STEAM BOILER 333 heating surfaces consist wholly of tubes. They are connected by, a peculiarly formed series of chambered caps, and the ends are made tight by packing with India-rubber grummets. The proportions of steam boilers vary with the type, and are to some extent determined by special considerations. Efficiency is affected by the proportions of area of heating surface to fuel consumed, of area of grate surface to the same quantity, and by general arrangement of parts. The method of producing 'draught and the intensity of combustion are also influ- ential in a great degree in determining efficien- cy. The efficiency of the boiler is to be studied in two parts: the efficiency of the furnace proper, or of the heat-generating apparatus, and that of the boiler proper, or of the heat- absorbing apparatus. In securing efficiency, the engineer first seeks to obtain the highest possible temperature of furnace by thorough combustion of the fuel with a minimum quan- tity of air. An excess of air, by diluting the products of combustion, diminishes the tem- perature of the furnace gases. As shown by Prof. Thurston, the abstract efficiency of the furnace in any ordinary case is represented by the formula, E=^^= -, where E repre- T l T 3 T! T 3 sents the efficiency and TI and r 2 are the abso- lute temperatures at which the heat is gener- ated, and at which wasted heat is discharged, and TS that of the external air. Ti, T 2 , T 3 are temperatures on the Fahrenheit scale. Sup- pose, in two instances, the temperatures of furnace gases, including excess of air, were 2118 F. and 919 F. respectively, and that the corresponding temperatures of chimney were 544 and 452, while the temperature of exter- nal air was 74 and 86-5. In these cases E= E=-- 2118 740 919 86-5C and the first is nearly 40 per cent, higher than the second. By increasing the temperature of the furnace in the first case to 2644, which is not an unusual figure, the available heat be- 2644 _ 544 comes E= 26640 _ 74 o =0 ' 81 of the whole amount generated. The remaining 19 per cent, passes up the chimney, producing or assisting in the production of draught. Where fuel is wet, a portion of the lost heat disappears in vapor- izing the water contained in the fuel. The highest temperature attainable without dilution of gases by an excess of air is given by Prof. Ranldne at 4580 F. with pure carbon, and 5050^ with olefiant gas. "With the more usual case, in which the air supplied is double that theoretically demanded, these temperatures are reduced to 2440 and 2710. The rate of com- bustion of good coal, per square foot of grate per hour, depends upon the height of the chimney. This rate is stated by Prof. Thurston as equal to one pound less than twice the square root of the height of the chimney in feet ; i. e., W= i/H 1. Pvankine determines the height of chimney by the formula, H= A-s-(o-96^ lY in which H is the height of chimney, the " head " required to produce the draught, as ob- tained from Peclet's formula, 7i= -Yl3 +^ 20 m ' and ti and t* the absolute temperatures of the chimney and of the air. In Peclet's formula, V is the velocity of flow, I is the length of chimney and flue, and m is its "hydraulic mean depth." For ordinary practice, Isher- wood found the proportion of chimney cross section to area of grate to be about one eighth. Probably a good rule for general practice would be : Make the area for draught one seventh at the bridge wall, one eighth through the flues, and one ninth in the chimney, of the area of grate. The area of heating surface determines the efficiency of the steam boiler as a heat- absorbing apparatus and reservoir. Eankine has given a formula ("Steam Engines and Prime Movers," p. 292, iv.) for determining the efficiency of fuel in ordinary steam-boiler practice, where the ratio of the area of heating surface, and of fuel burned per hour, to the square foot of grate surface, is known : = E in which is the q'uantity called above E, A and B are constants, and F and S are the ratio of fuel burned per hour to the square foot of grate, and the ratio of area of heating surface of grate area. The effect of exception- ally low temperature of furnace is to equalize the value of heating surface ; and the consider- able velocity of the gaseous current, which is a consequence of the unusually great volume of air passing through the furnace, increases this effect, the nearer surface is inefficient, and the most distant portions of the heating surface are therefore proportionally much more efficient than in the preceding case. (" Trans- actions of the American Society of Civil Engi- neers," 1874-'5, pp. 290, 303.) With high tem- perature and slow movement of gases, a lower relative amount of heating surface is efficient ; and with lower temperature of furnace and rapid movement of gases, the heating surface must be extended beyond the proportions upon which this estimate is based. The constants A and B have values varying from 1 and 0'5 re- spectively, in the best designed boilers, to 0'9 and 0-5 in ordinary cases, both having chimney draught, and to 0'95 and 0'3 for cases of ordi- nary practice with forced draught. These val- ues are changed very slightly by wide ranges of proportions of heating and grate surfaces, or F of the value of -g. The value of F has already been given. The value of S is variable with the style of boiler used, and with the value of fuel. The ratio S of area of heating surface to grate area, in ordinary good practice, and un- der ordinary conditions, may be taken at 15 with plain cylindrical boilers, 20 with Cornish, 25 with flue, 28 with fire-tubular, and 30 with
