SECT . .] PROPERTIES OF STEAM. 99 



repaired a working model of a steam engine for the university of Glasgow, in 

 1763. The cylinder of the model was O5 feet stroke, and 2 inches, or one- 

 sixth of a foot diameter. He " was surprised to find that its boiler would not 

 supply it with steam, though apparently quite large enough." By blowing the 

 fire it was made to make a few strokes, but required an enormous quantity of 

 injection water, though it was very lightly loaded by the column of water in the 

 pump. It soon occurred, that this was caused by the little cylinder exposing 

 a greater surface to condense the steam, than the cylinders of larger engines did 

 in proportion to their respective contents. 1 



There is no doubt this difficulty was the cause of Mr. Watt turning his thoughts 

 to improve the steam engine. Our rule being applied to this case, / = i, d = i, 

 and, 



1300 (I + d) 1300 a + i) in/im , 10400 + 967 



;, T ; = - =10400; and - ~<x*, or 12 times the volume 



id -% x g- yo/ 



of steam which would fill the cylinder would be consumed to condense at 160. 

 By lessening the load lifted, and consequently not condensing the steam to so low 

 a temperature, Mr. Watt made the engine work. 



165. Now in our formula it will be observed, that 26 is half the degrees the 

 temperature of the steam falls by condensation, and that if we lessen this, the 

 quantity of heat lost will lessen in the same proportion, but the loss by uncon- 

 densed steam will be greater. The effect of the engine will be greatest when 

 the sum of these losses is a minimum, and its load should be arranged 

 accordingly. 



The loss by cooling the cylinder is 



25 (212-Q (* + *). 



nr 



when t is the temperature of condensation. 

 The loss by imperfect condensation is 



1127 /' 

 30 



but by our formula (art. 86.) 



., 



- 



Hence, with respect to t, 



1127 (t + 100)6 25 (212 - t) (I + t) 



30x177- -~nr = a 



1 Robison's Mechan. Phil. vol. ii. p. 114. Note by Mr. Watt. 



