carriages. Consequently, their proper re- || middle part of the axletree itself of its usual In the foregoing tables, the average weight of a wagon was 4.78 t. That wagon, placed at the head of the train, had a resistance of 11.77 lbs. per ton, or 56 lbs. for the whole; while, placed in an intermediate situation, its resistance was 8.03 lbs. per ton, or 38 lbs. in all. The difference between the results was owing to the obstacle of the air. The air created, therefore, a resistance of 17 lbs. to 18 lbs. on a wagon of a moderate height, as those were, and at the average speed of the experiments. That speed was of about 12 miles an hour, or 16 feet per second, a space of 10,000 feet having been, on an average, run over in 10 minutes. CHAPTER IV. ENGINES. ARTICLE I. strength. In the Darlington wagons, on ON THE FRICTION OR RESISTANCE OF THE LOAD. § 1. Of the different modes of Deter mination. After having determined the resistance opposed by the loads that are to be moved, friction gave the following results :— With those wagons the experiments on it was also necessary to ascertain the reEXPERIMETS ON THE FRICTION OF Num exp'r- This determination agrees with direct experiments made on the force of the wind. We know that when the wind has a velocity of 20 feet per second, it causes on a surface of a square foot a pressure of 0.915 lbs. or a little less than 1 lb. In other words, a surface of one square foot cutting I the air with a velocity of 20 feet per second meets with a resistance of 0.915 lbs. II Thus a loaded wagon presenting a surface of about 22.5 square feet must meet, from III the atmosphere, with a resistance of about 20 lbs. The direct resistance of the air against the first carriage of the train once deducted, the resistance per ton does no longer depend upon the number of wagons. The remaining differences seem to be the effect of accidental circumstances, such as the state of the rails, or the wind, or the greasing of the wheels, &c., which prevent those experiments from presenting a mathematical preciseness. § 8. Experiments on the Friction of Wagons without Springs. ONS WITHOUT SPRINGS. Number of Distance run over ons in the trains by the wagons before they stopped. Difference of level be tween the Friction. starting and arri ving points. WAG Friction per ton lbs. 8.11 8.07 7.48 7.88 7.88 sistance belonging to the moters themselves, for it is only the surplus of their force, beyond the power they require to move themselves, which those moters can apply to the traction of loads. The friction of a locomotive engine is the resistance which that engine opposes to motion. It is the force that must be applied to it, to overcome all the frictions that oppose its progress, at the moment it executes the traction of a train. At that moment it must evidently possess: 1st, a certain power sufficient to make the train advance or to overcome the resistance of all the loaded carriages; 2nd, another power sufficient to repel the engine itself along and overcome its own friction. It is this second power, the power that propels the engine, which is the friction of that engine, or, rather, which is equal to the friction of that engine; whilst the first is the resistance of the load; and whilst both the powers together constitute the total During those experiments, the wind blew power applied by the moter. with a moderate strength in favour of the motion, which is a point to be considered; tive engine differs according to three dif The power required to move a locomofor we know that trains of wagons are some-ferent circumstances. times propelled to a considerable distance on railways, by the force of the wind alone. boiler without having any access to, or exer1st. If the steam remains shut up in the All the wagons were in good order, and par-cising any pressure on, the mechanism, so ticularly those of experiments III. and IV., that the progress of the engine be produced which were, besides, the best on the line. by an external agent, the engine, moreover, These experiments having, contrary to drawing no load. the naturnl expectation, given more advan2nd. If the steam is the agent that proobtained with wagons mounted on springs, case, there is no train attached to the engine. tageous results than those which had been duces the motion; but if, as in the first it became neccssary to determine exactly the influence of springs on the resistance drawing after it a load, the resistance of 3d. If the engine cannot move without which, creating an increase of pressure on In consequence, the platform of a wagon cessarily augment the friction on every all the parts of the mechanism, must nemounted on springs, having been wedged so as to raise it off the springs, the wagon tal resistance of the engine. one of its joints, and consequently, the towas loaded with pigs of lead, weighing 2 The foregoing experiments having been made with wagons mounted on springs and constructed on an improved principle, one might perhaps suppose that common wagons, having no springs, would offer a to motion. greater resistance to the motion. In order to clear up this point, some experiments were, at our request, undertaken on the Darlington Railway. They were conducted exactly on the same principle as The difference between the first and se the foregoing, by Mr. Robert B. Dockray. tons, and in that state it was left to its gravcond case cannot