The significance of measurement therefore lies in the fact that it applies the operation of counting with all its advantages (see p. 85) to _continuous_ things, which as such do not at first lend themselves to enumeration. By the application of the unit measure a discontinuity is at first artificially established through dividing the thing into pieces, each piece equal to the unit, or imagining it to be so divided. Then we count the pieces. When a quantity of liquid is _measured_ with a liter this general process is carried out physically. In all other less direct methods of measurement the physical process is substituted by an easier process equally good. Thus, in the example of the strip of paper we need not cut it up into pieces a millimeter in length. The divided rule is available for comparing the length of any number of millimeters that happen to come under consideration, and we need only read off from the figures on the rule the quantity of millimeters equal to the length of the strip, in order to infer that the strip can be cut up into an equal number of pieces each a millimeter in length. After it has been made possible to count continuous things in this way, the numeration of them can then be subjected to all the mathematical operations first developed only for discrete, directly countable things. When we reflect that our knowledge of things has given them to us _preponderatingly as continuous_, we at once see what an important step forward has been made through the invention of measurement in the intellectual domination of our experience. =37. The Function.= The concept of continuity makes possible the development of another concept of greater universality, which can be characterized as an extension of the concept of causation (p. 31). The latter is an expression of the experience, if A is, B is also, in which A is understood to be a definite thing at first conceived of as immutable. Now it may happen that A is not immutable, but represents a concept with continuously changing characteristics. Then, as a rule, B will also be of that nature, so that _every special value or state of B corresponds to every special value or state of A_. Here, in place of the reciprocal relation of two definite things, we have the reciprocal relation of two more or less extended groups of similar things. If these things are continuous, as is assumed here (and which is extremely often the case), both groups or series, even though they are finite, contain an endless quantity of individual cases. Such a relation between two variable things is called a function. Although this concept is used chiefly for the reciprocal relation of _continuous_ things, there is nothing to hinder its application to discrete things, and accordingly we distinguish between continuous and discontinuous functions.