MESSRS. EDITORS—"What is the horse power of a locomotive under the following circumstances, namely, eylindersfifteen inches in diameter ; stroke, twenty inches ; driving wheels, five feet diameter ; speed, forty miles per hour, with a working pressure of steam in the cylinder of one hundred pounds per inch, full stroke ? " I have worked out the question for myself, and have made the power of each cylinder 393 horse, nearly, or 787 total. An apprentice in a machine shop in this place recently asked me the above question, and when I gave him the foregoing answer, all the engineers in the shop laughed at me. I then asked quite a number of mechanics what was the power of such a locomotive, and they said from forty to eighty horse. An engineer of a looomotive of about the capacity given, told me that his engine was eighty horse power. There is either a very mistaken notion among mechanics generally concerning the power of locomotives, or else the rules laid down in books for estimating their horse power are not correct. Your opinion will throw light on the subject. G. B. F. Canton, N. Y., April, 1858. [Our correspondent is nearly right in the conclusions deducible from the question according to the data he has furnished. The nominal horse power of a locomotive of the dimensions given and performing, as described, is eight hundred. This is estimated by multiplying the pressure of the steam per inch on the area of piston into the velocity of the latter in feet per minute, and dividing the product by 33,000. The unit of a horse power is 33,000 pounds, lifted one foot per minute. In the above case, therefore, we have— 152 X '7854 = 176.715 inches area of piston. 1 5 X 3.1416 = 16.708 feet circumference f driver wheel. B280 -t- 16.708 = 336 revolutions of wheel per mile. 336 X 40 -f- 60 = 224 revolutions driven pel1 minute. 224 X 3 = 747 feet (nearly) velocity of piston per minute. Therefore, 176.715 X 100 X 747 -*? 33,000 = 400 X 2 (cylinders) = 800 horse power. A like result is obtained as follows:— (152 X 20 X 40 X 100) T (5 X 4500) = 80. This latter rule embraces the multiplying of the speed in miles per hour by the square of the diameter of the piston in inches, by the stroke in inches, by the effective mean pressure on the piston in pounds per inch, and dividing the product by the diameter of the driving wheel in feet, and by 4,500. The nominal and the efficient horse power of a locomotive are two very different questions, and the engineer to whom our correspondent refers may have given a correct answer so far as it related to the efficiency of his locomotive. In working out the above question no allowance is made for back pressure, which in locomotives sometimes amounts to one-seventh of the direct pressure. There is also a great difference between the pressure in the boiler and that in the cylinders, especially when running at high speeds and working expansively ; this difference of pressure is from 20 to 40 per cent in speeds of from twenty to sixty miles per hour, and is even greater when the cylinders are not protected. The question, " What is the horse power of a locomotive ?" is one of a complex character, and in some respects very different in its nature from that of a stationary steam engine. The efficient horse power of a locomotive may be very small, while its nominal horse power may be very large, and the very best locomotives expend a vast amount of power in proportion to their amount of efficiency. Redten-bacher, a German author of scientific attainments and a practical engineer, has published the results of quite a number of experiments on this head, and his conclusions are that the efficienthorse power ofalocomotiveperforming under the best possible conditions, according to his experiments, is only as 230 to 505—not fifty per cent of the power expended. Six wheeled drivers connected together, he found far more efficient than engines having either two or four driver wheels. He also found that the important element, adhesion, varied greatly with the character of the engine. Thus a locomotive of eleven tuns weight with two wheel drivers, possessed only 5.5 adhesion, whereas one of twenty-five tuns weight with six wheel drivers possessed 22.5 of adhesion ; the former only half the adhesion of its tun-nage ; the latter nearly the whole of it. There are quite a number of elements which necessarily enter into the computation of " the efficiency of locomotives."—[EDS.