be very great; for, in The wagons employed were the common wagons in use on that line. Their wheels are 3 feet in diameter, like those of Liverpool. Their weight when empty, is 1.30 t., and 4 t. including the load. They are not mounted on springs, and the axle is 3 inches in diameter at the bearing. ity on the inclined plane. The resulting Then the wedges were struck out, so as lbs. both circumstances, the load of the engine its own weight. Besides, by whatever remains the same, being nothing more than means it is made to move, it advances; so that at every turn of the wheel, there is a complete revolution, and, consequently, a We have seen t at in the Liverpool wagcomplete friction of the whole mechanism. There exists, consequently, a small ad- The steam would have applied a certain ons the axle in the same part is only 13 in- vantage in making use of springs; but that force to make the engine move. ches in diameter. This difference arises advantage is easily compensated by some force would have produced pressures, from the circumstance that in the Liverpool adventitious circumstances, as beiter pol-consequently, proportional frictions on all wagons, the support is outside the wheel, ished bearings, better greasing, a load giv- the compressed points, as upon the crank on a prolongation of the axle; and that ing less hold to the air, &c.; and, in one of the axletree and all the joints in general. part, the only service required of which, is case as well as in the other, the average. Now, as soon as we make the engine adto support the wagon, may be reduced to friction must be reckoned at 8 lbs. per vance, we apply a force equal to that which so small a diameter without depriving the ton, the steam would have applied. That and, Conse 21 quently, we produce on the crank and on We shall have recourse to experiments to pistons. If, moreover, I express the length the creation of the motion. But the only § 2. Friction of the Engines determined by the least Pressure. The considerations above stated, which than its own to overcome; the second was or pld TD D which, according to what we have said, gives the measure of the resistance of the engine. the total Here it must be noticed that we suppose the pressure of the steam in the cylinder to be equal to that in the boiler. The reason is, that in the experiments we shall The surface of the slide, on which the tend to prove that the power necessary to have occasion to make, the motion of the pressure of the steam takes place, is, in general, 7 inches long to 6 inches broad, whether the force of the steam itself, or any move an engine is very nearly the same, engines being always extremely slow and the regulator completely open, the two presor 45 square inches, which makes 90 square inches for the two slides together. ed us with two means of ascertaining the librium, and are consequently equal. It other external agent, is employed, furnish-sures have time to put themselves in equiWhen we talk of the engine moving alone, friction of engines without a load. The must also be observed that the effective and without drawing any load after it, we first consisted in seeking what was the pressure p of the steam, or the surplus of cannot suppose that the pressure of the steam in the boiler need to surpass 10 lbs. least pressure of steam required by a loco- the total pressure over that of the atmosmotive engine to put itself in motion en phere, is not the true moving power residWe shall find, by experiment, that it may the rails, when it had no other resistance ing in the steam. That moving power is happen not to be above 4 or 5 lbs. The pressure of the steam, which we pressure exercised by the steam on the slides, amounts, therefore, at most, to 900 the method already employed in regard to shall express by P. But, on the other lbs. So that, taking the friction of iron wagons. Both were successively tried, hand, the true resistance on the piston is on iron, ground and polished, at of the The principle upon which the first of neither that only which results from the these two methods is founded is the fol- traction of the engine. It comrpises also we shall have a friction of 90 pressure,* the atmospheric pressure, which takes place lowing:lbs. But we know that the real resistances on different points of an engine are in If we find that the steam, by causing other face of the piston, as well as upon either directly or intermediately on the the ratio of the velocity with which those known effective pressure per square inch, parts move. inches for each stroke of the piston, or half the two pistons in square inches being sides an equal quantity, viz. the atmosThe slide only moves three can make the engine advance, the area of every other body in communication with the atmosphere. So, we omit on both a foot for each turn of the wheels; that is known, it is easy to calculate the total pheric pressure. to say, that it only runs over a space of half force applied by the steam on those two here from simplifying in that manner; beNothing prevents us a foot, while the engine having a wheel of pistons. That force being sufficient to five feet, advances 15.71 ft. The friction make the engine advance, that is to say, the resistance only in a case of equality, cause having to compare the power and of the slide, considered as opposing itself to conquer its resistance, it gives of course that