CHEVALIER G. DE PAMBOUR'S 
 
 NEW THEORY 
 
 OF THE 
 
 STEAM ENGINE. 
 
 PRICE 2s. 
 LONDON : JOHN WEALE. 1838. 
 
A NEW THEORY 
 
 OF THE 
 
 STEAM ENGINE, 
 
 AND THE 
 
 MODE OF CALCULATION BY MEANS OF IT, 
 
 OF 
 
 THE EFFECTIVE POWER, &c. OF 
 
 EVERY KIND OF STEAM ENGINE, STATIONARY 
 OR LOCOMOT^V^ * V , 
 
 BY 
 
 qiMt? 
 THE CHEVALIER G./t)E PAMBOUR. 
 
 LONDON: 
 JOHN WEALE, ARCHITECTURAL LIBRARY, 
 
 59, HIGH HOLBORN. 
 
 1838. 
 

 or the proportions of steam-engines ; and a succinct 
 exposition of the method proposed. 
 
 Part ii. General formulae for the calculation of the 
 effects, &c. of rotative, stationary or locomotive, high 
 or low pressure, expansive or unexpansive, condensing 
 or uncondensing steam-engines, according to the pro- 
 posed theory. 
 
 Part in. Special application of these formulae to 
 the divers systems of steam-engines in use. 
 
 PART I. 
 
 PROOFS OF THE INEXACTITUDE OF THE ORDINARY ME- 
 THODS, AND EXPOSITION OF THE ONE PROPOSED. 
 
 1. Mode of calculation hitherto in use. All the 
 problems in the application of steam-engines merge 
 into these three 
 
 The velocity of the motion being given, to find the 
 
 load the engine will move at that velocity. 
 The load being given, to find the velocity at which 
 
 the engine will move that load ; 
 And, the load and the velocity being given, to find 
 the vaporization necessary, and consequently the 
 area of heating surface requisite for the boiler, in 
 order that the given load be set in motion at the 
 given velocity. 
 
 The problem, which consists in determining the 
 useful effect to be expected from an engine of which 
 the number of strokes of the piston per minute is 
 
counted, that is, whose velocity is known, evidently 
 amounts to determining the effective load correspond- 
 ing to that velocity ; for that load being once known, 
 by multiplying it by the velocity we have the useful 
 effect required. 
 
 According to the mode of calculation hitherto ad- 
 mitted, when it is wanted to know the useful effect an 
 engine will produce at a given velocity, or, in other 
 words, the effective load that it will set in motion at 
 that velocity, the area of the cylinder is multiplied by 
 the velocity of the piston, and that product by the 
 pressure of steam in the boiler ; this gives, in the first 
 place, what is called the theoretical effect of the 
 engine. Then, as experience has shown that steam- 
 engines can never completely produce this theoretical 
 effect, it is reduced in a certain proportion, indicated 
 by a constant number, which is the result of a com- 
 parison between the theoretical and practical effects of 
 some engines previously put to trial ; and thus is 
 obtained the number which is regarded as the prac- 
 tical effect of the engine, or the work it really ought 
 to execute. 
 
 A mode perfectly similar is followed, for deter- 
 mining the vaporization which an engine ought to 
 produce in order to produce a desired effect ; that is 
 to say, for resolving the third of the problems which 
 we have presented above. As to the second of these 
 problems, that which consists in determining the 
 velocity the engine will assume under a given load, no 
 solution of it has been proposed in this way, and we 
 shall expose, farther on, some fruitless essays that 
 have been made to resolve it in another way. 
 
As in the above-mentioned calculation no account is 
 taken of friction, nor of some other circumstances 
 which appear likely to diminish the power of the 
 engine, the difference observed between the theoretical 
 and the practical result excites no surprise, and is 
 readily attributed to the circumstances neglected in the 
 calculation. 
 
 2. First objection against this method of calculation. 
 This mode of calculation is liable to many ob- 
 jections, but for the sake of brevity we limit ourselves 
 to the following : 
 
 The coefficient adopted to represent the ratio of the 
 practical effects to the theoretical, varies from ^ to -f , 
 according to the various systems of steam-engines ; 
 that is to say, that from f to ^ of the power exerted 
 by the machine is considered to be absorbed by friction 
 and divers losses. Not that this friction and these 
 losses have been measured and found to be so much, 
 but merely because the calculation that had been 
 made, and which might have been inexact in prin- 
 ciple, wanted so much of coinciding with experience. 
 
 Now it is easy to demonstrate, that the friction and 
 losses which take place in a steam-engine can never 
 amount to f , nor to of the total force it developes. 
 It will suffice to cast an eye on the explanation at- 
 tempted, on this point, by Tredgold, who follows this 
 method in his Treatise on S team-Engines.* He says 
 (art. 367), that, for high pressure engines, a deduction 
 
 * The author here refers to the first edition of ' Tredgold on the 
 Steam-Engine :' in the new edition just published the algebraic 
 parts are transformed by the editor into easy practical rules, accom- 
 panied by examples familiarly explained for the working engineer. 
 
of H) must be made from the total pressure of the 
 steam, which amounts to a deduction of f- on the 
 ordinary effective pressure of such engines ; and to 
 justify this deduction, which however is still not 
 enough to harmonize the theoretical and practical 
 results in many circumstances, he is obliged to esti- 
 mate the friction of the piston, with the losses or 
 waste, at ^ of the power, and the force requisite for 
 opening the valves and overcoming the friction of the 
 parts of the machine, at TO^ of that power. Reflecting 
 that these numbers express fractions of the gross power 
 of .the engine, we must readily be convinced that they 
 cannot be correct ; for, in supposing the engine had a 
 useful effect of 100 horses, which, from the reduction 
 or coefficient employed, supposes a gross effect of 200 
 horses, 12 would be necessary to move the machinery, 
 40 to draw the piston, &c. ! The exaggeration is 
 evident. 
 
 Besides, in applying this evaluation of the friction 
 to a locomotive engine, which is also a high pressure 
 steam-engine, and supposing it to have 2 cylinders of 
 12 inches diameter, and to work at 75 ft>s. total press- 
 ure, which amounts to 60 Ibs. effective pressure, per 
 square inch, we find that from the preceding estimate, 
 the force necessary to draw the piston would be 5650 
 Ibs., whereas our own experiments on tjie locomotive en- 
 gine, the Atlas, which is of these dimensions, and works 
 at that pressure, demonstrate that the force necessary 
 to move, not only the two pistons, but all the rest of 
 the machinery, including the waste, &c., is but 48 Ibs. 
 applied to the wheel, or 283 Ibs. applied on the piston. 
 
8 
 
 It is then impossible to admit, that in steam-engines 
 the friction and losses can absorb the half, nor the 
 third, much less the f of the total power developed ; 
 and yet there do occur cases wherein, to reconcile the 
 practical effects with the theoretical ones thus calcu- 
 lated, it would be necessary to reduce the latter to the 
 fourth part, and even to less ; and what is more, it 
 often happens, that the same engine which in one case 
 requires a reduction of f , will not in other cases need 
 a reduction of more than about ^. This is observed 
 in calculating the effects of locomotive engines at very 
 great velocities, and afterwards at very small ones. 
 
 There is no doubt, -then, that the difference ob- 
 served between the theoretical effect of an engine 
 and the work which it really performs, does not arise 
 from so considerable a part of the applied force being 
 absorbed by friction and losses, but rather from the 
 error of calculating in this manner the theoretical 
 effect of the machine. In effect, this calculation sup- 
 poses that the motive force, that is, the pressure of 
 the steam against the piston or in the cylinder, is the 
 same as the pressure of the steam in the boiler ; 
 whereas we shall presently see, that the pressure in 
 the cylinder may be sometimes equal to that of the 
 boiler, sometimes not the half nor even the third of it, 
 and that it depends on the resistance overcome by the 
 engine. 
 
 3. Formula proposed by divers authors to deter ~ 
 mine the velocity of the piston under a given load, and 
 proofs of their inexactitude. We have said that this 
 problem was not resolved by the foregoing method. 
 
The following are the attempts made to that end by 
 another way. Tredgold, in his Treatise on Steam- 
 Engines (art. 127 and following), undertakes to cal- 
 culate the velocity of the piston from considerations 
 deduced from the velocity of the flowing of a gas, 
 supposed under a pressure equal to that of the boiler, 
 into a gas supposed at the pressure of the resistance. 
 He concludes from thence, that the velocity of the 
 piston would be expressed by this formula, 
 V = 6-5 V^- 
 
 in which V is the velocity in feet per second, and h 
 stands for the difference between the heights of two 
 homogeneous columns of vapour, one representing the 
 pressure in the boiler, the other that of the resistance. 
 But it is easily seen, that this calculation supposes the 
 boiler filled with an inexhaustible quantity of vapour, 
 since the effluent gas is supposed to rush into the 
 other with all the velocity it is susceptible of acquir- 
 ing, in consequence of the difference of pressure. 
 Now such an effect cannot be produced, unless the 
 boiler be capable of supplying the expenditure, how- 
 ever enormous it might be. This amounts conse- 
 quently to supposing that the production of steam in 
 the boiler is unlimited. But, in reality, this is far 
 from being the case. It is evident that the velocity of 
 the piston will soon be limited by the quantity of 
 steam producible by the boiler in a minute. If that 
 production suffice to fill the cylinder 200 times in a 
 minute, there will be 200 strokes of the piston per 
 minute ; if it suffice to fill it 300 times, there will be 
 300 strokes. It is then the vaporization of the boiler 
 
10 
 
 which must regulate the velocity, and no calculation 
 which shall exclude that element can possibly lead to 
 the true result ; consequently the preceding formula 
 cannot be exact. 
 
 This is why, in applying this formula to the case 
 of an ordinary locomotive engine of the Liverpool 
 Railway with a train of 100 tons, the velocity the 
 engine ought to assume is found to be 734 feet per 
 second, instead of twenty miles an hour, or five feet 
 per second, which is its real velocity. 
 
 Again, in his Treatise on Railways (page 83), Tred- 
 gold proposes the following formula, without in any 
 way founding it on reasoning or on fact : 
 
 V = 240 VHP 
 W 
 
 in which V is the velocity of the piston in feet per 
 minute, I the stroke of the piston, P the effective 
 pressure of the steam in the boiler, and W the resist- 
 ance of the load. But as this formula makes no 
 mention either of the diameter of the cylinder, or 
 of the quantity of steam supplied by the boiler in a 
 minute, it clearly cannot give the velocity sought ; for 
 if it could, the velocity of an engine would be the 
 same with a cylinder of one foot diameter as with a 
 cylinder of four feet, which expends sixteen times as 
 much steam. The area of heating surface, or the 
 vaporization of the boiler, would be equally indif- 
 ferent : an engine would not move quicker with a 
 boiler vaporizing a cubic foot of water per minute, 
 than with one that should vaporize but ^ or aV 
 Hence this formula is without basis. 
 
11 
 
 Wood, in his Treatise on Railways (page 351), pro- 
 poses the following formula also, without discussion, 
 
 m 
 
 where V is the velocity of the piston in feet per minute, 
 I the length of stroke of the piston, W the resistance 
 of the load, and P the surplus of the pressure in the 
 boiler, over and above what is necessary to balance 
 the load W. This formula being liable to the same 
 objections as the preceding, is also demonstrated in- 
 admissible a priori. 
 
 Consequently, of the three fundamental problems 
 of the calculation of steam-engines, two have received 
 inaccurate solutions by means of the coefficients, and 
 the third, as we have just seen, has received no solu- 
 tion at all. 
 
 4. Succinct exposition of the proposed theory. 
 After having made known the present state of science, 
 with regard to the theory and estimation of the effect- 
 ive power of steam-engines, it remains to exhibit the 
 theory we apply to them ourselves. 
 
