MECHANICS AND USEFUL ARTS. 59 



unabsorbed heat must escape by the chimney. An increase of heat- 

 ing surface, again, reduced the waste of heat, and promoted economy 

 of fuel, and added greatly to the economical evaporative power. In 

 short the -question resolved itself into the mutual adjustment of three 

 elements: the necessary rate of evaporation, the grate-area, 

 and the heating surface, consistent with the economical generation of 

 steam, at the assumed practical standard rate of 9lbs. of water per 

 pound of good coke. An investigation of the cases of economical 

 evaporation, in the table of experiments, conducted the author to 

 the following very important equation, expressing the relation of the 

 three elements of boiler-power : in which c was the maximum eco- 

 nomical evaporation, in feet of water, per foot of grate per hour, Jt 

 was the total heating surface, in square feet, measured inside, and g 

 was the grate-area in square feet : 



^h 

 c = .00222 



s 



From this it followed : 1st that the economical evaporative power 

 decreased directly as the area of grate was increased, even while the 

 heating surface remained the same. 2nd. That it increased directly 

 as the square of the heating surface, when the grate remained the 

 same. 3rd. That the necessary heating surface increased, only, as 

 the square-root of the economical evaporative power. 4th. That the 

 heating surface must be increased as the square-root of the grate area, 

 for a given economical evaporative power. It was contended thence, 

 that the heating surface would be economicallv weakened by an exten- 



<- t *f & 



sion of the grate, and would be strengthened by its reduction ; and that 

 whereas large grates were commonly thought to be an unmixed good, and 

 being generally recommended were usually adopted ; still they might 

 be made too large ; not that their extension affected the quality of 

 combustion, but that the economical evaporative power might be 

 reduced. Concentrated and rapid combustion was, alike, the true 

 practice for the largest and the smallest boilers ; and in locomotives 

 where lightness, compactness, and efficiency were primary objects, 

 the boilers should be designed for the highest average rates of evapo- 

 ration per foot of grate, that might be followed, in good practice, con- 

 sistently with the highest average rate at which coke could be prop- 

 erly consumed ; as, in this manner, the smallest grate, and the small- 

 est amount of heating surface, consistent with good practice, might be 

 employed. It was stated, that 1501bs. to 260lbs. of good sound coke 

 could be consumed, per foot of grate per hour ; and, allowing for 

 inferior fuel, an average maximum of 1 1 2lbs. per foot of grate, per 

 hour, was recommended as a general datum. This determined the 

 average maximum of economical evaporation to be 16 feet of water 

 per foot of grate per hour, allowing 9lbs. of water per pound of coke ; 

 for which 85 feet of heating surface per foot of grate should be pro- 

 vided. It was accordingly recommended, that a heating surface at least 85 

 times the grate-area should be adopted in practice. ^It was also shown, 

 by examples of inferior economy of evaporation, that the clearance 