equality is not destroyed by substractto the motion of the engine, creates, there-the value of that resistance. It must only ing an equal number on each side. 90 2 X 15.71 lbs. or the a To succeed in ascertaining the least pressure by which the engine could be moved, it was necessary to take the engine at the instant when it furnished the steam at a very low degree of elasticity. In the of the boiler began to lose its heat, and the evening, after the work was finished and the fire taken out of the fire-box, the water steam that it gererated also gradually lost ascertain the least pressure by means of its force. This was the proper moment to which the engines were able to advance on the rails. fore, a final resistance only be observed according to the principle known in mechanics by the name of the about 3 lbs. From which we see, that, in principle of virtual velocities, that the prespractice, the friction occasioned either in sure exercised on a part of an engine, being the first case or in the second, may be con- transmitted to another part of the same ensidered as being the true friction of the engine retains the same intensity only in case gine, when it draws no load. As for the difference between these two not, the force or pressure is reduced in an the two parts have the same velocity. If first cases and the third, we know that the inverse ratio to the velocity of the points friction is always in a direct ratio to the of application. This principle appears in pressure. Now, it is evident that the pres- an evident manner and a priori, in simple sures which take place on the rubbing machines like the lever, the roll, the pully, parts of the engine, vary in proportion to &c. Inspection alone is sufficient to dethe load it draws. That principle is true, monstrate, that if a force can, by the aid of provided the weight of the engine itself is the machine, raise a weight four times as taken as a part of the load. The only parts great as itself, it is only by travelling, in which are excepted from that rule are: the the same space of time, four times as far piston, which remains in all cases pressed as the weight it raises. In the case before in the same manner, the steam having no us, the velocity of the piston is to that of access into its interior; the slide, the fric- the engine as twice the stroke is to the cirtion of which varies with the pressure in cumference of the wheel, the piston giving the boiler, which depends only indirectly two strokes while the wheel turns once upon the load; and, lastly, the excentrics, round, A force applied on the piston prothe friction of which follows the friction of duces, therefore, in regard to the progress the slides. All the other parts of the en-of the engine an effect reduced in the same gine are subject to the rule laid down above. proportion, that is to say, as twice the stroke The principal pressure takes place on the is to the circumference of the wheel. crank of the axle, and that Let d be the diameter of the piston, and I. On the 5th of July, the ATLAS engine, actly in proportion to the load. the ratio of the circumference to the di-cylinders 12 inches diameter, stroke 16 There must consequently be a consid-ameter, d2 will be the area of one of inches, weight 11.40 t., wheels five feet, erable difference in the friction of an en-the two pistons; and p being the effective four wheels coupled, was submitted to the gine when loaded or when without a load.pressure of the steam per square inch, experiment separated from its tender, pressure is ex μπάρ According to the experiments of Coulomb on the will be the effective pressure upon the two" „aistance of surfaçon, ́ The spring-balance that shut the safety-valve enabled us to ascertain the pressure of the steam in the boiler, by loosening the spring until it stood in exact equilibrium with the pressure. It was then easy to calculate the pressure from the degree marked on the balance. Howthe engine was brought to the mercurial ever, to make all calculation unnecessary, gauge, which gave immediately the pressure per square inch in the boiler, at the moment of the experiment. It is in that manner that the following experiments were made: successively loosened, to show the pres The spring of the balance having been At 6 lbs. pressure by the balance, the engine started, followed by its tender full of coke and water. enough to move. sure of the steam in the boiler in propor-||ders 11 inches, stroke 16 inches, weight|| and backwards. The pressure diminishtion as it went down, the following trials 7.91 tons, wheels 5 feet; only one pair of ing a little more, the engine has just power were made:wheels worked by the piston, was submitAt 2 lbs. pressure, marked by the bal-ted to the same experiment. ance, the engine moved backwards and forwards, passing from a state of rest to one of motion, or conquering, besides the friction, what is called the vis inertia of the mass of the engine; that is to say, not only maintaining an acquired velocity, but acquiring one which proves a surplus of force in the moving power. At 1 lb. pressure, marked in the same way, the engine started, passing from a state of rest to one of motion. At 4 lbs. the same. At 1 lb. pressure the engine started also. With the weight of the lever alone, the balance marking no pressure at all, the engine started again. The pressure still a little further