Theory of Heat to the Steam-engine. 429 



culation introduce Briggs's logarithms (Log) in place of natural 

 logarithms (log) by dividing by M the modulus of this system, 

 the equation will take the form 



(,3=C + «LogJ, (49) 



wherein C and a are independent of Tg, and have the following 

 values : — 



M.AA(V-/c7) J 



Again, in equation (49) the first term on the right is greatest, 

 so that we can apply the method of successive approximation. 

 In the first place, Tg is put in the place of Tg, and we obtain the 

 first approximate value of yg, viz. 



/=C, (50) 



from which we can find the corresponding temperature t^ in the 

 tables, and thence the absolute temperature T'. This is now 

 substituted for Tg in (49), and gives 



y'=y+«Log|f, ...... (5o«) 



whence T" is found. Similarly we obtain 



. y"=/+«Logy„ . . ... . (504) 



and so forth. 



49. Before proceeding to the numerical application of the 

 equations (XVII), the magnitudes c and r alone remain to be 

 determined. 



The magnitude c, which is the specific heat of the liquid, has 

 hitherto been treated as constant in our development. Of course 

 this is not quite correct, for the specific heat increases a little 

 with increasing temperature. If, however, we select as a common 

 value the one which is correct for about the middle of the inter- 

 val over which the temperatures involved in the investigation 

 extend, the deviations cannot be important ones. In machines 

 driven by steam, this mean temperature may be taken at 100° C; 

 this being, in ordinary high-pressure engines, about equally 

 distant from the temperature of the boiler and that of the con- 

 denser. In the case of water, therefore, we will employ the 



