112 Prof. Tliomson on the Dynamical Theory of Heat. 



expression (8) will be found by subtracting the number in that 

 table corresponding to the value of T, from that corresponding 

 to the value of S. [Tables I. and II. of the former paper are 

 reprinted here, for the sake of convenience in referring to them.] 



Tables extracted from " Account of Carnot's Theory/' Trans. R. 

 S. Ed. vol. xvi. part 5. 



Explanation of Table I. 



The mean values of fj, 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 results, 

 which must agree with what would have been obtained by direct 

 calculation from Rcgnault'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 '& to a body at T, if these 

 numbers be integers, we have merely to add the values of ft in 

 Table I. corresponding to the successive numbers, 



T + l, T + 2, S-2, S-J. 



Explanation of Table II. 



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 ex- 

 hibited. The sums thus tabulated are the values of the integrals 



/ iidt, I fjidt, I yudt, ' • • I fJ'dt', 



and if we denote / p,dt by the letter M, Table II. may be re- 



garded 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 a^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. 



* 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. 



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