diminished, the engine did not start, but, once put in motion, continued going. The pressure diminishing a little more, the engine continued moving. At that mo- At that instant we brought it under the ment we brought it under the mercurial mercurial gauge; it marked 5 lbs. presgauge. It marked 4 lbs. effective pres-sure per square inch, so that at that pressure per square inch in the boiler, the valve sure the engine can move, followed by its then bearing no more than the weight of tender. the lever, or a little less, which could not be ascertained, the balance not going below Thus, as we have seen that the engine continued moving at the moment it was brought under the steam gauge, though the pressure was then reduced to 4 lbs., we see that the resistance of the engine did not exceed 154 lbs. This first experiment was made with the engine separate from its tender, with a view not to counteract one resistance by the other; but, in wishing to apply it to lighter engines, of which the wheels were not coupled, a difficulty occurred. The pressure required for the engine to move without tender was so very low that the springbalance could not mark it, that pressure being less than the weight of the lever itself. Another inconvenience of that low pressure was, that it could only be obtained at the moment the boiler generated no more steam at all; the consequence of which was that at that moment the pressure diminished so rapidly that no confidence could be put in the accuracy of the expe riment. But as the resistance of the tender could be easily calculated by the experiments made on the friction of the carriages, and already inserted above, it was also easy to take it into account. Thus, by having the tender attached to the engine, the experiment presented the same degree of accurateness, with more facility in observing the It is for that reason pressure of the steam. that, in the following experiments, the tender was no longer separated from the engine : II. On July 21, the SUN engine, cylins 1,045 5.887 At that moment it was brought to the mercurial gauge; the pressure was found to be 44 lbs. According to the proportions of the engine mentioned above, a pressure of 4 lbs. per square inch on the piston, produced a traction on the engine of 163 Ibs.; deducting 52 lbs. for the tender, there remained for the proper resistance of the engine 111 lbs. §3. Friction of the Engines determined by the Dynamometer. While the resistance of the engines was being determined in that manner, other trials were also made, to obtain a valuation of that same resistance by means of the dynamometer. V. On July 22, in the morning, the VULCAN engine, cylinders 11 in., stroke 16 in., wheels 5 ft., weight 8.34 t., one pair of wheels only worked by the piston, being ready to set off for Manchester, its boiler full of water, and its fire-box of coke, was The area of the two pistons (11 inches in diameter) being 190 square inches, a pressure of 5.5 lbs. per inch, produced on the piston a force of 190 × 5.5 lbs. = 1,045 lbs. at the velocity of the piston, and thus a A circular draft of = 177.5 lbs. at the veloci-separated from its tender. spring-balance was fixed to the engine, and ty of the engine. That was then the force a lever was passed through the ring of the required to move the engine and its tender. balance, so that two men might draw the Now, the tender filled with water and coke, engine by means of the lever. weighed 6.50 tons, and according to the experiments made on the friction of the carriages, each ton required to put it in motion a power of 8 lbs. The tender consumed, therefore, for its share, a force of 6.50 lbs. +852 lbs. Thus the resistance proper to the engine was 177 lbs.-52 lbs. 125 lbs. III. On July 23, the same engine, the SUN, was tried again at the least pressure, and gave the following results : At 4 lbs. marked on the balance, the engine started, followed by its tender filled with water and coke. At 1 lb. marked on the balance, it started rapidly. At 0 of the balance, it still started with facility. The engine was first put in motion by five or six men. The first impulse being given, the two men that pushed on the lever maintained it without difficulty in motion, at the rate of two or three miles an hour. The index of the balance oscillated very much. It varied generally from 130 to 170 lbs., giving an average traction of of 150 lbs. The balance was afterwards taken off from the front of the machine, and fixed behind on the Liverpool side, when the same experiment repeated, gave an aver age traction of 140 lbs. The index still oscillated about 20 lbs. above and below that point. Average of the two experiments, 145 lbs. The engine was ready to go off, and it At 2 lbs. under zero, it still moved at had already made some turns on the rails, the rate of two or 3 miles an hour. in order to light its fire and fill its boiler, so At that instant it was put under the mer- that the grease that anointed the rubbing curial gauge, which marked 4 lbs. We parts was melted, and the oil perfectly may consider that, in this experiment, we liquid. But the experiment taking place in had arrived at the lowest pressure by which the interior of the Liverpool station, in a the engine could move. According to the great thoroughfare, the rails were covered calculation established above, that pressure with cinders and dirt; a