 It is well known, that in every machine, when the 
 effort of the motive power becomes superior to the 
 resistance, a slow motion is created, which quickens 
 by degrees till the machine has attained a certain 
 velocity, beyond which it does not go, the motive 
 power being incapable of producing greater velocity 
 with the mass it has to move. Once this point at- 
 tained, which requires but a very short space of time, 
 the velocity continues the same, and the motion 
 remains uniform as long as the effort lasts. It is from 
 
12 
 
 this point only that the effects of engines begin to 
 be reckoned, because they are never employed but 
 in that state of uniform motion; and it is with 
 reason that the few minutes, during which the velo- 
 city regulates itself, and the transitory effects which 
 take place before the uniform velocity is acquired, are 
 neglected. 
 
 Now, in an engine arrived at uniform motion, the 
 force applied by the motive power forms strictly an 
 equilibrium with the resistance ; for if that force were 
 greater or less, the motion would be accelerated or 
 retarded, which is contrary to the hypothesis. In a 
 steam-engine the force applied by the motive agent 
 is nothing more than the pressure of the steam against 
 the piston, or in the cylinder. The pressure therefore 
 in the cylinder is strictly equal to the resistance of the 
 load against the piston. 
 
 Consequently the steam, in passing from the boiler 
 to the cylinder, may change its pressure, and assume 
 that which is represented by the resistance of the 
 piston. This fact alone exposes all the theory of the 
 steam-engine, and in a manner lays its play open. 
 
 From what has been said, the force applied on the 
 piston, or the pressure of the steam in the cylinder, 
 is therefore strictly regulated by the resistance of the 
 load against the piston. Consequently calling F the 
 pressure of the steam in the cylinder, and R the 
 resistance of the load against the piston, we have as a 
 first analogy, 
 
 P' = R. 
 
 To obtain a second relation between the data and 
 
13 
 
 the qusesita of the problem, we shall observe that 
 there is a necessary equality between the quantity of 
 steam produced, and the quantity expended by the 
 machine ; the proposition is self-evident. Now if 
 we express by S the volume of water vaporized in the 
 boiler per minute, and effectively transmitted to the 
 cylinder, and by ra the ratio of the volume of the 
 steam generated under the pressure P of the boiler, 
 to the volume of water which produced it, it is clear 
 that 
 
 mS 
 
 will be the volume of steam formed per minute in the 
 boiler. This steam passes into the cylinder, and there 
 assumes the pressure P' ; but if we suppose that, in 
 this motion, the steam preserves its temperature in 
 passing from the boiler to the cylinder, or from the 
 pressure P to the pressure P', its volume increases in 
 the inverse ratio of the pressures. Thus the volume 
 m S of steam furnished per minute by the boiler will, 
 when transmitted to the cylinder, become 
 
 .,. ^ ^ : -a..*. -. 
 
 On another hand, v being the velocity of the piston, 
 and a the area of the cylinder, a v will be the volume 
 of steam expended by the cylinder in a minute. 
 Wherefore, by reason of the equality which necessarily 
 exists between the production of the steam and the 
 expenditure, we shall have the analogy of 
 
 av=m S. ; 
 which is the second relation sought. 
 
14 
 
 Consequently, by exterminating P' from the two 
 equations, we shall have as a definitive analytic rela- 
 tion among the different data of the problem : 
 
 ~~a~ IT 
 
 This relation is very simple, and suffices for the 
 solution of all questions regarding the determination 
 of the effects or the proportions of steam-engines. 
 As we shall develope its terms hereafter, in taking 
 it up in a more general manner, we content ourselves 
 to leave it for the present under this form, which will 
 render the discussion of it easier and clearer. 
 
 The preceding equation gives us the velocity as- 
 sumed by the piston of an engine under a given 
 resistance R. If, on the contrary, the velocity of 
 the motion be known, and it be required to calculate 
 what resistance the engine will move at that velocity, 
 it will suffice to resolve the same equation with refe- 
 rence to R, which will give 
 
 mSP 
 
 Jx = . 
 
 a v 
 
 Finally, supposing the velocity and the load to be 
 given beforehand, and that it be desired to know what 
 vaporization the boiler should have to set the given 
 load in motion at the prescribed velocity, it will still 
 suffice to draw from that analogy the value of S, 
 which will be 
 
 g _ a v R 
 
 On these three determinations we rest for the moment, 
 because, as will soon appear, they form the basis of 
 
15 
 
 all the problems that can be proposed on steam- 
 engines. 
 
 5. New proofs of the exactitude of this theory, 
 and of the inaccuracy of tht ordinary mode of calcula- 
 tion. The theory just developed demonstrates that 
 the steam may be generated in the boiler at a certain 
 pressure P, but that in passing to the cylinder it 
 necessarily assumes the pressure R, strictly deter- 
 mined by the resistance to the piston, whatever the 
 pressure in the boiler may be. Consequently, accord- 
 ing to the intensity of that resistance, the pressure in 
 the cylinder, far from being equal to that in the boiler, 
 or from differing from it in a certain constant ratio, 
 may at times be equal to it, and at other times very 
 considerably different. Hence those who, in perform- 
 ing the ordinary calculation, consider the force applied 
 on the piston as indicated by the pressure in the 
 boiler, begin by introducing into their calculation an 
 error altogether independent of the real losses to 
 which the engine is liable. To this cause, then, and 
 not to the friction and losses, which can form but 
 the smallest part of it, must be attributed the enor- 
 mous difference which, in this mode of calculation, is 
 found between the theoretical effect of the engine, and 
 the work which it really executes. 
 
 We have already proved the mode of action of the 
 steam in the cylinder by the consideration of uniform 
 motion ; but in examining what passes in the engine, 
 we shall immediately find many other proofs. 
 
 1st. The steam, in effect, being produced at a 
 
16 
 
 certain degree of pressure in the boiler, passes into 
 the tube of communication, and thence into the 
 cylinder. It first dilates, because the area of the 
 cylinder is from ten to twenty-five times that of the 
 tube ; but it would promptly rise to the same degree as 
 in the boiler, were the piston immoveable. But as 
 the piston, on the contrary, opposes only a certain 
 resistance, determined by the load sustained by the 
 engine, it will yield as soon as the elastic force of the 
 steam in the cylinder shall have attained that point. 
 The piston, in consequence, will be a valve to the 
 cylinder. Hence the pressure in the cylinder can 
 never exceed the resistance of the piston, for that 
 would be supposing a vessel full of steam, in which 
 the pressure of the steam would be greater than that 
 of the safety valve. 
 
 2nd. Were it true, that the steam flowed into the 
 cylinder, either at the pressure of the boiler, or at 
 any other pressure which were to that of the boiler 
 in any fixed ratio, as the quantity of steam generated 
 per minute in the boiler would then flow at an iden- 
 tical pressure in all cases, and would consequently 
 fill the cylinder an identical number of times per 
 minute ; it would follow, that as long as the engine 
 should work with the same pressure in the boiler, it 
 would assume the same velocity with all loads. Now 
 we know that precisely the contrary takes place, the 
 velocity increasing when the load diminishes ; and 
 the reason of it is, that when the load is half, the 
 steam flowing also at a half pressure into the cylinder, 
 
17 
 
 and consequently acquiring a volume double what it 
 had before, will serve for double the number of strokes 
 of the piston. 
 
 3rd. Applying the same reasoning inversely, we per- 
 ceive that were the pressure in the cylinder really 
 bearing a constant ratio to that in the boiler, or if it 
 be preferred, constant so long as that in the boiler did 
 not vary, we should, in calculating the effort of which 
 the engine would be capable, always find it the same, 
 whatever be the velocity of the piston. Thus, at any 
 velocity whatever, the engine would always be capable 
 of drawing the same load ; which experience again 
 contradicts, for the greater the velocity of the piston, 
 the lower the pressure of the steam in the cylinder, 
 whence results, that the load of the engine lessens at 
 the same time. 
 
 4th. Another no less evident proof of this is easily 
 adduced. Were it true that the pressure in the 
 cylinder were to that in the boiler in any fixed pro- 
 portion, since the same locomotive engine always 
 requires the same number of revolutions of the wheel, 
 or the same number of strokes of the piston to tra- 
 verse the same distance, it would follow that, as long 
 as those engines worked at the same pressure, they 
 would consume iri all cases the same quantity of 
 water for the same distance. Now the quantity of 
 water, far from remaining constant, decreases on the 
 contrary with the load, as may be seen by the experi- 
 ments we have published on this subject. Here 
 therefore again it is proved, that, notwithstanding the 
 equality of pressure in the boiler, the density of the 
 
18 
 
 steam expended follows the intensity of the resistance, 
 that is to say, the pressure in the cylinder is regulated 
 by that resistance. 
 
 5th. Similarly, the consumption of fuel being in 
 proportion to the vaporization effected, it would fol- 
 low, if the ordinary theory were exact, that the quan- 
 tity of fuel consumed by a given locomotive, for the 
 same distance, would always be the same, with what- 
 ever load. Now we again find by experience that 
 the quantity of fuel diminishes with the load, con- 
 formably to the explanation we have given of the 
 effects of the steam in the engine. 
 
 6th. It is again clear that if the pressure in the 
 cylinder were, as it is believed, constant for a given 
 pressure in the boiler, that so soon as it was recog- 
 nised that an engine could draw a certain load with 
 a certain pressure, and communicate to it a uniform 
 motion, it would follow, that the same engine could 
 never draw a less load with the same pressure, with- 
 out communicating to it a velocity indefinitely ac- 
 celerated ; since the power, having been found equal 
 to the resistance of the first load, would necessarily 
 be superior to that of the second. Now experience 
 proves, that in the second case the velocity is greater, 
 but that the motion is no less uniform than in the 
 first ; and the reason of this is, that though the steam 
 may indeed be produced in the boiler at a greater or 
 less pressure, and that it matters little, yet on passing 
 into the cylinder, it always assumes the pressure of 
 the resistance, whence results that the motion must 
 remain uniform as before. 
 
19 
 
 7th. Finally, in looking over our experiments on 
 locomotives, it will be seen that the same engine will 
 sometimes draw a light load with a very high pressure 
 in the boiler, and sometimes a heavy load with a very 
 low pressure. It is then impossible to admit, as the 
 ordinary calculation supposes, that any fixed ratio 
 whatever has existed between the two pressures. 
 Moreover, the effect just cited is easy to explain, for 
 it depends simply on this, that in both cases the 
 pressure in the boiler was superior to the resistance on 
 the piston ; and it needed no more for the steam, 
 generated at that pressure or at any other, satisfying 
 merely that condition, to pass into the cylinder and 
 assume the pressure of the resistance. 
 
 It is then visible, from these various proofs, that 
 the pressure in the cylinder is strictly regulated by 
 the resistance on the piston, and by nothing else ; 
 and that any method like that of the coefficients in 
 the ordinary calculation, which tends to establish a 
 fixed ratio between the pressure in the cylinder and 
 that of the boiler, must necessarily be inexact. 
 
 $ 6. Verification of the two modes of calculation 
 by particular examples. We have sufficiently demon- 
 strated the want of basis of the ordinary calculation ; 
 but as the inaccuracy we have just exposed in that 
 method might by some be supposed to be of slight 
 importance, and they might conceive that, in practical 
 examples, it amounted to the obtaining of results, 
 which if not quite exact, were at least very near the 
 truth, we will now attempt to apply it to some par- 
 ticular cases. 
 
