156 OF THE POWER OF STEAM, [SECT. iv. 



308. This equation has a maximum, which will be when 



hyp. log. n ( S + F ) = a maximum. 



That is, when 



Consequently, we shall have the greatest possible quantity of mechanical power 



when f - in inserted for n ; or 



/ + F 



5418 (459 + t) w hyp. log. ,, = the greatest mechanical power. 



And where a table of hyperbolic logarithms cannot be conveniently referred 

 to, the result may be obtained by multiplying the logarithm of , F , found 



from the common tables of logarithms, by 2'302585, which will give the cor- 

 responding hyperbolic logarithm. 



309. In the best constructed engines, the waste of steam is not less than 

 one-tenth ; and, to get the extreme power of the steam of a given quantity of 

 water at this rate of waste, we have 1 T V = w '9; and the expression becomes 



4876 (459 + hyp. 



for the greatest possible power the steam of a cubic foot of water can afford, 

 when acting expansively. 



310. In like manner taking the same loss by waste, we have from art. 304. 



4876 



(459 + (l - ^' + F ) 



for the greatest possible power of the steam of a cubic foot of water, when the 

 expansive power of the steam is not used. Consequently, 



4876 



(459 + ,) { hyp . log. ^ - (l - 





is the gain by employing the expansive power. 



311. Though these equations show us the limits of steam power, and are 

 fittest for illustrating the advantages or disadvantages of difference of temperature 

 and elastic force, clearly exhibiting the economy of using steam of considerable 



