CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 559 
Explanation of Table I. 
37. The mean values of » for the first, for the eleventh, for the twenty-first, 
and so on, up to the 231st* degree of the air-thermometer, have been calculated in 
the manner explained in the preceding paragraphs. These, and interpolated re- 
results, which must agree with what would have been obtained, by direct calcu- 
lation from ReGNautt’s data, to three significant places of figures (and even for 
the temperatures between 0° and 100°, the experimental data do not justify us in 
relying on any of the results to a greater degree of accuracy), are exhibited in 
Table I. 
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 add the values of » in Table I. corresponding to the successive numbers. 
aL 2, othe ee Loy Bee ek, 
Explanation of Table I. 
38. The calculation of the mechanical effect, in any case, which might al- 
ways 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 
Hibs zi, ys 231 
fonds fiwas frwas . 2. [mars 
and, if we denote va ; # dt by the letter M, Table II. may be regarded as a table 
of the values 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 + 1, from the value for the number S, 
given in Table IT. 
* In strictness, the 230th is the last degree for which the experimental data are complete ; but 
the data for the 231st may readily be assumed in a sufficiently satisfactory manner. 