20 
 
 The coefficient of reduction for high pressure en- 
 gines, working without expansion and without con- 
 densation, not being given by the authors who have 
 treated on these subjects, we propose, in order to 
 determine it, the two following facts, which took place 
 before our eyes : 
 
 i. The Leeds locomotive engine, which has two 
 cylinders eleven inches in diameter, stroke of the 
 piston sixteen inches, wheel five feet in diameter, drew 
 a load of 88 '34 tons, in ascending a plane inclined 
 1 in 1300, at the velocity of 20'34 miles an hour; 
 the effective pressure in the boiler being 541fos. per 
 square inch, or the total pressure 68*71 ibs. per square 
 inch. 
 
 ii. The same day, the same engine drew a load of 
 38' 52 tons in descending a plane inclined 1 in 1094, at 
 the velocity of 29 '09 ; the pressure in the boiler being 
 precisely the same as in the preceding trial, and the 
 regulator open to the same degree. These experiments 
 may be seen in pages 233 and 234 of our Treatise on 
 Locomotives. 
 
 If on one hand be reckoned, according to the 
 ordinary method, the theoretic effort applied to the 
 piston, and on the other hand the effect really pro- 
 duced, viz., the resistance opposed by the load plus 
 that of the air against the train, we find, on refer- 
 ring the pressure and the area of the pistons to the 
 foot square : 
 
21 
 
 1st case. Theoretic effort applied on the 
 piston, according to the ordinary 
 calculation 1*32 x (6871 x 144) . 13,060 fts. 
 Real effect .' . * . . . . . 8,846 
 
 Coefficient of correction 0'68 
 
 2nd case. Theoretic effort, the same as 
 
 above 13,060 
 
 Real effect . ... 1 *. ' . . 6,473 
 
 Coefficient of correction . . 0*50 
 The mean coefficient, to apply to the total pressure, 
 to convert the theoretic effects to the practical, is 
 then -59. 
 
 We find, then, three very different coefficients : 
 choose the first case, then an error occurs in the 
 second ; choose the second, and an error must arise in 
 the first ; by taking the third, you will only divide 
 the error between the two. In every way an error is 
 inevitable, and that alone suffices to prove that every 
 method, like the ordinary one, which consists in the 
 use of a constant coefficient, is necessarily inexact, 
 whatever be the coefficient chosen, and to whatever 
 engine the application be made ; for it is evident that 
 the same fact would occur in every kind of steam- 
 engine. Only that it might be less marked, if the 
 velocities at which the engine were taken were less 
 different ; and this is what has hitherto prevented the 
 error of this method from being perceived, for all the 
 engines of the same system being imitated from each 
 
22 
 
 other, and moving nearly at the same velocity, the 
 same coefficient of correction seems tolerably to suit 
 them, from the factitious limit that had been laid down 
 for the speed of the piston. 
 
 Besides, in stationary engines, one cannot, for want 
 of precise determinations of the friction, disengage in 
 the result the part which is really attributable to it 
 from that which constitutes a positive error. But 
 here we may easily be convinced that neither of these 
 coefficients of correction represents, as the ordinary 
 theory would have it, the friction, losses, and various 
 resistances of the machine ; for direct experiments 
 made on the engine under consideration, and noted in 
 our Treatise on Locomotives, enable us to estimate 
 separately all these frictions, losses, and resistances. 
 Reckoning, then, the friction of the engine at 82 fts., 
 taking account besides of its additional friction per ton 
 of load, and adding for each case the pressure subsist- 
 ing on the opposite side of the piston by the effect of 
 the blast pipe, we find, as the sum of the friction and 
 indirect resistances 
 
 1st case.- Friction 1,257 ft>s. 
 
 or 10 of the theoretic result. 
 
 2nd case. Friction 873 fos. 
 
 or '07 of the theoretic result. 
 
 Thus we see that in each of the two cases, the fric- 
 tion and indirect resistances, omitted in the calcula- 
 tion, do not in reality amount to more than 10 or 7 
 hundredths of the theoretic result ; and if we should 
 be disposed to add to that ^ or '05, for the filling of 
 
23 
 
 the vacant spaces of the cylinder, which we could not 
 estimate in ffis., it will be *15 and *12; whereas the 
 coefficients of correction would raise them to *32 in 
 one case, and "50 in the other; that is, to 2 and 4 
 times what they really are. If, then, from these co- 
 efficients, be deducted the true value of the friction 
 and losses, it will appear that the theoretic error, 
 introduced into the calculation under the denomination 
 of friction, is 17 per cent, of the total power of the 
 engine in the one case, and 38 per cent, in the other. 
 
 But it is to be remarked, that, from the preceding 
 evaluations, viz., of the direct resistances first, and then 
 of the friction and indirect resistances, we have, for 
 each of the two cases in question, the sum of the total 
 effects really produced by the machine, as follows : 
 
 1st case. Direct resistances .... 8,846 Ibs. 
 Friction . .... . . 1,257 
 
 10,103 
 
 2nd case. Direct resistances . . . . 5,473 
 Friction 873 
 
 6,346 
 We are therefore enabled now to compare these 
 
 effects produced with the results either of the ordinary 
 
 calculation or of our theory. 
 
 1. In applying the ordinary calculation with the 
 
 mean coefficient ' 56 determined above, and comparing 
 
 its result with the real effect, we find 
 
24 
 
 1st case. Effort applied on the piston, 
 according to the ordinary calcula- 
 tion, 1-32 x (6871 x 144) x '59 . 7,705 fos. 
 Effect produced, including friction 
 
 and every resistance . . V. . 1 0, 1 03 
 
 Error over and above the friction and 
 
 resistances 2,398 
 
 2nd case. Effort applied on the piston, 
 according to the ordinary calcula- 
 tion, the same as above . . . 7,705 tbs. 
 Effect produced, including friction 
 
 and every resistance - .... 7,346 
 
 Error over and above the friction and 
 
 resistances 359 
 
 Mean error of the two cases . . . 1,378 
 It is then evident what error would have been com- 
 mitted in calculating the effects of this engine from 
 the coefficient * 59 ; but it is equally evident, that in 
 applying any other coefficient whatever, the error would 
 onl] transfer itself from one case to the other, without 
 ever disappearing ; and thus it is that the coefficient 
 59 has almost annulled the error of the second case, 
 by transferring it to the first. 
 
 To apply our formula with reference to the same 
 
 problem, viz. : 
 
 a R = mS P 
 
 a v 
 
 we have nothing more to do than to substitute for the 
 letters their value, taking care to refer all the measures 
 to the same unit. In making then these substitutions, 
 
25 
 
 which give P = 68- 71 x!44 tts., m = 411, a = 1'32, 
 and observing that the effective vaporization of the 
 engine has been S = 77 cubic foot of water per 
 minute, we find, 
 
 1st case. Effort applied by the engine at 
 the given velocity, according to our 
 
 411 x 0-77 x (6871x144) 
 theory, ~298~~ " 10 ' 507 %>* 
 
 Effect produced, including friction and 
 
 resistances, as above . ;. . 10,103 
 
 Difference 404 
 
 2nd case. Effort applied by the engine at 
 the given velocity, according to our 
 
 41 1 x Q- 77 x (68- 71x144) 
 theory,- 7,215 
 
 Effect produced, including friction, &c. 7,346 
 
 Difference 131 
 
 Mean difference of the two cases . 267 
 
 It appears, then, that by this method, the useful 
 effect is found with a difference only of 267 Ibs., a 
 very inconsiderable difference in experiments of this 
 kind, wherein so much depends on the management of 
 the fire. 
 
 2. To continue the same comparison of the two 
 theories, let it be required to calculate what quantity 
 of water per minute the boiler ought to vaporize, to 
 produce either the first effect or the second. The 
 method followed by the ordinary theory, again consists 
 in previously supposing that the volume described by 
 the piston has been filled with steam at the same 
 
26 
 
 pressure as in the boiler, and then in applying to it a 
 fractional coefficient to account for the losses. 
 
 Now, in the first case, the volume described by the 
 piston at the given velocity, is 1*32 x 298 =393 cubic 
 feet. Had this volume been filled with steam at the 
 pressure of the boiler, it would have required a vapor- 
 
 393 
 ization of -~yy ='96 cubic foot of water per minute. 
 
 But the real vaporization was but '77 ; wherefore, in 
 the first case, the coefficient necessary to lead from 
 the vaporization indicated by the ordinary calculation, 
 
 to the real vaporization, 7^- = '81. 
 
 In the second case, we find in the same manner, that 
 the coefficient should be * 55 ; whence, in this problem, 
 as in the preceding one, no constant coefficient what- 
 ever can suffice. 
 
 Performing, however, the calculation with the mean 
 coefficient, '68, we find, 
 
 1st case. Vaporization per minute, calculated by 
 the ordinary theory, with the coefficient, 
 
 1-32x298 
 
 ^p: x-68 -65 
 
 Real vaporization '77 
 
 Error '12 
 
 2nd case. Vaporization per minute, calculated 
 by the ordinary theory, with the coefficient, 
 1-32x434 
 
 TTT 
 Real vaporization , ... . . . . '77 
 
 Error '18 
 
27 
 
 The mean error committed is then -5- of the vaporiza- 
 tion, and being, as it is, a mean, it may, in extreme 
 cases, become f , or amount to half of the whole vapor- 
 ization. 
 
 This is the error committed in seeking a coefficient 
 expressly for the vaporization. But when the coeffi- 
 cient, determined in the preceding case, that is, by 
 the comparison of the theoretical and practical effects, 
 is used as a divisor, as by many authors it is, much 
 greater errors are induced, which we will show by an 
 example farther on. 
 
 In our theory, on the contrary, the vaporization 
 necessary to set in motion the resistance a R at the 
 velocity v, is given by the formula 
 ~ a R xv 
 
 ~^TP~- 
 
 We have then, 
 1st case. Vaporization calculated from our 
 
 10103x298 
 ^eory, 4nx(68 . nxl44 - 
 
 Real vaporization 77 
 
 Difference . . . . . ... . . . -03 
 
 2nd case. Vaporization calculated from our 
 
 7346x434 
 
 41 lx (68^71x144) ' 
 Real vaporization -77 
 
 Difference -01 
 
 3. Lastly, in the case of finding the velocity of the 
 piston, supposing the resistance to be given, any me- 
 thod similar to the ordinary one must inevitably lead 
 
28 . 
 
 to errors ; but we must dispense with comparison, 
 since this problem has never been resolved, and we 
 shall therefore in this case merely show the verification 
 of our own theory. The formula relative to this pro- 
 blem is 
 
 = mSP 
 
 We find then, 
 
 1st case. Velocity of the piston in feet per 
 minute, calculated from our theory, 
 41 lx -77 x (68-71 x!44) 
 
 10103 
 Real velocity 298 
 
 Difference ......... 12 
 
 2nd case. Velocity of the piston from our 
 
 411 x-77x(68-71 xl44) 
 theory, 1 jkda * * 
 
 Real velocity 434 
 
 Difference 8 
 
 It consequently appears, that in each of the three 
 problems in question, our theory leads to the true re- 
 sult ; whereas the ordinary theory, besides that it leaves 
 the third problem unresolved, may, in the other two, 
 lead to very serious errors. 
 
 Before abandoning this comparison, we request at- 
 tention to an effect, in calculating by the ordinary 
 theory, which we have already mentioned, but which 
 is here demonstrated, viz., that this calculation gives 
 the same force applied by the engine in both the cases 
 considered, notwithstanding their difference of velocity; 
 
29 
 
 and such will always be the result, since the calcula- 
 tion consists merely in multiplying the area of the 
 piston by the pressure in the boiler, and reducing the 
 product in a constant proportion. This theory there- 
 fore maintains, in principle, that the engine can always 
 draw the same load at all imaginable velocities. Again 
 we see, that, in the same calculation of the load or 
 effort applied, the vaporization of the engine does not 
 appear, which would imply that the engine would 
 always draw the same load at all velocities, whatever 
 might be the vaporization of the boiler, which is in- 
 admissible. 
 
