MEMOIR OF DANIEL TREADWELL 



513 



and train is the same, whether the engine be large or small ; therefore the whole cost of transportation 

 must be much enhanced by the employment of small rather than large engine-.* 



III. The comparative power of the same engine if sing steam of a giv< n elastic force wfo n running 



at different velocities. — It is well known that the power of any steam-engine driven by steam of a given 

 elastic force, measured by the pressure exerted by the piston rod. is greater in some inverse proportion 

 to the velocity of the piston. Thus, for example, a locomotive engine running without any resisting train 

 upon a level railway will acquire such velocity that the elastic force of the steam and the resistance op- 

 posed to it in the several pipes and narrow passages through which it must pass is such that in following 

 the pistons a very small force is displayed upon them. When, however, we add a resisting train to an 

 engine under the above condition, we reduce the speed, and consequently reduce the resistance to the pas- 

 sage of the steam itself, and it is only when we increase the resisting train so that the velocity becomes 

 barely sensible that the full effect of the elastic force of the steam is communicated to the piston. We 

 ma}' determine some of the relations of the power of an engine under different velocities from data fur- 

 nished in the preceding accounts of my experiments. 



It appears that the Lion, when ascending the inclination between the tenth and thirteenth mile 

 drawing a load of 141,800 lb., exerted during one mile a mean force of 1,21!) lb., and moved at the rate 

 of 4 miles an hour. During a portion of the time the motion was something less than 2j miles an hour, 

 and the drag was then 1,350 lb. upon the dynamometer. 



The driving wheels of this engine are five feet in diameter, the strokes in the cylinder sixteen inches ; 

 therefore the motion of the engine over the rails is to that of the piston as 32 to 188.5, or 1 to 5.9 nearly. 

 Hence the whole force upon the pistons must have been 7,192 lb. Here are two cylinders, containing 

 together an area of 190 square inches. The force then which was communicated from the piston to the 

 dynamometer alone must have required a constant pressure upon the pistons of 37.8 H>. per inch. In 

 addition to the above pressure, which was measured by the dynamometer, there was the power required 

 to move the engine itself and its tender, being fifteen tons, which was not measured bv the dynamometer. 

 Taking into the account the large journals (or gudgeons) of the engine and tender, we may take this to 

 have required 400 lb., which would give 12.4 lb. per inch upon the pistons. The steam during this time 

 was blowing freely from the safety valve loaded with 60 lb. per inch, and giving probably a pressure in 

 the boiler of 56 11). to the inch. The 5.8 lb. difference between 50.2 lb., required upon the pistons, and 

 56 lb., the pressure in the boiler, may fairly be assigned to overcoming the resistance of passing the 

 pipes, the friction of the pistons, slides, and other working parts of the engine, and the resistance of the 

 forcing pumps. 



From the foregoing statements we may conclude that a locomotive engine using steam of 60 lb. per 

 inch, as shown by the safety valve of common construction, will produce a useful effect upon a train of 

 38 lb. upon each square inch of its pistons when the velocity upon the road is not greater than four miles 

 an hour. 



To find the effect of the steam upon the engine at higher velocities requires more extensive experi- 

 ments made upon a road containing longer levels, or planes of equal inclination, than those of the Wor- 

 cester road. I may, however, make one comparison, which I consider as indicating a solution of this 

 question worthy of some reliance. The road from the first to the fifth mile-post, containing but one 

 ascending plane, was passed over by the Lion and train, steam being 60 lb. as measured by the safety 

 valve, in 14™ 15 s ', or at the rate of 17 miles an hour, nearly; the mean draft upon the dynamometer 

 being 606 lb. This required, following the former mode of computation, an effect upon the pistons 

 to be communicated to the train of 18.7 lb. to the inch. We have, then, when the steam is 60 lb. in 

 the boiler, 38 lb. useful effect upon the pistons, the velocity being 4 miles an hour, and 18 lb. when 

 the velocity is 17 miles an hour. It may be observed that these forces are to each other very nearly 

 in the inverse proportion of the square roots of the velocities. The experiments, however, were much 

 too limited to warrant the inference of a general law from them. 



* Mr. Treadwell's view has been fully confirmed by subsequent observation. — W. 