circumstance of 43 lbs gave a force of 902.5 lbs., which, which considerably augmented the resist referred to the motion of the engine, pro-ance to the motion. duced a traction of 153 lbs. Deducting VI. On July 23, in the evening, the SUN 52 lbs for the resistance of the tender, there engine, of which the proportions have alremained 101 lbs. for the resistance of the ready been givnn above, and the weight of engine. which is 7.90 t., was tried in the same man ner. It gave 100 lbs. traction towards Manchester, and 130 lbs. backwards, to wards Liverpool. Average 115 lbs. The boiler of the engine was full of water; the fire-box empty. IV. The same day, the FIREFLY engine, cylinders 11 inches, stroke 18 inches, weight 8.74 tons, wheels 5 feet, one pair of wheels worked only by the piston, was submitted to the same trial At 3 lbs. marked on the balance, it started, followed by its tender filled with water and coke. At 2 lbs. also. At 0 it started also, came back, and went off again in a contrary direction. At 1 lb, under 0, it still started forwards VII, On the same day, the FIREFLY, already described, the weight of which is 8.74 t,, drawn by the dynamometer, required 125 lbs. in one direction, and 130 lbs, in the other. Average traction 127 lbs. The boiler of the engine was full of water; the fire-box was empty, VIII. On the same day, the FURY engine, cylinders 11 in., stroke 16 in., wheels 5 ft., of which only one pair are worked by the piston, weight 8.20 t., required in advancing towards Manchester 100 lbs. traction, and 110 lbs. going back towards Liverpool. Average 105 lbs. These experiments took place on the engines separated from their tenders. They were made on a part which is considered as being exactly level. We may, however, suppose, that on the precise spot where the engine was, the soil was not perfectly horizontal, and that that was the cause of the slight difference in the resistance, observed between one direction and the other. § 4. Friction of the Engines calculated by the Angle of Friction. These results did not differ considerably from the preceding ones; but as in all the experiments, the index of the balance varied extremely, in consequence either of the slight inequalities of the road, or of the jerks given by the men that drew the engine, the average traction was very difficult to ascertain exactly. Besides, the dirtiness of the rails augmented considerably the resistance. It was, consequently, desirable to get those results verified by a different method, admitting of greater accuracy. For that reason the same engines were submitted to experiments similar to those which had served to calculate the friction of the wagons. includes the direct resistance of the air at it continued in motion to 33 ft. beyond pos This engine had been repaired, since which it had only made two or three trips at the time of the experiment. The different pieces were not yet well fitted, nor the joints very easy. Thence arose the increase of resistance observed in it, comparatively with the other engines. XIII. On August 2, the FURY engine, cylinders 11 in., stroke 16 in., wheels 5 ft., The distance travelled by the engine not coupled, weight 8.20 t., left the usual was 5454 ft., and the difference in level starting-point, and stopped at 48 ft. beyond between the points of departure and arri- the post No. 18, running in 7' over a space val, 32.07 ft. Thus the friction was of 5,988 ft., with a difference of level beof the weight, or 150 lbs. This calcula- tween the points of departure and arrival tion includes the direct resistance of the of 36.68 ft.; which puts the friction at air, at an average velocity of 8 to 9 miles of the weight, or 113 lbs. an hour. XI. On August 1, the same engine, the ATLAS, brought to Sutton inclined plane, and the centre of the engine being carefully placed facing the usual starting-post, was left to its gravity on the plane. It ran until 45 ft. beyond the post No. 14. Distance travelled in 5′ 40′′, 4665 ft., total descent 35.40 ft.; friction of the weight, or 194 lbs. The engine had been repaired the night before. The connecting-rods being toc weak had been changed, and the new ones IX. On July 30, the JUPITER engine, were not yet exactly adjusted to their proper cylinders 11 in., stroke 16 in., wheels 5 ft., length. The resistance they produced, only one pair of wheels worked by the pis-acting upon the wheel at the end of a lever ton, weight 7.90 t., was brought on the in- of one foot, which is the radius of the clined plane of Sutton, to the same place crank-arm by which they turn the wheel, where the experiments on the friction of the wagons had been made. It was separated from its tender, and left to its gravity on the plane. produced the effect of a powerful brake to XIV. On August 2, the VULCAN engine, cylinders 11 in., stroke 16 in., wheels 5 ft., not coupled, weight 8.34 t., left to its gravtiy from a point situated at 27 ft. above the usual starting-point, ran in 6′ 30′′ over a space of 5,391 ft. with a difference of level of 36.52 ft., which puts the friction at 48 of the weight, or 127 lbs. XV. On August 4, the LEEDS engine, having the same proportions as the FURY and the VULCAN, weight 7.07 t., ran in 6' 30" over a space of 5,472 ft., on a slope of 36.32 ft. Thus the friction of the engine was of its weight, or 105 lbs. (one of the pistons of the engine creaked for want