 We shall also remark, that in calculating by the 
 ordinary theory the vaporization of the engine, no 
 notice is taken of the resistance which the engine is 
 supposed to move ; so that the vaporization necessary 
 to draw a given load would be independent of that load 
 another result equally impossible. 
 
 To these omissions, therefore, or rather to these 
 errors in principle, are to be attributed the variations 
 observable in the results given of the ordinary theory 
 in the examples proposed. 
 
PART II. 
 
 ANALYTIC THEORY OF THE STEAM-ENGINE. 
 
 ARTICLE I. 
 
 CASE OF A GIVEN EXPANSION WITH ANY VELOCITY 
 OR LOAD WHATEVER. 
 
 $ 1 . Of the change of temperature of the steam during 
 its action in the engine. When an engine is at work, 
 the steam is generated in the boiler at a certain 
 pressure ; it passes from thence into the cylinder, 
 assuming a different pressure, and, in an expansive 
 engine, the steam, after its separation from the boiler, 
 continues to dilate itself more and more in the cylinder, 
 till the piston is at the end of the stroke. It is 
 generally supposed, that in all the changes of pressure 
 which the steam may undergo, its temperature remains 
 the same ; and it is consequently concluded, that 
 during the action of the steam in the engine, the 
 density and volume of that steam follow the law of 
 Mariotte, namely, that its volume varies in the inverse 
 
31 
 
 ratio of the pressure. This supposition greatly sim- 
 plifies the formulae ; but, as reason and experience 
 prove it to be altogether inexact, we are compelled to 
 renounce it, and will substitute in its place another 
 law, deduced from observation of the facts them- 
 selves. 
 
 We have recognised in a numerous series of ex- 
 periments, by applying simultaneously a manometer 
 and a thermometer, both to the boiler of a steam- 
 engine, and also to the tube through which the steam, 
 after having terminated its effect, escaped into the 
 atmosphere, that during all its action in the engine 
 the steam remains in the state denoted by the name of 
 saturated steam, that is, at the maximum density for 
 its temperature. The steam in fact was produced in 
 the boiler at a very high pressure, and escaped from 
 the engine at a very low one ; but on its issuing forth, 
 as well as at the moment of its formation, the ther- 
 mometer indicated the temperature corresponding to 
 the pressure marked by the manometer, as if the steam 
 were immediately generated at the pressure it had at 
 that moment. 
 
 Thus during its whole action in the engine, the 
 steam remains constantly at the maximum density for 
 its temperature. 
 
 Now, in all steams, the volume depends at once on 
 the pressure and the temperature ; but in the steam at 
 the maximum density, the temperature itself depends 
 on the pressure. It should then be possible to express 
 the volume of steam of maximum density, in terms of 
 the pressure alone. 
 
32 
 
 The equation which gives the volume of the steam 
 in any state whatever, in terms of the pressure and 
 temperature, is very simple : it is deduced from Ma- 
 riotte's law combined with that of M. Gay-Lussac. 
 The equation which gives the temperature in terms of 
 the pressure, for the steam at the maximum density, 
 is also known : it has heen deduced from the fine 
 experiments of Messrs. Arago and Dulong on steam 
 at high pressures, and from those of Southern and 
 other experimenters on steam produced under low 
 pressures. By eliminating then the temperature in 
 these two equations, we shall obtain the analogy re- 
 quired, which will give immediately, with regard to 
 steam at the maximum density, for its temperature, the 
 volume in terms of the pressure alone. 
 
 But here arises the difficulty. The equation of the 
 temperatures is not invariable ; or rather, the same 
 equation does not apply to all points of the scale. 
 To be used with accuracy, it requires to be changed 
 according as the pressure is under that of one atmo- 
 sphere, or comprised between one and four atmospheres, 
 or again if it be above four atmospheres. Now when 
 the steam is acting in an engine, it may happen, 
 according to the load, or to other conditions of its 
 motion, that the steam generated at first at a very high 
 pressure, may act or be expanded in the engine some- 
 times at a pressure exceeding four atmospheres, some- 
 times at a pressure less than four atmospheres, but 
 yet exceeding one, and sometimes at a pressure under 
 that of one atmosphere. It is impossible then to know 
 which of the three formulae is to be used in the elimi- 
 
33 
 
 nation ; and consequently it is impossible by this 
 means to attain a general formula representing the 
 effects of the engine in all cases. 
 
 Moreover, were either one of these formulae adopted, 
 the high radical quantities they contain would so 
 complicate the calculations as to render them unfit for 
 practical purposes. And it is to be remarked, that 
 these divers formulae, after all, are not the expression 
 of the true mathematical law which connects the tem- 
 perature and the pressure in saturated steam, but 
 merely empirical relations, which experiment alone 
 has demonstrated to have a greater or less degree of 
 approximation. 
 
 A formula of temperatures given by M. Biot is 
 indeed adapted to all points of the scale, and may be 
 useful in a great number of delicate researches relative 
 to the effects of steam ; but as it gives only the 
 pressure in terms of the temperature, and is, from its 
 form, incapable of the inverse solution, namely, the 
 general determination of temperatures in terms of the 
 pressure, it is unfit for the elimination proposed. 
 
 Under these circumstances the only resource is to 
 seek a direct relation in terms of the pressure alone, 
 whose results shall represent immediately those of the 
 two preceding formulas combined ; that is, to calculate 
 first by means of those formulae a table of volumes of 
 the steam, and then to seek a direct and simple re- 
 lation to represent those results. This we have done. 
 
 M. Navier had proposed a formula for this purpose. 
 But that formula, though sufficiently exact in high 
 pressures, differs widely from experience in pressures 
 
 c 
 

 34 
 
 below that of the atmosphere, which are useful in con- 
 densing engines ; and it is possible to find one much 
 more exact for non-condensing engines, namely, that 
 we are about to offer. We propose then, for this 
 purpose, the following formulae, in which p represents 
 the pressure of the steam expressed in pounds per 
 square foot, and p the ratio of the volume of the steam 
 to that occupied by the same weight of water : 
 
 Formula for high or lo\\n 10000 
 
 pressure engines with S M =0-4227 +0-002580 
 condensation J 
 
 Formula for high press- "| 10000 
 
 we non-condensing en- [. M = 1 . 421+0 . 0023 
 gmes J 
 
 The first formula is equally suitable to pressures 
 above and below that of the atmosphere, at least within 
 the limits likely to be considered in applying it to 
 condensing steam-engines. Those limits are eight or 
 ten atmospheres for the highest pressures ; and eight 
 or ten pounds per square inch for the lowest, in con- 
 sequence of the friction of the engine, the pressure 
 subsisting against the piston after imperfect con- 
 densation in the cylinder, and the resistance of the 
 load. Within these limits then the proposed formula 
 will be found to give very approximate results. 
 
 This first formula might also be applied, without any 
 error worthy of notice, to non-condensing engines. 
 But as, in these, the steam can scarcely operate with a 
 pressure less than two atmospheres, by reason of the 
 friction of the engine and the resistance of the load, it 
 is needless to require of the formula exact results of 
 volumes for pressures under two atmospheres. 
 
35 
 
 In this case then the second formula will be found 
 to give those results with much greater accuracy, and 
 will consequently be preferred in practice. This will 
 be readily recognised in a table annexed to the work, 
 presenting a comparison of the volume of the steam 
 calculated by the ordinary formulae in terms of the 
 pressure and temperature, and by the proposed formulae 
 in terms of the pressure alone. 
 
 We state then generally this analogy : 
 
 = 1_ , x 
 
 n + qp 
 
 Consequently, if the steam pass in the engine, 
 from a certain volume m to another known volume m, 
 and thereby abandon its primitive pressure F, to as- 
 sume an unknown pressure p, it is easy to recognise 
 that the following relation will exist between those 
 two pressures, and will serve to determine the un- 
 known quantity p, viz. : 
 
 p m' 1 n fA 
 
 "P 7 " ~7~* 1 -nm' ' 
 
 This is the relation which we substitute in lieu of 
 that hitherto employed, and according to which the 
 volume appears to vary in the inverse ratio of the 
 pressure. It will be observed that such an hypothesis 
 may be deduced from the analogy we have just offered, 
 
 7/iP 
 
 by making n = 0, and q = , m being the volume, 
 
 and P the pressure of the steam in the boiler ; for it 
 is plain that we shall then have, 
 
 m P 
 
 that is to say, the volumes are inversely as the 
 pressures. 
 
36 
 
 $ 2. Of the divers problems which present themselves 
 in the calculation of steam-engines. We distinguish 
 three cases in an engine : that wherein it works with 
 a given rate of expansion of the steam, and with a load 
 or a velocity indefinite ; that in which it works with a 
 given rate of expansion, and with the load and velocity 
 proper to produce its maximum of useful effect with 
 that expansion ; and lastly that wherein, the engine 
 having been previously regulated for the expansion of 
 the steam most favourable in that engine, it bears, 
 moreover, the load most advantageous for that expan- 
 sion ; which, consequently, produces the absolute 
 maximum of useful effect in the engine. 
 
 We have said that the three fundamental problems 
 of the calculation of steam-engines consist in finding 
 successively the velocity, the load, and the vaporiza- 
 tion of the engine. After the solution of these three 
 problems, that which first presents itself, as a corollary 
 to them, consists in determining the useful effect of 
 the engine, which may be expressed under six different 
 forms, viz. : by the work done, or the number of 
 pounds raised one foot high by the engine in a minute ; 
 by the horse power of the engine ; by the actual duty 
 or useful effect of one pound of coal ; by the useful 
 effect of a cubic foot of water converted into steam ; 
 and by the number of pounds of coal, or of cubic feet 
 of water, that are necessary to produce one horse 
 power. 
 
 Another research, in fine, no less important, is the 
 rate of expansion at which the steam must work in an 
 engine, in order that it may produce given effects. 
 
37 
 
 We shall present successively the solution of all these 
 questions. 
 
 The various problems will be resolved in each of 
 the three cases above mentioned. In the two last, the 
 question will be to calculate the rate of expansion, the 
 velocity, the load, and the effects which correspond to 
 the maximum of, relative or absolute, useful effect of 
 the engine. 
 
 In the ordinary calculations of steam-engines, the 
 solution of three questions only had been attempted, 
 viz., to find the load, the vaporization, and the useful 
 effect, under its different forms ; which solution is, as 
 we have seen, faulty. As to the determining of the 
 velocity for a given load, and that of the rate of expan- 
 sion for given effects, the calculation of these had not 
 been proposed. Moreover, the very nature of the 
 theory employed in those calculations did not allow of 
 distinguishing, in the machine, the existence of the 
 three cases which are really found in it. The distinc- 
 tion we establish may, therefore, at first appear ob- 
 scure, expressed, as it is, in general terms, and inclu- 
 ding relations unusual in the consideration of steam- 
 engines ; but, on a closer view of the question, these 
 relations will be seen to be of indispensable necessity, 
 in order to calculate with exactitude either the effects 
 or the proportions of steam-engines of all systems. 
 
 3. Of the velocity of the piston under a given load. 
 To embrace at once the most complete mode of 
 action of the steam, we will suppose an engine work- 
 ing by expansion, by condensation, and with an in- 
 definite pressure in the boiler ; and to pass on to 
 
38 
 
 unexpansive or uncondensing engines, it will suffice to 
 make the proper suppressions or substitutions in the 
 general equations. 
 
 From what has been already shown of our theory, 
 the relations sought between the various data of the 
 problem are necessarily deduced from two general con- 
 ditions : the first expressing that the engine has at- 
 tained a uniform motion, and consequently that the 
 quantity of labour impressed by the motive power is 
 equal to the quantity of action developed by the 
 resistance : the second, that there is a necessary 
 equality between the emission of steam through the 
 cylinder and the production by the boiler. 
 
