Page:IntroductionToMathematicsWhitehead.pdf/29

The way in which the idea of variables satisfying a relation occurs in the applications of mathematics is worth thought, and by devoting some time to it we shall clear up our thoughts on the whole subject.

Let us start with the simplest of examples:—Suppose that building costs ${\displaystyle 1s}$. per cubic foot and that ${\displaystyle 20s}$. make £${\displaystyle 1}$. Then in all the complex circumstances which attend the building of a new house, amid all the various sensations and emotions of the owner, the architect, the builder, the workmen, and the onlookers as the house has grown to completion, this fixed correlation is by the law assumed to hold between the cubic content and the cost to the owner, namely that if be the number of cubic feet, and £${\displaystyle y}$ the cost, then ${\displaystyle 20y=x}$. This correlation of ${\displaystyle x}$ and ${\displaystyle y}$ is assumed to be true for the building of any house by any owner. Also, the volume of the house and the cost are not supposed to have been perceived or apprehended by any particular sensation or faculty, or by any