Experience teaches that the sense-elements [alpha beta gamma delta ...] into which the world may be decomposed, are subject to change. It tells us further, that certain of these elements are _connected_ with other elements, so that they appear and disappear together; or, that the appearance of the elements of one class is connected with the disappearance of the elements of the other class. We will avoid here the notions of cause and effect because of their obscurity and equivocalness. The result of experience may be expressed as follows: _The sensuous elements of the world ([alpha beta gamma delta ...]) show themselves to be interdependent._ This interdependence is best represented by some such conception as is in geometry that of the mutual dependence of the sides and angles of a triangle, only much more varied and complex. As an example, we may take a mass of gas enclosed in a cylinder and possessed of a definite volume ([alpha]), which we change by a pressure ([beta]) on the piston, at the same time feeling the cylinder with our hand and receiving a sensation of heat ([gamma]). Increase of pressure diminishes the volume and increases the sensation of heat. The various facts of experience are not in all respects alike. Their common sensuous elements are placed in relief by a process of abstraction and thus impressed upon the memory. In this way the expression is obtained of the features of _agreement_ of extensive groups of facts. The simplest sentence which we can utter is, by the very nature of language, an abstraction of this kind. But account must also be taken of the _differences_ of related facts. Facts may be so nearly related as to contain the same kind of a [alpha beta gamma ...], but the relation be such that the [alpha beta gamma ...] of the one differ from the [alpha beta gamma ...] of the other only by the number of equal parts into which they can be divided. Such being the case, if rules can be given for deducing _from one another_ the numbers which are the measures of these [alpha beta gamma ...], then we possess in such rules the _most general_ expression of a group of facts, as also that expression which corresponds to all its differences. This is the goal of quantitative investigation. If this goal be reached what we have found is that between the [alpha beta gamma ...] of a group of facts, or better, between the numbers which are their measures, a number of equations exists. The simple fact of change brings it about that the number of these equations must be smaller than the number of the [alpha beta gamma ...]. If the former be smaller by one than the latter, then one portion of the [alpha beta gamma ...] is _uniquely_ determined by the other portion.