 The limits of this extract will not allow us to de- 
 velop those calculations, simple as they may be ; but 
 that the proceeding may be understood, we shall state 
 that, expressing by P the pressure of the steam in the 
 boiler, and by K the pressure of the same steam in 
 the cylinder before the expansion, by L the length of 
 stroke of the piston, and by L' the portion traversed 
 at the moment the expansion begins, by a the area of 
 the piston, and by c the clearance of the cylinder, or 
 the space at each end of the cylinder beyond the portion 
 traversed by the piston, and which necessarily fills 
 with steam at each stroke ; lastly, by r the resistance 
 of the load, by p the pressure subsisting on the other 
 side of the piston after imperfect condensation, by / 
 the friction of the engine when not loaded, and by 
 S the increase of that friction per unit of the load r, 
 these four forces, as well as the pressures, being more- 
 over referred to the unit of surface of the piston ; the 
 
39 
 
 first of the above conditions produces the following 
 analogy : 
 
 P'(L' + c) f L' L + c T l 
 
 - - v ' ; ^ : F7 - -flog. =-7-- -- na L >- = 
 l-a(L' + c) L L + c L + c J 
 
 This equation expressing that the labour developed by 
 the mover is found entire in the effect produced, be 
 it remarked, that it is not essentially necessary for the 
 motion to be strictly uniform. It may equally be 
 composed of equal oscillations, beginning from no 
 velocity, and returning to no velocity, provided the 
 change of velocity take place by insensible degrees, so 
 as to avoid the loss of vis viva, and that the successive 
 oscillations be performed in equal times. 
 
 As to the second condition of the motion ; if we 
 denote by S the volume of water vaporized by the 
 boiler in a unit of time and transmitted to the cylinder, 
 by m the volume of the steam formed under the press- 
 ure P of the boiler, compared with the volume of the 
 same weight of water unvaporized, and by v the velocity 
 of the piston, the equality between the production of 
 the steam and its consumption will be found to fur- 
 nish the second general analogy : 
 
 Consequently, by eliminating P' from these two equa 
 tions, and writing, for greater simplicity, 
 
 J-T-. -- naL> 
 L -t-e 
 
 L' 
 
 we find definitively : 
 

 40 
 
 ... (1) 
 
 an equation which gives the velocity of the motion in 
 terms of the load and of the other data of the problem. 
 
 This formula is quite general, and suits every kind 
 of steam-engine with continued motion. If the engine 
 be expansive, L' will be replaced by its value corre- 
 sponding to the point of the stroke where the steam 
 begins to be intercepted ; if the engine be unexpansive, 
 it will suffice to make L'= L, which will give at the 
 same time K = 1. If it be a condensing engine, p 
 must stand for the pressure of condensation ; if it be 
 not a condenser, p will represent the atmospheric press- 
 ure. And finally, the quantities n and q will have, 
 according to the case considered, the above-mentioned 
 value. 
 
 4. Of the load and useful effects of the engine. 
 If, instead of seeking the velocity in terms of the load 
 it be required, on the contrary, to know the load suit- 
 able to a given velocity, the same equation resolved 
 with reference to r becomes, 
 L 
 
 nav 
 
 3. To find the vaporization of which the engine 
 ought to be capable, in order to put in motion a re- 
 sistance r with a known velocity v, the value of S 
 must be drawn from the same analogy thus : 
 
 S = ?.a 
 4. The useful effect produced by the machine, in 
 
41 
 
 the unit of time } at the velocity v, is evidently arv. 
 Hence that useful effect will have for its measure, 
 
 5. If it be desired to know the useful effect, in 
 horse power, of which the engine is capable at the 
 velocity v or when loaded with the resistance r, it 
 suffices to observe that what is called one horse power 
 represents an effect of 33,000 fts. raised one foot per 
 minute. All consists then in referring the useful 
 effect produced by the engine in a unit of time, to the 
 new unity just chosen, viz. to one horse power ; and 
 it will consequently suffice to divide the expression 
 already obtained in the equation (4) by 33,000. Thus, 
 the useful effect in horse power will be, 
 
 uHP. = -0i _____ (5) 
 33000 
 
 6. We have just expressed, in the two preceding 
 questions, the effect of the engine by the work which 
 it is capable of performing. We are now on the con- 
 trary about to express that effect by the force which 
 the engine expends to produce a given quantity of 
 work. The useful effect of the equation (4) being that 
 which is due to the volume of water S converted into 
 steam, in the unit of time, if we suppose that in the 
 same unit of time N pounds of fuel be consumed, it 
 is clear that the useful effect produced by each pound 
 of fuel will be the Nth part of the above effect. It 
 will then be, 
 
 uE. 1 ft. co. = ....... (6) 
 
42 
 
 To apply this formula, it will suffice to know the 
 quantity of coal consumed in the furnace per minute, 
 that is, during the production of the vaporization S ; 
 and this datum may be deduced from a direct experi- 
 ment on the engine, or from known experiments on 
 boilers of a similar construction. 
 
 7. The useful effect of the equation (4) being that 
 which proceeds from the vaporization of the volume 
 of water S, if it be required to know the useful effect 
 that will be produced by each cubic foot of water, or 
 by each unit of S, it will be sufficient to divide the 
 total effect uE. by the number of units in S. It will 
 then be, 
 
 uE.lft.wa.= ^l ..... (7) 
 o 
 
 8. In the sixth problem we have obtained the 
 useful effect produced by one pound of fuel. We 
 may then, by a simple proportion, deduce from thence 
 the quantity of fuel necessary to produce one horse 
 power, viz. 
 
 9. And similarly, the quantity or volume of water 
 necessary to produce one horse power will be, 
 
 Q. wa.for 1 hp. = 330 S ...... (9) 
 
 UJii. 
 
 $ 5. Of the expansion of steam, to be adopted in an 
 expansive engine, in order to produce wanted effects. 
 
 10. Finally, if it be required to know what rate of 
 expansion the engine must work at, in order to obtain 
 from it determined effects, the value of L' must be 
 
43 
 
 drawn from equation (1). It will be given by the 
 formula, 
 
 v L'+c 
 
 -= -- nav j 
 
 This formula not being of a direct application, we 
 annex to the work a table which gives its solutions for 
 the expansion from hundredth to hundredth, with a 
 very short calculation. 
 
 We confine ourselves to these inquiries as being 
 those which may most commonly be wanted ; but it is 
 clear that by means of the same general analogies, any 
 one whatever of the other quantities which figure in 
 the problem may be determined, as the case may 
 require. Thus, for instance, may be determined the 
 area of the piston, or the pressure in the boiler, or the 
 pressure in the condenser, corresponding to determined 
 effects of the machine, as has been done for locomo- 
 tives in our work on that subject. 
 
 ART. II. 
 
 CASE OF THE MAXIMUM USEFUL EFFECT, WITH 
 A GIVEN RATE OF EXPANSION. 
 
 1. Of the velocity of the maximum -useful effect. 
 We have resolved the above problems in all their 
 generality, that is, supposing the engine to move any 
 load whatever with any velocity whatever, under this 
 

 44 
 
 single condition, that the load and the velocity be 
 compatible with the capability of the machine. The 
 question is now to find what velocity and what load 
 are most advantageous for the working of the engine, 
 and what are the effects which, in this case, may be 
 expected from it ; that is to say, its maxima effects for 
 a given rate of expansion. 
 
 1. In examining the general expression of the 
 useful effect produced by the engine at a given velo- 
 city, we perceive that the expression attains its maxi- 
 mum for a given rate of expansion when the velocity 
 is a minimum ; now from the equation (B) the 
 smallest value of v will be given by P / =P.' The 
 velocity corresponding to the maximum useful effect 
 will therefore be, 
 
 ' * L . (ii) 
 
 ' 
 
 , 
 
 Let us however remark, that, mathematically speaking 
 the pressure P' of the steam in the cylinder can never 
 be quite equal to P, which is the pressure in the 
 boiler ; because there exist between the boiler and 
 the cylinder conduits through which the steam has to 
 pass, and the passage of these conduits offers a certain 
 resistance to the motion of the steam ; whence results 
 that there must exist, on the side of the boiler, a trifling 
 surplus of pressure equivalent to the overcoming of 
 the obstacle. But as we have proved elsewhere, that, 
 with the usual dimensions of engines, this difference 
 of pressure is not appreciable by the instruments used 
 to measure the pressure in the boiler, the introduction 
 of it into the calculations would render the formulae 
 
45 
 
 more complicated without making them more exact. 
 For this reason we neglect that difference here. 
 
 The velocity given by the preceding equation is, 
 then, that at which the engine will produce its maxi- 
 mum effect for a given expansion. This velocity will 
 result from the condition P'=P, or reciprocally, when 
 this velocity takes place in the engine, the steam 
 enters the cylinder with full pressure, that is, with the 
 same pressure it has in the boiler. It is necessary to 
 remark that the velocity of full pressure will not be 
 the same for all engines ; on the contrary, it will vary 
 in direct ratio with the vaporization, and in the in- 
 verse ratio of the area of the cylinder. It may then 
 occur to be, in one engine, the half or the double of 
 what it would be in another ; which shows that it is 
 an error to believe that, because the piston of sta- 
 tionary engines does not in general exceed a certain 
 velocity of from 150 to 250 English feet per minute, 
 the steam of the boiler necessarily reaches the cylinder 
 with no change of pressure. 
 
 It is easy to be seen that a fixed limit, whatever it 
 may be, cannot in this respect suit all engines ; and 
 that the only means of knowing the velocity of the 
 maximum effect, or of full pressure of an engine, is to 
 calculate it directly for that engine. Such is the 
 object of the formula we have just given. This for- 
 mula, moreover, is of a remarkable simplicity, and 
 requires no other experimental knowledge than that 
 of the production of steam of which the boiler is 
 capable. 
 
 2. Of the load and maximum useful effect of the 
 
46 
 
 engine. 2. The useful resistance which the machine is 
 capable of putting in motion at its velocity of the 
 maximum effect above, is to be drawn from equation 
 (2), substituting for v the value just obtained. Calling 
 the load / we shall find it expressed by 
 
 and it is at the same time visible that this load is the 
 greatest the engine can put in motion with the given 
 expansion L', for it corresponds to the lowest value of 
 v in equation (2). Thus, the greatest effect of the 
 machine, with a given rate of expansion, is attainable 
 by working the machine at its smallest velocity and 
 with its maximum load. 
 
 It will be observed, that this equation may be used 
 to determine the friction of the engine without a load, 
 and its additional friction per unit of the load, upon 
 the same principles that we have employed in our 
 Treatise of Locomotive Engines for similar determina- 
 tions. This is also the mode we propose for steam- 
 engines of every system. 
 
 3. The vaporization necessary to an engine, in 
 order to exert a certain maximum effort / at its 
 minimum velocity v, will be given by equation (3), by 
 substituting in it r and v, or will be drawn more 
 simply from equation (11), thus : 
 
 S=(n + qP)m/. L/ T +C ---- (13) 
 Li 
 
 4. The maximum of useful effect producible in the 
 unit of time, by an engine working with a given ex- 
 pansion, will be known by formula (4), by introducing 
 
47 
 
 for v the velocity proper to produce that effect. Thus 
 is found, 
 
 max.uE. = - ---- - - I ( + /) I ..... (14) 
 
 L' + c (1+8) (n + qP) I K U^/'I 
 
 It will be observed that this maximum useful effect 
 depends particularly on the quantity of water S, eva- 
 porated per minute in the boiler. Hence we see plainly 
 the error of those who pretend to calculate the useful 
 effect or the power of engines from the area and the 
 velocity of the piston, which they set in the place of 
 the vaporization produced ; this vaporization not only 
 entering not into their calculation, but forming no part 
 of their observations. 
 
 5. The useful effect, in horse power, of the engine 
 will be expressed by 
 
 33000 
 
 6. T. 8. 9. The various measures of the useful 
 effect will here be deduced from equations similar to 
 those (6), (7), (8), and (9). 
 
