W. P. Trowbridge—Efficiency of Steam Boilers. 83 
perature, 6, of the water in the boiler; this difference being 
constant for the whole furnace surface. It is presumed that the 
law of Dulong and Petit for the cooling of bodies by contact of a 
cooler gas is also the law of heating by a hot gas; the side on 
Which the excess of temperature exists being a matter of 
indifference, 
_ For the transfer of heat by contact in the flues, the applica- 
ton of the law renders it necessary to take into account the 
diminution of temperature, from the initial temperature ¢, to 
the temperature ¢,, of the gases, as they leave the flues and pass 
into the chimney. 
t the combined flue surfaces be represented by a single 
cylindrical surface in 
the form of a tube, as 
Y in the figure below, 
t peat and the other perpen- 
dicular to it; and let 
; —- t, be the difference of 
ds gases and the water 
j 1 outside of the tube, 
th . at the entrance, and 
4 the corresponding difference of temperature at the exit of 
the gases, 
_ Let ¢ represent the quantity of heat transferred in a unit of 
Siok our) at any point of the tube from one unit (square 
Sot) of surface. When a boiler is at work the temperature of 
© gases at any pant or of the plates in contact with the gases, 
ed as constant, and it will not, therefore, be 
ined only when the surfaces of the plates undergo a change 
Tr patare, as in getting up steam. 
be dj the heating surface represented by the surface of the tube 
t vided into elementary portions by planes perpendicular to 
ee axis, the element of the surface between two planes may be 
ee ented by ds, and the quantity of heat transferred by 
Th, trough the element will be represented by gs. : 
weight sca by c the specific heat of the gases, by W the 
= hour), and by dt the element of time; it is evident that 
ino oling of the gas in the time dé will be ¢ W dt, expressed 
‘nits of heat, and this quantity must be equivalent to that 
tt or absorbed by the water, represented above by gds: 
tion expressed by the equation : 
