By what has been shown, it is evident that the first principle of locomotion is the hold or bite of the wheels on the road. Unless this exceed the amount of traction force, steampower is 'thrown away, the wheels will slide round, and no motion can ensue, or be kept up, after it is attained. When the bite is ample, and the steam turned on upon a stationary engine, its want of vent rapidly raises the temperature of the boiler, and, consequently, the quantity and pressure of the steam on the piston. A gradually increasing motion is the consequence. But as this motion increases, so do the strokes of the piston and consumption of the steam; and it results, that the temperature of the boiler sinks again, until it has reached that point at which the temperature carried off by the consumed steam, balances that communicated by the fire to the boiler. At this point, a uniform motion in the train will commence, and be maintained, without any regard to the bite of the wheels being in excess of the traction of the load. An engine of a less weight will therefore preserve that velocity it could never have given. However, it will in all cases be advisable to have more bite than is wanting; especially as the expense of propelling an additional ton or two is immaterial, and might always be made up in the structure of the carriages of the train. Objections I know arise to weighty engines, but where the question is one of efficiency or inefficiency, there is little room for choice. I would much rather increase the strength of the rails, which, wearing but little,

Υ

will be thrown chiefly on the first cost, than be deficient in that which is indispensable for success, namely, power in the engine.

If we suppose a piston one half the area of another, it must evidently travel with twice the velocity to consume the same quantity of steam at the same elasticity and temperature, and its force will, of course, be just one half. Therefore a half load, under such a circumstance, would be driven with a double velocity. In the same way a third and fourth of a , load would be driven with three or four times the velocity; and, generally, other things being alike, the velocity would be inversely as the load, the area of the piston varying as the load.

But supposing the piston and fire to remain the same, what would be the velocity of a double, triple, &c. load? This is a question which I am not aware has ever been satisfactorily answered, physically or experimentally. Indeed, on the received doctrine of airs, I do not think it admits of an answer. I shall endeavour to solve the problem physically, on the only reasonable principle I can imagine, and on laws of aeriform bodies published and constated with experiment by me fifteen years since in the Annals of Philosophy. It will immediately be seen that the solution of this problem will have the merit of bringing within the grasp of physical science one of the most important points in the action of the steam-engine.

The principle referred to is this:-That the number of steam particles emitted every moment, drawn into the temperature of the steam, is always proportional to the heat simultaneously communicated by the fire to the water.

If, therefore, the heat communicated be uniform, and N denote the number of particles momentarily emitted, and T the true temperature of them,

NT is a constant quantity.

But if E be the elasticity of the steam, and n the number of its particles contained in a given space,

Eαn T2,

by Prop. 8, Annals for May 1821, p. 345. And if V be the velocity of the piston, n V is evidently as the number of particles of steam momentarily carried off or emitted. Therefore,

n Vα N, and Tn Va NT a constant.

(according to Cor. 2, Prop. 1, p. 98, Annals for Aug. 1821,) F being the Fahr. temperature. But E, the elasticity, will be as the load or force of traction, and V as the velocity of the engine. Consequently

(1

1 +

h

2/2) WV α ✓ F + 448.

WV α F +448(4)

Moreover, because when the elasticity of steam, at its proper tension, is tripled, the right hand member of the equation will increase only about 5 per cent., we may consider this member constant for all practical purposes; and hence the velocity of transit, other things alike, will be inversely as the load and force of traction; that is, it will be inversely as the product of the load and the force of traction in No. (3).

In the above solution I have assumed that the steam is in no way throttled in its passage from the boiler to the engine, and that the fire continues to communicate the same quantity of heat under every velocity. The former circumstance, though most essential, I have reason to apprehend is not satisfied in any engine yet made when the velocity is high; but it is out of any one's power, without having the exact measures of every part of the engine with many other data, to make a just allowance for the defect. With regard to the constancy of the fire, gentlemen who have had great experience with locomotive engines have assured me that the fire loses much of its vivacity and vigour with the diminution of velocity in the engine. Probably this may be the case; and I think there is an experiment of mine made on one of the Manchester inclines which confirms it, but as I have not repeated the calculations I at present do not like to adduce it. However, one of the reasons brought to support it is very good. They say that as the discarded steam is used in being discharged up the chimney to blow the fire, and as there is a greater quantity so discarded at high than at low velocities, the current of air to the fire, and consequently the intensity of the fire, must be greater in the former than in the latter case, But another argument that I have heard is, taken per se, most fallacious. It is urged in proof of the fire being stronger at high than at low velocities, that the quantity of water evaporated with a high velocity is greater than with a low. Now it has long since been proved by myself in the

coincidence of the laws deduced with facts, that the superincumbent steam is perpetually condensing on the water according to its temperature and density, and the water perpetually evaporating without any regard to the quantity or density of the steam over it. When these counter-operations balance, then and then only it is that the steam or vapour reaches what Dr. Dalton has very appropriately called its tension. At this time the water is apparently not evaporating at all, yet in reality its absolute evaporation is just as great, its temperature being the same, as if the steam was carried off momentarily as produced. Hence the apparent evaporation under such circumstances is no measure at all of the real, nor therefore of the intensity of the fire.

Mathematicians will immediately perceive that the direct solution of the above problem-that of finding the velocity under a change of load, the velocity under a particular load being given, simple as it appears, is beyond the reach of the ordinary principles of science. That clumsy application of the dynamical principle that a given force will generate double, triple, &c. velocities in half, third, &c. weights which one individual has used, is here perfectly absurd and ridiculous, and only tends to prove that the man who wrote it was treading on ground to which he was a stranger. Mr. Wood and Mr. Pambour have both endeavoured to give formulæ for the relation of the velocity to the load, but they are merely empirical, and the latter gentleman seems exceedingly careful not to endanger the credit of his calculated comparisons with facts, though it would seem he is not deficient in experiments. In his tabular evidence against the Great Western Railway, Dr. Lardner appears to have used, but without acknowledging whence he had them, the theorems I have given above, which I had then not long published.

If a practical rule is wanting, some one velocity on a level must be fixed on to which all must be referred, and the load being found corresponding thereto will be the standard of the engine's performance. In our table we have considered 30 miles an hour to be this standard. Now, if thirty times the weight of the whole train corresponding to thirty miles an hour, be divided by the product of the weight of the whole train multiplied into the force of traction found by the foregoing rule, the quotient will be the velocity in miles per hour of the engine's performance up or down the given plane, supposing the whole steam to be applied, the resistance of the atmosphere nothing, and in descents that the velocity does not exceed 40 or at most 50 miles an hour.