cabnot'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 tvi^enty-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 Regnault'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 Sto a body at T, if these numbers be integers, we have merely 

 to add the values of fn in Table I. corresponding to the successive numbers. 



T + 1, T + 2, S-2, S-1, 



Explanation of Table II. 



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 



7lhd t, I lid t, I u,dt, . . . . I u, dt; 



and, if we denote / /u dthy 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 ofM, for the number T + \,from tlie value for the number S, 

 given in Table II. 



* In strictness, the 230th is the last degree for which the experimental data are complete ; but 

 the data for the 231st may readily he assumed in a sufficiently satisfactory manner. 



