ABSTRACT
Consider Charles's Law, according to which the volume υ of a fixed mass of gas at constant pressure p is proportional to the absolute temperature T (Experiment No. I X ) ; and consider the Boyle-Mariotte Law according to which the volume υ at constant temperature T is inversely proportional to the pressure p (Ex periment No. X) . What happens if the volume, pressure, and temperature are all allowed to vary? And how is the pressure related to the absolute temperature if the volume is kept con stant? The latter is answered by a simple experiment, which yields a law-also due to Charles. But both questions can be answered by means of a little mathematics alone. If all three vary, a little algebra shows that the volume υ is proportional to the quotient of the absolute temperature divided by the pressure T/p, which is equivalent to the statement that the product pv is proportional to T.* To deal with the second question: from the
result just mentioned it follows that if υ is kept constant the pressure p is proportional to the absolute temperature T ; and this law can be confirmed directly by means of a constant-volume apparatus which allows us to compare pressure and temperature. This new law could be found independently with such apparatus, without knowing the other two laws; but it is instructive to deduce it from previous knowledge.
