Page:IntroductionToMathematicsWhitehead.pdf/26

or coal-gas or steam—at a constant temperature. Let ${\displaystyle v}$ be the number of cubic feet in its volume and ${\displaystyle p}$ its pressure in lb. weight per square inch. Then the law, known as Boyle's law, expressing the relation between ${\displaystyle p}$ and ${\displaystyle v}$ as both vary, is that the product ${\displaystyle pv}$ is constant, always supposing that the temperature does not alter. Let us suppose, for example, that the quantity of the gas and its other circumstances are such that we can put ${\displaystyle pv=1}$ (the exact number on the right-hand side of the equation makes no essential difference).

Then in Fig. 2 we take two lines, ${\displaystyle OV}$ and ${\displaystyle OP}$, at right angles and draw ${\displaystyle OM}$ along ${\displaystyle 0V}$ to represent ${\displaystyle v}$ units of volume, and ${\displaystyle ON}$ along