82 W. P. Trowbridge— Efficiency of Steam Boilers. 
exposed to direct radiation, the amount of heating surface 
exposed to the contact of the gases, and the laws of absorption 
or transfer of heat under these conditions. 
The quantity of air supplied to the furnace, in a unit of time, 
depends upon the chimney, or other apparatus for producing 
the draft, and the surface of contact of air and fuel; upon 
the kind of fuel, size of lumps, thickness of bed, etc. There 
are other conditions which influence the evaporative efficiency 
of boilers, when the total heat of combustion is to be compared 
with the quantity of heat transferred to the water; such as the 
losses from imperfect combustion, diffusion of heat, escape of 
heat through the chimney, etc., making an aggregate of losses 
which must be estimated. 
The following general discussion of the problems involved is 
given, as suggesting a mode of investigation which may lead to 
more satisfactory experiments on the laws of transfer of heat. 
Let Q represent the quantity of heat transferred to the water 
of the boiler in a unit of time, one hour for instance 
Q, the portion of this heat which is transferred by radiation 
in the furnace. 
Q. that part which is transferred by contact of heated gases 
in the furnace. 
Q, the part which is transferred by contact of heated gases 
in the flues. 
Then Q=Q,+Q,+Q,,. 
In this expression, the first member may be regarded as 
known, because it may be easily ascertained by experiment. 
Of the terms of the second member, Q, represents the quantity 
of heat transferred by radiation from the surface of the fuel. 
According to the laws of Dulong and Petit, this quantity may 
be represented by 
Q,=¢xG=C. a® (a'—1).xG. 7 
in which gq represents the quantity of heat transferred by 
radiation from one square foot of grate surface in a unit of 
time, G the grate surface in square feet, C a constant, a=1-0077. 
6 represents the temperature of the absorbent body, or the water 
in the boiler (a constant which may be determined by obser 
vation), and ¢ the difference between this temperature and the — 
fuel = 
higher temperature of the incandescent 
el. a. 
By the law of transfer of heat by contact of gases, given by 
Dulong and Petit, we shal] have 
OE A oe CARE lon 
¥ representing in square feet the furnace surface, O’¢,'"*° . 
the quantity of heat transferred by contact of the gases in the 
farnace in a unit of time; in which ¢, represents the difference of © : 
temperature between the gases in the furnace, and the tem- — 
