STEAM ENGIKE 351 condenser ; the pressure drops to e at the end of the stroke, and as condensation becomes completed during the return stroke, the mini- mum pressure is soon reached and retained until at/ 1 the closing of the exhaust valve shuts up a small portion remaining in the cylinder, and it is compressed by the returning piston and its pressure thus increased to a, where the end of the return stroke is reached, the steam valve again opens, and a new cycle of opera- tions begins. A B is the atmospheric line, and C D that of absolute vacuum. In consequence of the slow closing of the steam or cut-off valve in this case, the steam is not completely cut off until the point h is reached, where the change in the character of the curve shows that only from h to d does the steam expansion line truly represent the law of change of vol- ume with pressure. From c to Ji the steam "wire-draws" through the steam port, and the benefit of expansion is not fully secured. Were "le steam port closed instantaneously at c, the line c g would be the expansion line, and would losely correspond with that described already (see STEAM) for the special conditions under which it may have been formed. It is to se- ire this sudden closing and this full benefit )f expansion that the drop cut-offs of Sickels, Corliss, Greene, and others have been adopt- Eef erring again to the diagram, should the "lead" be increased, and steam thus admit- ted earlier in the stroke, the line a I would be formed parallel with but in advance of its present position. With less lead, the point & would be moved also, the line a 5 becoming inclined to the left. With a greater or less expansion, the point e moves to the right or the left. With a rapidly closing cut-off valve, the curve c h becomes shorter, and the curve c h g more nearly like eg. A better vacuum rould bring the line ef nearer CD. In a )n-condensing engine ef would be above A . The distance of ef above A B or above D indicates the back pressure produced by sistances in the exhaust passages, or the de- of imperfection of the vacuum which is lue to the presence of both vapor and air in nail quantity. With a three-ported valve, ich as is used on locomotives, a shorter cut- off would cause an earlier closing of the ex- lust on the return stroke, and the point f ould fall at the left of its present position. The mean value of the steam pressure in " cylinder, as determined by measuring the Ititude of the diagram at several points, or >y obtaining its area with a planimeter and 'ividing by its length, is termed the mean )ressure. The horse power is determined by nultiplying the mean pressure by the area of Hston and the speed of piston, and dividing the value of a horse power. That is, HP = where P is the mean pressure per ^ pare inch, A the area of piston in square inches, V the speed of piston or the product " the length of stroke in feet by twice the T63 VOL. xv. 23 number of revolutions per minute. The horse power was assumed by James Watt as equiv- alent to 33,000 Ibs. raised one foot high in a minute, 550 foot pounds a second, or 1,980,- 000 foot pounds of work an hour. This is about the maximum which the best London draught horses were then considered capable of performing. An average actual horse pow- er is about 26,000 Ibs. a minute, but Watt's figure is retained by engineers. With engines of ordinary proportions, the mean pressure may be determined with considerable accuracy also by the formula p=T? 1+A ^ oglE B-CP, the assumption being very nearly correct that steam expands in such cases according to Mari- otte's law, the curve of pressure being a hyper- bola and the product of pressure and volume constant. The values of the constants A, B, and 0, as determined by Francis B. Stevens, are A=2'3, B=5, and 0=0-06. P is the ini- tial pressure and p the mean pressure. With engines working at moderate pressure, with unjacketed cylinders and medium speed of pis- ton, the point of cut-off giving maximum econ- omy is at about 0*4 or 0*5 the stroke. With high steam and rapid motion, and with steam- jacketed cylinders, economy is gained until the steam is expanded four to six times. In com- pound engines it is not unusual to expand from eight to twelve times, but experiment has not indicated that such great expansion is attended with economy. The losses which accompany great expansion are due to internal condensa- tion of steam and its reevaporation on the opening of the exhaust valve, when it carries away a large proportion of unutilized heat into the condenser. This loss sometimes exceeds the amount of heat actually utilized. In re- cent experiments the steam jacket has been found to save 20 per cent, by checking this condensation, which is the principal source of loss of economy in such engines. Superheat- ing the steam sufficiently to cause it to pass through the cylinder "dry" diminishes it also. The minimum expenditure of steam in the best engines is about 16 or 18 Ibs. per horse pow- er per hour. The amount used in the single cylinder engine with moderate expansion and comparatively low pressure is seldom less than 30 Ibs., and in old styles of engines worked with a pressure of 20 Ibs. per square inch and cutting off at three fourths stroke, the con- sumption of fuel is often 6 Ibs. and of steam 40 to 50 Ibs. per horse power per hour. The- expenditure of coal has been reduced by suc- cessive improvements, as the increase of steam pressure, greater expansion, surface condensa- tion, high piston speed, the use of the steam jacket, and minor changes in both engine and boiler, until the best steam engines of the present day consume but about 2 Ibs. of coal per horse power per hour, in ordinary work, and in some instances as little as 1 H>. Even the latter, however, is but about one eighth the efficiency which would be given by a per-