 10. The expansion at which the engine ought to 
 be regulated, in order to draw a given load at the 
 most advantageous velocity, or producing the maxi- 
 mum of useful effect with that load, will be derived 
 from equation (12), which gives, 
 
 L' + cr L' , L + c-j _ (1+*) r+p+f 
 
 ~LlL' + c 3 'L'+c/~ P 
 
 (20) 
 
 and the solutions of this formula will be found imme- 
 diately, and without calculation, by means of the table 
 given above, as suggested by equation (10). 
 
48 
 
 ART. III. 
 
 CASE OF THE ABSOLUTE MAXIMUM OF USEFUL 
 EFFECT. 
 
 The preceding inquiries suffice for engines work- 
 ing without expansion, merely by making L'=L ; be- 
 cause those engines fall under the case of expansion 
 fixed a priori. But it is otherwise with engines in 
 which the rate of expansion may be varied at will. 
 We have seen that, for a given expansion, the most 
 advantageous way of working the engine is to give it 
 the maximum load, which is calculated a priori from 
 equation (12). Hence we know what load is to be 
 preferred for every rate of expansion. But the ques- 
 tion now is to determine, among the various rates of 
 expansion of which the engine is susceptible, each 
 accompanied by its corresponding load, which will 
 produce the greatest useful effect. 
 
 For this purpose we must recur to equation (14), 
 which gives the useful effect produced with a maxi- 
 mum load /, and seek among all the values assignable 
 to L', that which will raise the useful effect to a 
 maximum. Now by making the differential coefficient 
 of that expression, taken with reference to L', equal 
 to nothing, we find as the condition of the maximum 
 sought : 
 
 . L + c / L' 
 
 L ) 
 
49 
 
 This equation will be resolved in the same manner 
 as the equations (10) and (20), by means of the table 
 already given ; and after having found the value of 
 
 > 
 
 , it will be introduced in the equations of article 
 JL 
 
 n. ; and the corresponding velocity, load, and useful 
 effects, will be determined. 
 
 However, as the supposition of n=o, q= -- , that 
 
 Tfl Jr 
 
 is to say, the supposition that the steam preserves its 
 temperature during its action in the engine, will give 
 a sufficient approximation in a great many cases, we 
 present here the corresponding results of all the for- 
 mulae. They will show, already to a very near degree, 
 the maximum absolute effects which it is possible to 
 obtain from an engine, in adopting simultaneously the 
 most advantageous rate of expansion and the most 
 advantageous load. 
 
 " - m S _ L P __ Velocity of the absolute maximum 
 ~~' useful effect. ' 
 
 (22) ar" = a - - Load of the piston corresponding 
 
 > T , < ^ to the absolute maximum useful 
 
 log __ (L + C > P effect. 
 
 LCp+/) + PC 
 
 (23) S = ^. MJP+/H-P* Vaporization. 
 
 m L P 
 
 (24) ab.max.u. E = ay J' v 
 
 1 + 8 Absolute maximum of useful ef- 
 fect ' 
 
 U -HP ab ' max ' u ' E Absolute maximum of useful force 
 
 33000 in horse power. 
 
 /->ru T i k (/*+./) ^ ate ^ expansion which produces 
 
 ~Y~ these effects, 
 
 D 
 
50 
 
 The four determinations of the useful effects of a 
 given quantity of fuel or water will be furnished by 
 equations similar to those (6), (7), (8), and (9). 
 
 The only remark we shah 1 make on the subject of 
 these formulse is, that the load suitable to the pro- 
 ducing of the absolute maximum useful effect is not 
 the maximum load that may be imposed on the engine. 
 In effect, from equation (12), we know that the maxi- 
 mum load for the engine takes place when L' = L, 
 and not when 
 
 Thus the greatest possible load of the engine is that 
 of the maximum useful effect without expansion ; but 
 by applying a lighter load, that of equation (22), and 
 at the same time the expansion of equation (30), a 
 still greater useful effect will be obtained. 
 
PART III. 
 
 APPLICATION OF THE FORMULA TO THE VARIOUS 
 SYSTEMS OF STEAM-ENGINES. 
 
 WE shall not give here the applications to different 
 systems of steam-engines, which are developed in this 
 part of the work. We shall confine ourselves to what 
 concerns Watt's steam-engines, because they are the 
 most generally employed in the arts. 
 
 Watt's rotative double-acting steam-engine. These 
 engines being without expansion, the proper formulae 
 for calculating their effects will be deduced from the 
 general formulse by making L' = L, which will give also 
 K = 1 , and by replacing the quantity p by the pressure 
 of condensation. We see, moreover, that for these en- 
 gines, the expansion being susceptible of no variation, 
 since that detent does not exist, the third case, con- 
 sidered as to engines in general, cannot occur. There 
 will be then but two circumstances to consider in their 
 working, viz., the case wherein they operate with their 
 maximum load, or load of greatest useful effect, and the 
 case in which they operate with any load juhatever. 
 The effects therefore of these engines will visibly be 
 determined by the following equations : 
 
i 
 
 i 
 
 s 
 
 SD >-} 
 
 PH 
 
 + + 
 
 V 
 
 PH 
 ffi 
 
 a? 
 
 ro 
 
 GO 
 
 a 
 
 * 
 
 ^ 
 
 H ii 
 
 0? 
 
 w 
 ' 
 
 o 
 ^ 
 
 QQ f 
 
 OQ 
 
 + 
 
 + 
 
 + + 
 
 s 
 II 
 
 H 
 
53 
 
 Although these formula? may at first sight appear 
 complicated, they will nevertheless be found very 
 simple in the calculation. It is only necessary to 
 fix attention to refer all the measures to the same 
 unit, as will be seen in the following example. It 
 must be remarked also, that as soon as the velocity 
 and load of the engine are determined, the useful 
 effect will be known immediately, being their pro- 
 duce. 
 
 To apply, however, these formulae, some previous 
 observations are necessary. 
 
 In good engines of that system the pressure in the 
 condenser is usually l'5ft. per square inch, but the 
 pressure in the cylinder itself, and under the piston, 
 is in general 2*5fts. more, which gives p=4x 144fts. 
 It has been deduced, moreover, from a great number 
 of trials made on Watt's engines, that their friction, 
 when working with a moderate load, varies from 
 2*5 fts. per square inch of the piston, in engines of 
 smaller dimensions; to 1*5 ft), in the more powerful 
 ones ; which includes the friction of the parts of the 
 machinery and the force necessary for the action of the 
 feeding and discharging pumps, &c. By moderate 
 load in these engines is meant about 8 fts. per square 
 inch of the piston. Now our experiments on loco- 
 motives, showing the additional friction of an engine 
 to be ^ of the resistance, give room to think, that the 
 additional friction caused in the engine by that load 
 may be about 1 ft. per square inch. The above in- 
 formation attributes then to Watt's engines, working 
 unloaded, a friction of from 1'5 ft. to '5 ft. per square 
 inch, according to their dimensions, which would give 
 
54 
 
 1 tb. for engines of a medium size : this information, 
 agreeing with what we have deduced from our in- 
 quiries on locomotives, as has been said above, we 
 shall continue to admit, in this place, respecting the 
 friction, the data already indicated in this respect, 
 
 viz. : 
 
 /= 1 x 144H5S. 8 = '14. 
 
 As an application of these formulae, we will submit 
 to calculation an engine constructed by Watt at the 
 Albion Mills near London. The following were its 
 dimensions : 
 
 Diameter of the cylinder, 34 inches, or a= 6*287 
 
 square feet ; 
 
 Stroke of the piston, 8 feet, or L=8 feet ; 
 Clearance of the cylinder, - of the stroke, or c='4 
 
 foot; 
 Effective vaporization, '927 cubic foot of water per 
 
 minute, or S='927 cubic foot ; 
 Consumption of coal in the same time, 6*71 ft>s., or 
 
 N = 6'71ft>s. ; 
 Pressure in the boiler, 16'51bs. per square inch, or 
 
 P= 16-5 x 144 fts. ; 
 Mean pressure of condensation, 4fts. per square 
 
 inch, or p=4 x 144 ft>s. 
 And finally, the engine being a condensing one, we 
 
 haverc=-4227 and ^ = '000000258. 
 The engine had been constructed to work at the 
 velocity of 256 feet per minute, which was considered 
 its normal velocity ; but when put to trial by Watt 
 himself, shortly after its construction, it assumed, in 
 performing its regular work, esteemed 50 horse- 
 power, the velocity of 286 feet per minute, consuming 
 
55 
 
 at the same time the quantity of water and fuel which 
 we have just reported. 
 
 If then we seek the effects it was capable of pro- 
 ducing at its velocity of maximum effect, and then at 
 those of 256 and 286 feet per minute, we shall find, 
 by the formulae already exposed : 
 
 Maximum useful effect. 
 
 v = 286 256 v'= 214 Velocity of the piston 
 
 in feet per minute ; 
 
 ar = 5,621 6,850 9,133 Total load of the pis- 
 
 ton in Bbs. ; 
 
 r = 6-21 7'57 10-09 Load of the piston in 
 
 Bbs. per square inch ; 
 
 S = '927 *927 '927 Vaporization in cubic 
 
 feet of water per 
 minute ; 
 
 U -E = 1,607,610 1,753,600 1,957,180 Useful effect in fbs. 
 
 raised to one foot 
 per minute. 
 
 u-HP = 49 53 59 Useful effect in horse 
 
 power. 
 
 u . E iib. C o. = 239,585 261,340 291,680 Useful effect of 1ft. of 
 
 coal, in fos. raised to 
 one foot per minute. 
 
 u-Eip. e. = 1,734,200 1,891,700 2,111,300 Useful effect due to 
 
 the vaporization of 
 one cubic foot of 
 water, in fcs. raised 
 to one foot per mi- 
 nute. 
 
 Qco.forih. -_ -138 -126 -113 Quantity of coal in 
 
 fts., producing the 
 effect of one horse 
 power. 
 
 Q wa. for 1 h. Q 1 9 '017 *0 1 6 Quantity of water, in 
 
 cubic feet, producing 
 the effect of one 
 horse power. 
 
56 
 
 Such are the effects that this engine should produce, 
 and we see, in consequence, that in performing a 
 labour estimated at fifty horses, it was to be expected 
 the engine would acquire the velocity which in fact it 
 did, viz., that of 286 feet per minute. 
 
 Let us now see to what results we should have been 
 led, had we applied the ordinary calculations to the 
 experiment of Watt, which we have just reported. In 
 this experiment, the engine vaporizing *927 cubic foot 
 of water, and exerting the force of fifty horses, as- 
 sumed a velocity of 286 feet per minute. 
 
 We then find that, since the engine had a useful 
 effect of no more than fifty horses, and that the theo- 
 retical force, calculated according to that method, 
 from the area of the cylinder, the effective pressure in 
 the boiler, and the velocity of the piston, was, 
 
 6-287x (16-5-4) x 144x286 
 
 33QOQ =98 horses. 
 
 It resulted that, to pass from the theoretical effects 
 to the practical, it was necessary to use the coefficient 
 51. Consequently, by following the reasonings of 
 that theory, the following conclusions were to be 
 drawn : 
 
 1. The observed velocity being 286 feet per minute, 
 the vaporization calculated on the quantity of water, 
 which reduced to steam at the pressure of the boiler, 
 might occupy the volume described by the piston, and 
 afterwards divided, as is done, by the coefficient, to 
 take the losses into account, would have been : 
 
 isVo* 6 ' 287x286 QAK ,. f 
 
 i_5J_2 = 2*305 cubic feet per minute, 
 
 D 1 
 
 instead of -927. 
 