of greasing.) XVI. On August 15, the same engine, the LEEDS, went off from the same point, and ran over 5,061 ft. in 6', on a slope of 35.86 ft., which puts the friction of this engine at, or 112 lbs. (one of the pistons creaked, as in the foregoing experi ment.) Gone off from the post No. 0, it continued its motion until 249 ft. beyond the post No. XII. On August 1, the VESTA engine, All these results include the direct resist18, and ran during 7' 12". This experi- cylinders 11 in., (this engine had origin-ance of the air against the engine, at an ment gives: Distance travelled, 6189 ftally cylinders 11 in. diameter, but in re average velocity of 10 to 12 miles an hour. difference in level between the points of pairing it, the cylinders were newly bored, departure and arrival, 36.78 ft.; conse- which augmented their diameter by one-§ 5. Table of the results of the foregoing 1 of the weight, or eighth of an inch,) stroke 16 in., wheels quently, friction 5 ft., two wheels only worked by the pis17,696 lbs. tons, weight 8.71 t., was submitted to the 168 same trial. Setting off from post No. 0, 7.90 t. 168. 168 105 lbs. This result Experiments on the Friction of Engines. Placing all those experiments next to each other, we form the following table :- Considering these results, we see that, AI 5 A 10 Aug. 2 XIII - AX 5 by the angle of Aug. 1 VESTA IIX We have already observed, that the exsetting aside the VESTA, which was parperiments with the dynamometer and by ticularly circumstanced, the locomotive en- the least pressure, were made on a spot gines, with uncoupled wheels, had an average resistance of only 115 lbs.; and the ATLAS, with coupled wheels, and of a considerable weight, only 152 lbs., when not thwarted by his connecting-rods. where the rails offered more resistance than along the line. On the other hand, the experiments on the angle of friction took place at a point of the railway where there were nine crossings to get over. These However, to provide a datum for all obstacles acted more particularly on the cases, it may be concluded from the total engines, because they occurred in a place weight of the engines, compared with their where the velocity of the motion was alfriction, that locomotive engines, well con-ready considerably dimmished. We may, structed and in good order, have a resist therefore, when we have engines well con ance of 15 lbs. per ton of their weight. structed, kept in good repair, and on the This is the result which may be reckoned Liverpool model, calculate on the result we upon, when an engine is not yet construct- have obtained, without fear of putting the ed, and when, consequently, one can esti- resistance too low. mate only by guess what will be its future friction. In each of the experiments with the engines, which we shall have occasion to re § 1. Of the Mode of Calculation. We have now determined the friction or resistance of locomotive engines, when they draw no load. We have, however, already shown, that the friction must increase in proportion to the load the engine draws. The aim of our researches must, therefore, now be, to discover the amount of friction for different loads, in order to deduce from it the surplus of resistance created in the engine by each ton of the load. When an engine executes the traction of a train, we know the pressure in the boiler by inspecting the spring-balance; but we do not know the pressure of the steam in the cylinder, because, in passing from the boiler to the cylinder, the elastic force of the steam changes, as will be seen hereafter. If we could know, a priori, the pressure in the cylinder; if, for instance, it were possible to apply a mercurial guage to it, we might immediately deduce the friction of the engine corresponding to that load. In fact, if by hypothesis we know the pressure in the cylinder, or on the piston, by calculating the total effect of that pressure on the area of the piston, we find the exact valuation of the power applied by the engine, On the other hand, we also know the resistance opposed to the motion; it being composed of the resistance of the train and of the engine. Besides, if the engine, in drawing that load, increased constantly in velocity, it is clear that there would be an excess of power over the resistance. If, on the contrary, the velocity were to diminish gradually, the power would be inferior to the resistance; but if we take the engine at the moment it has acquired a certain uniform velocity, and if that velocity be maintained without alteration, the power the engine thus applies must necessarily be exactly equal to the resistance it undergoes, or else there would be either acceleration or retardation in the motion. Thus we know the power applied by the engine; we know the resistance to the motion, which is the sum of the resistance of the train and that of the engine; and, besides, this sum is equal to the power applied: consequently, the resistance of the engine is equal to the power applied, less the resistance of the train. This mode would give thus immediately the friction of the engine, if we knew the pressure in the cylinder. But there are cases in which the pressure in the cylinder is known a priori, and is equal to the pressure in the boiler. These cases are those in which the engine attains the limit of its power with the pressure at which it is working that is to say, when it |