Mechanical Theory of Heat to the Steam Engine. 33 
_. In this manner we might continue as long as we please; but 
the third approximate value differs only by the ;3; of a degree, 
and the fourth by less than the +5; of a degree, from the true 
value of the temperature ¢,. pay © 
48. The treatment of the third of the equations xvuz is quite 
similar. If we divide this by V—Io, and for the'sake of more 
easy calculation introduce Briggs’s logarithms, which may be de- 
noted by the symbol Log., in place of the natural logarithms de- 
noted by the symbol log., in which case it is only necessary to 
add the modulus M of this system as a divisor, the equation 
7. 
(49) - 9,= C+alog 7, 
3 
in which (’ and a have the following values independent of 7’. 
o—* V—lo 
= Puls 9? 
(49a) eV ) 
e(? a . 
“=. Ak(V—Ie) 
Tn equation (49) the first term on the right side is again prepon- 
derant, so that we may apply the process of successive approx- 
mation. If we substitute in the first place 7, in the place of 
T;, we obtain as a first approximate value of g,: 
; (0) g m4 # * ° 
and can find in the table, the temperature ¢’ which belongs to it, 
and from this easily form the absolute temperature 7’. If we 
Substitute this in (49) for 7',, we have 
T, 
(50a) g"=xy/-alog 72, | 
ftom which 7” is found. In like manner, we obtain farther 
i dee : 
(508) 9" =9" +4 log Fy: | 
49. It only remains to determine the uantities ¢ and 7 in 
order to be able to proceed to the ntti application of nary 
“ions xvi, The quantity c, that is the specific heat of the 
liquid, has been siti edal 
ment, This, iti 
