203 



The unit of length adopted is the English foot ; the unit of weight, 

 the pound ; the unit of work, a " foot-pound ;" and the unit of heat, 

 that quantity which, when added to a pound of water at C, will 

 produce an elevation of 1° in temperature. In making the calcula- 

 tion, the factor tf, in the expression for //,, which for all tempera- 

 tures between 0° and 100° is less than ttVc is neglected. The 



dt'p 

 mean value of -^ for any degree of the scale is found to a suffi- 

 ciently high degree of approximation by merely taking the difference, 

 the pressures given by Rcgnault at the temperatures immediately 

 above and below it ; and, to complete the calculation on the same 

 system, the denominator of the fraction is taken as the mean value 

 of k for that degree. The amount of mechanical effect due to the 

 descent of a unit of heat through the nih. degree of the scale, will be 

 simply the «th value of /a in the table thus calculated. 



The following abstract of the table, exhibits the sum of the 

 first twenty values of (i, of the second twenty, of the third twenty, 

 and so on ; as well as the first value, the twenty-first, the forty- 

 first, &c. 



As an example of the usefulness of these tables, let it be required 

 to find the amount of mechanical effect produced by a steam-engine 

 working with perfect economy, for each unit of heat which, after en- 



