558 PROFKSSOR WILLIAM THOMSON'S ACCOUNT OF 



34. Such are the experimental data on which the mean values of ^ for the 

 successive degi-ees of the air-thermometer, from 0° to 230°, at present laid before 

 the Ro}'al Society, is founded. The unit of length adopted is the English foot ; 

 tho 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 0°, will produce 

 an elevation of 1° in temperature. The mean value of ^ for any degree is found 



to a sufficient degree of approximation, by taking, in place of a, ^, and k; in the 



expression 



dp 



(1-tf) 



k ' 



the mean values of those elements ; or, what is equivalent to the corresponding 

 accuracy of aproximation, by taking, in place of i and k respectively, the mean 

 of the values of those elements for the limits of temperature, and in place of 



— . the difference of the values oi p, at the same limits. 



35. In Regnault's work (at the end of the eighth Memoire), a table of the 

 pressures of saturated steam for the successive temperatures 0°, 1°, 2°, . . . 230', 

 expressed in millimetres of mercury, is given. On account of the units adopted 

 in this paper, these pressures must be estimated in pounds on the square foot, 

 which we may do by multiplying each number of millimetres by '2.-7SQG, the 

 weight in pounds of a sheet of mercury, one millimetre thick, and a square foot 

 in area. 



36. The value of h, the latent heat of a cubic foot, for any temperature t, is 

 found from x, the latent heat of a pound of saturated steam, by the equation 



. p 1+00366x100 „o«o«Q , 



where p denotes the pressure in millimetres, and ^ the latent heat of a pound of 

 saturated steam ; the values of x being calculated by the empirical formula* 



X = (606-5 + 0-305 l)-(l + -00002 1- + 0000000 1^), 

 given by Regnault as representing, between the extreme limits of his observa- 

 tions, the latent heat of a unit weight of saturated steam. 



* The part of this expression in the first vinculum (see Regnault, end of ninth Memoire) is 

 what is known as " the total heat" of a pound of steam, or the amount of heat necessary to conyert 

 a pound of water at 0' into a pound of saturated steam at t° ; which, according to " Watt's law," 

 thus approximately verified, would be constant. The second part, which would consist of the single 

 term t, if the specific heat of water were constant for all temperatures, is the numlier of thermic 

 units necessary to raise the temperature of a pound of water from 0° to t°, and e.-^presses empirically 

 the results of Regnault's experiments on the specific heat of water (see end of the tenth Memoire), 

 descriljed in the work already referred to. 



