Page:Reflections on the Motive Power of Heat.djvu/195

Explanation of Table II.

38. The calculation of the mechanical effect, in any case, which might always be effected in the manner described in § 37 (with the proper modification for fractions of degrees, when necessary), is much simplified by the use of Table II., where the first number of Table I., the sum of the first and second, the sum of the first three, the sum of the first four, and so on, are successively exhibited. The sums thus tabulated are the values of the integrals

$\int _{0}^{1}\mu dt,\int _{0}^{2}\mu dt,\int _{0}^{3}\mu dt,....\int _{0}^{231}\mu dt;$

and, if we denote $\int _{0}^{t}\mu dt$ by the letter M, Table II. may be regarded as a table of the value of M.

To find the amount of mechanical effect due to a unit of heat descending from a body at a temperature S to a body at T, if these numbers be integers, we have merely to subtract the value of M, for the number T, from the value for the number S, given in Table II