Page:Reflections on the Motive Power of Heat.djvu/121

operation will be ${\tfrac {1}{116}}$ + ${\tfrac {1}{267}}$ of the primitive volume; this is a very slight increase, absolutely speaking, but great relatively to the difference of temperature between the bodies A and B.

The motive power developed by the whole of the two operations described (page 70) will be very nearly proportional to the increase of volume and to the difference between the two pressures exercised by the air, when it is found at the temperatures 0°.001 and zero.

This difference is, according to the law of M. Gay-Lussac, ${\tfrac {1}{267000}}$ of the elastic force of the gas, or very nearly ${\tfrac {1}{267000}}$ of the atmospheric pressure.

The atmospheric pressure balances at 10.40 metres head of water; ${\tfrac {1}{267000}}$ of this pressure equals ${\tfrac {1}{267000}}$ × 10^m.40 of head of water.

As to the increase of volume, it is, by supposition, ${\tfrac {1}{116}}$ + ${\tfrac {1}{267}}$ of the original volume, that is, of the volume occupied by one kilogram of air at zero, a volume equal to 0^mc.77, allowing for the specific weight of the air. So then the product,

   $({\tfrac {1}{116}}$ + ${\tfrac {1}{267}})$ × 0.77 x ${\tfrac {1}{267000}}$ × 10.40,

will express the motive power developed. This power is estimated here in cubic metres of water raised one metre.