Note 22 — III. REFLECTIONS ON THE MOTIVE POWER OF HEAT, AND ON MACHINES FITTED TO DEVELOP THAT POWER.[4]
Robert Henry Thurston translation
When the volume is reduced ¹⁄₁₁₆, that is, when it becomes ¹¹⁵⁄₁₁₆ of what it was at first, the temperature rises one degree. Another reduction of ¹⁄₁₁₆ carries the volume to (¹¹⁵⁄₁₁₆)2, and the temperature should rise another degree. After x similar reductions the volume becomes (¹¹⁵⁄₁₁₆)x, and the temperature should be raised x degrees. If we suppose (¹¹⁵⁄₁₁₆)x = ¹⁄₁₄, and if we take the logarithms of both, we find
x = about 300°.
If we suppose (¹¹⁵⁄₁₁₆)x = ½, we find
x = 80°;
which shows that air compressed one half rises 80°.
All this is subject to the hypothesis that the specific heat of air does not change, although the volume diminishes. But if, for the reasons hereafter given (pp. 86, 89), we regard the specific heat of air compressed one half as reduced in the relation of 700 to 616, the number 80° must be multiplied by ⁷⁰⁰⁄₆₁₆, which raises it to 90°.