Each unit or B.T.U. represents the amount of heat required to raise one pound of water at 32° Fahr. 1° Fahr., and it is equal to 778 foot-pounds of work. In other words, 778 foot-pounds of work is said to be the mechanical equivalent of one heat-unit. The amount of work, therefore, which one pound of dry steam is capable of performing at any given pressure and at the corresponding temperature may readily be found by multiplying the number of available heat-units which it contains, and which may be readily computed if not already known, by 778, or as in a pumping-engine duty trial, knowing by observation the number of pounds of steam at a given pressure and temperature supplied through the steam-cylinders, the number of heat-units supplied in that steam is at once known or may easily be computed. Then observing or computing the total weight of water raised by the pumping-engine, as well as the total head (the dynamic head) against which the pumping-engine has worked, the total number of foot-pounds of work performed can be at once deduced. This latter quantity divided by the number of million heat-units will give the desired duty. [Illustration: Section of Worthington Pump.] =201. Three Methods of Estimating Duty.=—At the present time it is frequently, and perhaps usually, customary to give the duty in terms of 100 pounds of coal consumed, as well as in terms of 1,000,000 heat-units. Frequently, also, the duty is expressed in terms of 1000 pounds of dry steam containing about 1,000,000 heat-units. As has sometimes been written, the duty unit is 100 for coal, 1000 for steam, and 1,000,000 for heat-units. =202. Trial Test and Duty of Allis Pumping-engine.=—The following data are taken from a duty test of an Allis pumping-engine at Hackensack, N. J., in 1899 by Prof. James E. Denton. This pumping-engine was built to give a duty not less than 145,000,000 foot-pounds for each “1000 pounds of dry steam consumed by the engine, assuming the weight of water delivered to be that of the number of cubic feet displaced by the plungers on their inward stroke, i.e., to be 145,000,000 foot-pounds at a steam pressure of 175 pounds gauge.” The capacity of the engine was to be 12,000,000 gallons per twenty-four hours at a piston speed not exceeding 217 feet per minute. The engine was of the vertical triple-expansion type with cylinders 25.5 inches, 47 inches, and 73 inches in diameter with a stroke of 42¹/₁₆ inches, the single-acting plunger being 25.524 inches in diameter. The following data and figures illustrate the manner of computing the duty: DUTY PER 1000 POUNDS OF DRY STEAM BY PLUNGER DISPLACEMENT. 1. Circumference of plungers, _Cl_ 80.1875 ins. 2. Length of stroke, 7 42.0625 ins. 3. Number of plungers (single-acting) 3 4. Aggregate displacement of plunger per revolution =