57 
 
 2. The engine having vaporized only '927 cubic 
 foot of water per minute, the velocity calculated on 
 the volume of steam formed, at the pressure of the 
 boiler, and afterwards reduced by the coefficient, not 
 as has been done, since this problem was not resolved, 
 but as must naturally be concluded from the significa- 
 tion attributed to that coefficient, could but be 
 
 1 530 x- 927 
 
 x * 51 = 1 15 per minute, instead of 28o. 
 
 3. The coefficient found by the comparison of the 
 theoretical effects to the practical being 51 , the various 
 frictions, losses, and resistances of the engine would 
 amount to 49 of the effective power ; whereas these 
 frictions, losses, and resistances, consisting merely of 
 the friction of the engine and the clearance of the 
 cylinder, could be estimated only as follows : 
 Total friction (including the additional friction) 
 2 ffis. per square inch, or as a fraction of the 
 effectual pressure, ^ 2 . . . . j . * -17 
 Clearance of the cylinder, ^ of the effective 
 force, or . . .:,*,;, ^ * . gj * '. *05 
 
 22 
 
 Some authors also employ constant coefficients, not 
 however using the same to determine the vaporization 
 as to find the useful effect. This manner of calculating 
 has arisen from those authors having recognised from 
 experience, that the steam has in the cylinder a less 
 pressure and density than in the boiler ; but as they 
 cannot settle a priori what is that pressure in the 
 cylinder, and that they always seek to deduce it from 
 
11 PUBLISHED BY JOHN WEALE. 
 
 C. DAVY, Esq., C.E. 
 
 SAMUEL HALL, Esq., C.E. 
 
 F. HUMPHRIES, Esq., C.E. 
 
 R. AYRES, Esq., C.E., Newcastle. 
 
 ROBERT STEPHENSON, Esq., C.E. 
 
 GEORGE BIDDER, Esq., C.E. 
 
 CHEV. DE BENKHAUSEN, H.I.M. Consul-General. 
 
 J. BEALE, Esq., C.E. 
 
 J. SIMPSON, Esq., C.E. 
 
 CAPTAIN ANDREW HENDERSON. 
 
 SOME OF THE NEW SUBJECTS IN THIS EDITION CONSIST OF THE WORKS OF 
 
 Messrs. Boulton and Watt The Butterley Company Messrs. Maudslay, Son, 
 and Field Messrs. Seaward Robert Napier, Esq., Glasgow Messrs. Fairbairn 
 and Murray William Morgan, Esq. Messrs. Hall, Dartford Messrs. Hague 
 Messrs. Cla'ude, Girdwoord, and Co. 
 
 PUBLIC WORKS OF GREAT BRITAIN, 
 
 CONSISTING OF 
 
 Railways, Rails, Chairs, Blocks, Cuttings, Embankments, Tunnels, Oblique Arches, 
 Viaducts, Bridges, Stations, Locomotive Engines, &c. Cast-iron Bridges, Iron 
 and Gas Works, Canals, Lock-gates, Centering, Masonry and Brickwork for Canal 
 Tunnels, Canal Boats, the London and Liverpool Docks, Plans and Dimensions, 
 Dock-gates, Walls, Quays, and their Masomy, Mooring-chains, Plan of the 
 Harbour and Port of London, and other important Engineering Works, with 
 Descriptions and Specifications ; the whole rendered of the utmost utility to the 
 Civil Engineer and to the Nobility and Gentry, as Monuments of the useful Arts 
 in this Country, and as Examples to the Foreign Engineer. 
 
 Edited by F. W. SIMMS, C.E. 
 
 153 Plates, engraved in the best style of art, half-bound, very neat, price 4 4s. 
 This Work is on an Imperial Folio size, the Drawings and Engravings have 
 been executed by Eminent Artists, and no Expense has been spared in rendering 
 it highly essential to the Civil Engineer and Student ; also, as an ornamental 
 Volume of Practical Representations of important Engineering Works in several 
 Parts of the kingdom. The work is bound in half-morocco. There are some 
 Plates in the Volume that may be preferred in Colours, viz., the elaborate subject 
 of the Blisworth Cuttings, in the Birmingham Rail Line, 18 Plates, geologically 
 coloured ; Glasgow and Gairnkirk Railway Cutting through Moss, geologically 
 coloured ; the Plan and Map of the port of London, showing its Docks, Wharfs, 
 Manufactories, Steam Engines, and Iron Works, &c., making 21 Plates, to be 
 carefully coloured, and for which an additional 1 will be charged. 
 
 Comprising the Engineering Works of 
 
 Brindley Jessop Rhodes 
 
 Brunei Landmann Telford 
 
 Buck M'Adam Thomas 
 
 George and Robert Stephenson Palmer Tierney Clark 
 
 Hartley Rennie Walker 
 
 Hosking 
 
 Second Edition, with Additional Corrections, in 8vo, with a fine Frontispiece of .a 
 Locomotive Engine, price 8s. 
 
 ANALYSIS OF RAILWAYS, 
 
 Consisting of Reports of RAILWAYS projected in England and Wales \ to which 
 are added, a Table of Distances from the proposed London Terminus to Eight 
 well-known Places in the Metropolis, with a copious GLOSSARY, and several 
 Useful Tables. 
 
 By FRANCIS WISHAW, C.E., M. Inst. C.E. 
 
JOHN WEALE, 
 
 ARCHITECTURAL LIBRARY, No. 59, HIGH HOLBORN, 
 
 HAS JUST PUBLISHED THE TWO FOLLOWING NATIONAL WORKS ON 
 
 eitril iinfc $*trf)awcal iEngtuewug* 
 
 *** Export Orders Executed. 
 
 TREDGOLD 
 
 ON THE 
 
 ; STEAM ENGINE, v 
 
 AND 
 
 ON STEAM NAVIGATION, 
 
 Is now before the public. These very important and interesting Volumes, comprising 
 118 very elaborate and beautifully engraved Plates, are, in Sections, Elevations, Plans, 
 Details, c., of the highest utility to the Engineer and Student, to Manufacturers of 
 Marine, Locomotive, and Land Engines ; its comprehensiveness, its science and pur- 
 pose, made manifest by elucidation and explanation, assisted by the most eminent 
 Practical Men of Britain, The Work is in Two 4to. Vols., Price 3 3s,, and is 
 entitled 
 
 THE STEAM ENGINE, 
 
 Comprising an Account of its Invention and Progressive Improvement, with an 
 INVESTIGATION of its PRINCIPLES, and the PROPORTIONS of its PARTS, for EFFICIENCY 
 and STRENGTH ; detailing also its Application to NAVIGATION, MINING, IMPELLING 
 MACHINES, &c., and the Result in numerous Tables for Practical Use, with Notes, Cor- 
 rection.s, and New Examples, relating to Locomotive and other Engines. 
 
 BY W. S. B. WOOLHOUSE, ESQ., F.R.A.S. 
 
 The Algebraic Parts transformed into easy Practical Rules, accompanied by Ex- 
 amples familiarly explained for the Working Engineer, with an ample 
 
 APPENDIX ON STEAM NAVIGATION, 
 
 Its Present and Progressive State, by Illustration of the various Examples of Engines 
 constructed for Sea, War, and Packet Vessels, and River Boats, by the most Eminent 
 Makers of England and Scotland, drawn out in Plans, Elevations, Sections, and 
 Details, with a Scientific Account of each, and on 
 
 STEAM NAVAL ARCHITECTURE, 
 
 Showing, by existing and the latest Examples, the Construction of War, Sea, and 
 Packet Vessels ; their Naval Architecture, as applied to the Impelling Power of 
 Steam for Sea and River purposes. This portion of the Work is edited by four very 
 eminent Shipbuilders 
 
 OLIVER LANG, Esq., of H.M. Dockyard, Woolwich, 
 
 J. FINCHAM, Esq., H.M. Dockyard, Sheerness, 
 T. J. DITCHBURN, Esq., Union Dock, Limehouse, 
 JOHN WOOD, Es^ Port Glasgow, 
 
2 
 TREDGOLD continued. 
 
 CONTRIBUTORS, BESIDE THOSE BEFORE NAMED. 
 
 J. DINNEN, Esq., Assistant Engineer H.M. Dockyard, Woolwich. 
 
 THOMAS BALDOCK, Esq., K.T.S., Lieut. R.N. 
 
 P. W. BARLOW, Esq., C.E. 
 
 CAPTAIN OLIVER, R.N., Commodore of Bombay War Steam Flotilla. 
 
 A. A. MORNAY, Esq., C.E. 
 
 PROFESSOR RENWICK, Colombia College, New York. 
 
 W. S. B. WOOLHOUSE, Esq., F.R.A.S. 
 
 J. HANN, Esq., King's College. 
 
 JOHN MACNEILL, Esq., C.E. 
 
 CAPTAIN AUSTEN, R.N., late Commander of H.M.S.S. Medea. 
 
 GEORGE PEACOCK, Esq., late Master of the Medea. 
 
 ALEXANDER GORDON, Esq., C.E. 
 
 C. DAVY, Esq., C.E. 
 
 SAMUEL HALL, Esq., C.E. 
 
 F. HUMPHRIES, Esq., C.E. 
 
 R. AYRES, Esq., C.E., Newcastle. 
 
 ROBERT STEPHENSON, Esq., C.E. 
 
 GEORGE BIDDER, Esq., C.E. 
 
 CHEV. DE BENKHAUSEN, H.I.M. Consul General. 
 
 J. BEALE, Esq., C.E. 
 
 J. SIMPSON, Esq., C.E. 
 
 Some of the new subjects in this Edition consist of the Works of 
 Messrs. Boulton and Watt. 
 The Butterley Company. 
 Messrs. Maudslay, Son, and Field. 
 Messrs. Seaward. 
 Robert Napier, Esq., Glasgow. 
 Messrs. Fairbairn and Murray. 
 William Morgan, Esq. 
 Messrs. Hall, Dartford. 
 Messrs. Hague. 
 Messrs. Claude, Girdwoord, and Co. 
 
 LIST OF PLATES. 
 Plate. 
 1 to 20. The same subjects as in the previous Edition, with several Corrections. 
 
 NEW PLATES. 
 
 10 B. The several Orders of Parallel Motion. 
 
 21. Mr. Kingston's Valves, as fitted on board Sea-going Steam-vessels for Blow-( 
 
 Injection, and Hand Pump Sea Valves. 
 
 22. Boilers of H.M. Steam Vessel of War African. 
 
 23. Boilers of H.M. Steam Vessel of War Medea. 
 
 24. Morgan's Paddle Wheel Seaward' s Paddle Wheel. 
 
 25. Positions of a Float of a Radiating Paddle Wheel in a Vessel in Motion Po 
 
 tions of a Float of a Vertically Acting Wheel in a Vessel in Motion. 
 
'?! at !; . TREDGOLD-ewi/iy/. 
 
 A. ^ycloidal Paddle Wheel fitted to the Great Western Steam Vessel, by Messr*. 
 Maudslay, Field and Co. Position of a Float of a Cycloidal Paddle Wheel. 
 
 27. Captain Oliver's, R.N., Five Points from Courses of Sailing a Steam Vessel. 
 
 28. Her Majesty's Steam Ship of War sailing at Different Points in the Wind. 4 views. 
 
 29. Trial at sailing her Majesty's Steam Ship of War Medea against the Caledonia, 
 
 Vanguard, and Asia. 
 
 30. Engine of the Red Rover, Side Elevation, and Plan. 
 
 31. Longitudinal Section of ditto. 
 
 32. Cross Sections ditto, with Paddles. 
 
 33. Side Elevation of the Engine of the Pasha of Egypt's Steam Ship Nile. 
 
 34. Plan of ditto, with Paddles. 
 
 35. Cross Sections ditto, showing Boilers and Furnace. 
 
 36. Section at Paddle Wheel ditto. 
 
 37: Plan of Engine of her Majesty's Steam Ship of War Phoenix. 
 
