Page:Reflections on the Motive Power of Heat.djvu/104

the same if the volume is further reduced from a half litre to a quarter litre, from a quarter litre to an eighth, and so on.

If, instead of compressing the air, we carry it successively to two litres, four litres, eight litres, etc., it will be necessary to supply to it always equal quantities of heat in order to maintain a constant temperature.

This readily accounts for the high temperature attained by air when rapidly compressed. We know that this temperature inflames tinder and even makes air luminous. If, for a moment, we suppose the specific heat of air to be constant, in spite of the changes of volume and temperature, the temperature will increase in arithmetical progression for reduction of volume in geometrical progression.

Starting from this datum, and admitting that one degree of elevation in the temperature corresponds to a compression of ${\tfrac {1}{116}}$, we shall readily come to the conclusion that air reduced to ${\tfrac {1}{14}}$ of its primitive volume should rise in temperature about 300 degrees, which is sufficient to inflame tinder.^[1]

1. When the volume is reduced ${\tfrac {1}{116}}$, that is, when it becomes ${\tfrac {115}{116}}$ of what it was at first, the temperature rises one degree. Another reduction of ${\tfrac {1}{116}}$ carries the volume