the cut made is insufficient to subdivide the continuum _C_. To classify the physical continua, we will examine precisely what are the cuts which must be made to subdivide them. If a physical continuum _C_ can be subdivided by a cut reducing to a finite number of elements all distinguishable from one another (and consequently forming neither a continuum, nor several continua), we shall say _C_ is a _one-dimensional_ continuum. If, on the contrary, _C_ can be subdivided only by cuts which are themselves continua, we shall say _C_ has several dimensions. If cuts which are continua of one dimension suffice, we shall say _C_ has two dimensions; if cuts of two dimensions suffice, we shall say _C_ has three dimensions, and so on. Thus is defined the notion of the physical continuum of several dimensions, thanks to this very simple fact that two aggregates of sensations are distinguishable or indistinguishable.