 38. Side Elevation of ditto. 
 
 39. Cross Section of ditto, showing Paddles and Construction of Ship. 
 
 40. Engine of the Ruby Steam Vessel (Gravesend Packet). Plan and Elevation. 
 
 41. Section of one of the Engines of the Don Juan, Peninsular Company Packet. 
 
 42. Boilers of her Majesty's Ships Hermes, Spitfire, and Firefly. 
 
 43. Plan of the Engines of the Imperial Russian Steam Ships Jason and Colchis. 
 44 Section of ditto. 
 
 45. Longitudinal Section of ditto. 
 
 46. Section at the Shaft, Section abaft Boilers, ditto. 
 
 47. Elevation of Mr. Samuel Hall's Patent Condensing Engines. 
 
 48. Section of ditto, 
 
 49. Elevation of the Engine of her Majesty's Steam Ship Megaera, fitted with 
 
 Messrs. Seaward's Engines and Mr. Samuel Hall's Condenser. 
 
 50. Section of ditto. 
 
 51. Messrs. Hall's, of Dartford, Engines of the William Wilberforce, Hull and 
 
 London Packet, fitted with Mr. Samuel Hall's Condensers. Plan. 
 
 52. Elevation of ditto. 
 
 53. Cross Section of ditto. 
 
 54. Longitudinal Section of ditto. 
 
 55 A. Messrs. Hall's, of Dartford, Patent Engines, fitted in the Steam Packet Dartford. 
 
 55 B. Ditto, Plan. Elevation ditto. 
 
 56 A. Cross Section ditto. Longitudinal Section ditto. 
 56 B. Ditto. Ditto. 
 
 57. Messrs. Fairbairn and Murray's Engine of Twenty Horse Power. Plan. 
 
 58. Ditto Section. 
 
 59. Ditto Front Elevation and Back Elevation. 
 
 60. Messrs. Fairbairn and Co.'s Ten Horse Power Engine. Elevation. 
 
 61. Plan. Sectional Plan. 
 
 62. Sectional Elevation. 
 
 63. Cross Sectional Elevation. 
 
 64. Elevation of a Locomotive Engine, manufactured by Messrs. Stephenson, of 
 
 Newcastle, for the Stanhope and Tyne Railway. 
 
 65. Longitudinal Section of ditto. 
 
 66. Spring and Balance Safety Valves. 
 
 67 A. Cylinder Cover and Connecting Rods. 
 67 B. Piston and Cylinder. 
 
 68. Boiler Seating of 20-horse Engine, at the manufactory of Messrs. Whitworth 
 
 and Co., Manchester. 
 
 69, Messrs, Hague's Double ActingiCylinder, Slides^Sections, &c. ' 
 
Plate. PUBLIC 
 
 12. Bridge near Watford. 
 
 13. Bridge over Railroad at Watford. 
 
 14. Viaduct over Colne, near Watford. 
 
 15. Bridge over Excavation, South of Watford Tunnel. 
 
 16. Boxmoor Skew Bridge. 
 
 17 and 18. Sections of Primrose-hill and North Church Tunnels. 
 
 19. Architectural Front of Further Entrance. 
 
 20 to 29. Working Sections of Embankments and Cuttings on the Line near Blisworth. 
 
 30 and 31. Undersetting Rock at Blisworth (Large Scale). 
 
 32 and 33. Retaining Walls, Details, &c., ditto. 
 
 34 and 35. Undersetting ditto. 
 
 36 and 37. West End of Blisworth Cutting. 
 
 38. Kilsby Tunnel Elevation of Entrance. 
 
 39. Ditto Section, Details, &c. 
 40 to 47. Ditto, ditto, ditto. 
 
 48. Rails, fifty pounds weight. 
 
 49. Ditto, sixty-five pounds weight. 
 
 50. Mr. Buck's Chairs. 
 
 51. Plans of Crossings from one Line to another. 
 
 52. Turnrails. 
 
 53. First Class Carriages. 
 
 GREAT WESTERN RAILWAY. 
 
 J. K. BRUNEL, ESQ., C.E. 
 54 to 56. Brent Viaduct. 
 57 and 58. Maidenhead Bridge. 
 
 SOUTHAMPTON RAILWAY. 
 G. LOCK, ESQ., C.E. 
 
 59. Occupation Bridge over Railway. 
 60 and 61. Ditto Bridge under ditto. 
 
 62. Embankment. 
 
 63. Bridge under Railway. 
 
 64. Earth and Timber Waggons. 
 
 GREENWICH RAILWAY. 
 COL. LANDMANN, C.E. 
 
 65. Neckinger Viaduct. 
 
 66. Section of ditto. 
 
 67. Spa Road Viaduct. 
 
 68. Section of ditto. 
 
 69 and 70. Viaducts and Oblique Arches. 
 
 CROYDON RAILWAY. 
 Jos. GIBBS, ESQ. C.E. 
 
 71 and 72. New Cross Bridge Section of Rails, and Continuous Bearing Embank- 
 ments, Earth Carriage, and Details. 
 
 THAMES AND BRISTOL JUNCTION RAILWAY. 
 
 W. HOSKING, ESQ., C.E. 
 73 and 74. Tunnels, Bridges, Rails, Chairs, Details, Foundations, &c. 
 
 GLASGOW AND GAIRNKIRK. 
 
 Messrs. MILLER and GRAINGER, Edinburgh, C.E. 
 
 75. Transverse Section at Robroyston, Moss, &c. 
 
 76. Comparison of Rails of different Railways. 
 
 77. Comet, Locomotive Engine, on Newcastle and Carlisle Railway. 
 

 7 
 
 Plate - PUBLIC WORKS-co*<;w/. 
 
 I 79' W^ on*' 8 Engine> Harve >' Combe, on Birmingham Railway. 
 80.' FlatRai'ls. 
 
 81. Losh, Wilson, and Bell's Rail. 
 
 82. Ditto Hetton Rail. 
 
 83. Sidelings. 
 
 CANALS. 
 W. T. CLARK, ESQ., C.E, 
 
 84. Section Thames and Medway Canal. 
 
 85. Transit Instruments for ditto. 
 
 86. Tunnel Entrance and Cross Section ditto. 
 
 87. Tide Locks ditto. 
 
 88. Gates, &c., ditto. 
 
 89. Centering ditto. 
 
 90. Passing Place ditto. 
 
 91. Perspective View ditto. 
 
 92. Harecastle Tunnel. 
 
 93. Montgomeryshire Canal. G. Buck, Esq., C.E. 
 
 94. Gloucester and Berkeley Canal. T. Telford, Esq., C.E. 
 95 to 97. Fishmongers' Hall Wharf. Sir J. Rennie, C.E. 
 98. Dcptford Pier. 
 
 99 to 101. High Bridge (cast-iron), Staffordshire. 
 102. Double-tumingBridge. R. Walker, Esq., C.E. 
 103 and 104. Road Bridges. 
 
 105. Birmingham and Liverpool Canal. 
 
 106. Lock with Single Gate ditto. 
 
 107. Gates and Valves ditto. 
 
 108. Racks and Pinions ditto. 
 
 109. Double Valve ditto. 
 
 110. Lever Valve, Rochdale Canal. 
 
 111. Mersey and Irwell Boats. 
 
 112. Grand Trunk Boat. 
 
 1 13 and 1 14. Highgate Road. J. Macneill, Esq., C.E. 
 
 115. Geese Bridge Valley. 
 
 116, 117, and 118. Roads, Culverts, &c. 
 
 119. Coke Ovens. 
 
 120. Coking Coal. 
 
 121 and 122. Blast Furnace. 
 
 123. Lift Hammer. 
 
 124 to 127. Steel Furnaces. 
 
 128. Mine ditto. 
 
 129 and 130. Gas Works. William Richardson, Esq., C.E., Dudley. 
 
 131. Liverpool Docks. 
 
 PORT OF LONDON. 
 
 132. Plan of Port and Harbour. 
 
 133. Hemisphere, showing the Position of London as the Centre of the World. 
 
 134. London Bridge. 
 
 135. Plan of St. Katharine Docks. 
 
 136. Gates of ditto. 
 137- Plan of Gates ditto. 
 
 138. Anchor for the Collar of Heel Post and Lock Gates ditto. 
 
 139. Cast Iron Swivel Bridge, St. Katharine Docks. 
 
 140. Plan of London Docks. 
 
 141. Front Elevation of Lock Gates, London Docks. 
 
 142. Back ditto ditto. 
 
 143. Details ditto ditto. 
 
 144. Plan of West India Docks. 
 
 145. Plan of East India ditto. 
 
 146. Entrance of Lock-gate ditto. 
 
 147. Plan of Commercial Docks. 
 
8 
 
 Plate. PUBLIC WORKS continued. 
 
 148. New Mooring Chain Lighter. 
 
 149. Plan of the Moorings, Deptford Reach. 
 
 150. Plan of Mooring Chain 18 Links, 1 Swivel, and 2 Shackles, &c. 
 
 151. Mooring Ships. 
 
 152. Section of River. 
 
 153. Coffer-dams. 
 
 THE HARBOUR AND PORT OF LONDON, 
 
 SCIENTIFICALLY, COMMERCIALLY, AND HISTORICALLY DESCRIBED, 
 
 Containing Accounts of the History, Privileges, Functions, and Government 
 thereof; of its Extent, Divisions, and Jurisdictions, Municipal and Commercial ; of 
 its Docks, Piers, Quays, Embankments, Moorings, and other Engineering Works ; 
 Tidal and other Observations, and every other necessary Information relative thereto, 
 accompanied by Charts of the Port and its Dependencies, its Shoals and Soundings, 
 surveyed by Order of the Port of London Improvement Committee 5 Plans of Docks, 
 Gates, Piers, Swivel Bridges, Methods of Mooring Vessels, c., as directed by the 
 Corporation By-Laws, &c., &c., &c. 
 
 By JAMES ELMES, 
 
 Architect and Civil Engineer, Surveyor of the Port of London. 
 22 Plates, large Folio, bound, price II. Is. 
 
 Second Edition, with Additional Corrections, in 8vo., with a fine Frontispiece of a 
 Locomotive Engine, price 8s. 
 
 ANALYSIS OF RAILWAYS, 
 
 Consisting of Reports of RAILWAYS projected in England and Wales; to which 
 are added, a Table of Distances from the proposed London Terminus to Eight well- 
 known Places in the Metropolis, with a copious GLOSSARY, and several Useful 
 
 Tables. 
 
 By FRANCIS WHISHAW, C.E., M.Inst.C.E. 
 
 SECTIO-PLANOGRAPHY. 
 
 A DESCRIPTION OF MR. MACNEILL'S METHOD OF LAYING DOWN 
 RAILWAY SECTIONS AND PLANS IN JUXTA-POSITION, 
 
 As adopted by the Standing Order Committee of the House of Commons, 1837. 
 
 By FRED. W. SIMMS, Civil Engineer. 
 
 With folding Plates, in 4to., price 3s. 
 
 AN TAVUm, , -., -, 
 
RETURN CIRCULATION DEPARTMENT 
 
 TO ^ 202 Main Library 
 
 LOAN PERIOD 1 
 HOME USE 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS 
 
 Renewals and Recharges may be made 4 days prior to the due date. 
 
 Books may be Renewed by calling 642-3405. 
 
 DUE AS STAMPED BELOW 
 
 '" n 1989 
 
 
 
 AUTO. DISC, 
 
 
 
 ijuUAWfc 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 UNIVERSITY OF CALIFORNIA, BERKELEY 
 
 FORM NO. DD6 BERKELEY, CA 94720 
 
 $ 
 
020^7315 
 
 97375,' 
 
 THE UNIVERSITY OF CALIFORNIA LIBRARY