460 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[Decp:mbkr, 



REVIEVSrS. 



Theory of the Steam Engine. By Comte de rAMBOiii. London : 

 John Wcale, 1839. 



(SECOND NOTICE.) 



In our September niiinbcr we noticed tins work, and made some 

 remarks on (lie first cliapter, in wliich the aiitlior criticises tlie ordi- 

 nary mode of calculating the ellect of steam-engines, and exposes the 

 principles of his own theory. We then assented to these principles 

 generally, but at the same time expressed our opinion, that it would 

 not be very easy to apply them practically, for want of i)roper means 

 of ascertaining with accuracy the data on wliich the calculations are 

 grounded, and showed that the same results might be arrived at, by a 

 method similar to the ordinary one, witli much greater facility than by 

 the Count's method. 



The second chapter treats of the laws \ihich govern the mechanical 

 action of the steam. Li the first section of this chapter the auth.or 

 justly observes that the formula wduch he uses to calculate the tem- 

 perature of steam at its raaxinunn density under dirtt>rent pressures, 

 have the inconvenience of suiting only a limited part of the scale of 

 temperatures. At the time when the work was written no formula 

 had been discovered, to express the relation existing between the tem- 

 perature and elastic force of steam, which would suit the whole scale, 

 even as far as it had been ascertained by experiment ; but in the June 

 number of this Journal a fornnda was jiroposed by Mr. Mornay, which, 

 though in one part of the scale it dives not accord so well with experi- 

 ment as Tredgold's rule, follows the natural law much more nearly in 

 general, and can therefore be used in investigating the action of steam 

 when its elastic force varies, as in the case of expansive engines ; 

 particularly as the original elastic force and density of the steam need 

 not be calculated by the proposed fornnda, but nuiy be ascertained 

 directly or taken from tables constructed so as to accord more exactly 

 with experiment. 



M. de Pambour proposes the two following formula-, to express the 

 relation which exists between the elastic force and relative volume of 

 steam, of the maxinuini density for its temperature : 



Formula for coiidtnsing ctigints of various svstems ; 



_ _ 10000 

 '^ ~'4227+^025ft^' 

 Formula for non-condensing engints ; 



10000 



^ ~ l-121-f~O023/ 



In these formula; ^l represents the relative volume, and jj the clastic 

 force in ])Ounds per square foot. 



The application of these formula: is attended with a serious incon- 

 venience in some cases, namely, when the steam enters the cylinder of 

 an engine at a high pressure, and is there caused to expand to a very 

 low one. In this case the second formula would suit ;it the cumnience- 

 inent of the stroke, after a certain portion of which it would cease to 

 be applicable: and, unless the action (jf the steam were divided into 

 two parts, and the effect of each calculated by the respective formula 

 (which would double the length of the calculation), we should be ob- 

 liged to content ourselves w ilh a less accurate result than in purely 

 high pressure, or low pressure engines. But the formulrc adopted by 

 W. de Pambour do not agree so well as Mr. Mornay's with the results 

 obtained by means of the ordinary fornnilcC from the table of elastici- 

 ties constructed so as to accord with experiment, even in those por- 

 tions of the scale for which they were severally intended. The rela- 

 tive volume of steam of five pounds pressure is (according to the table, 

 page b3j -Ui'^l, and the volume calculated by the formula for condensing 

 engines is found to be 43Sj ; Sir. Mornay "s formula gives 4G00. At 

 10 lbs. pressure the volume is, by the same table, 2-127 ; calculated by 

 the formula for condensing engines it is 2417, and by j\ir. Mornay's 

 formula, 2424. At 20 lbs. the volume is 12S0 ; M. de Pambour's for- 

 mula for c(mdei;siug engines gives 1273, that for non-condensing en- 

 gines, 1243, and Mr. Mornay's, 1281. At CO lbs. tlie volume is 4G7 ; 

 the formula for condensing engines gives 410, that for non-coudensing 

 engines 470, and Mr. Mornay's formula 4 i'.l. At SO lbs. the voh\me 

 is 323, the fornnda for non-condensing engines gives 320, and Mr. 

 Mornay's formula 321. 



The two expressions of the relative volume of steam adopted by M. 

 de Pambour, page SO, were no doubt chosen on account of the facility 

 which they afford in calculating the mean pressm-e on the piston, when 

 the steam is used expansively; but they do not agree, that is, they 

 are not identical with the general ecjuation, page 75. The former are 

 of the form 



and the latter 



Elinunaling n betwi 



i^ = r 



1-f « (/— 32 



3n these two equations, we obtain 

 _ «r[l-f8(/-32)] 



^ l-^r[l + n'-32J] 



which differs in form from all the equations previously adopted, page 

 tJS, to calculate the elastic force of the steam in terms of its tempera- 

 tiu'e. 



In the thiril chapter the author develops more fully the theory, of 

 wliich the outline was given in the Hrst chapter. Here the different 

 ]>roblenis regarding the effects of steam-engines are very clearly and 

 systematically stated, w itii reference to three cases wddch occur in the 

 working of an engine. These are : that in which it works at a given 

 rate of expansion, and with any load or velocity H'.^ii/t if r; that in 

 which it works at a given expansion, and with the load or velocity 

 proper to produce its iiiaximum nsiful (fftct with l/ial ixj/ansion ; and 

 lastly, that in which, the expansion having been previously regulated 

 for the most favourable working of the steam in that engine, it is 

 loaded with the most favourable load for that expansion, winch con- 

 sequently produces the ahsolule maximum ustj'id (Jflct for that engine. 

 The four problems proposed and solved by the author consist in finding 

 the Velocity, the Load, the Evaporation, and the Useful Effect of the 

 engine. Tl>e chapter is divided into three Articles, each of which is 

 devoted to one of the three above mentioned cases. 



The first jiroblem, to Jin 1 the velocttij of thi pislon under a giren load, 

 is treated in the second section of the Hrst Article. The author here 

 appears by the following passage to suppose the elastic force of the 

 steam in the cylinder not to vary so long as the influx of the steam 

 lasts. 



" Let P be the total pressure of the steam in the boiler, and 1" the pres- 

 sure the same steam will have on arriving la the cylinder, a pressure v.-fiich 

 will always be less than P, except in a particular case, %\luch we shall treat 

 of shortly. The steam then will enter the cylinder .it the pressure F', and 

 will continue to flow in with that pressure and to produce a corresponding 

 effect, till the communication between the boiler and the cyhndcr is inter- 

 cepted." 



That this is not .rigorously tlie fact is evident, on account of the 

 varying velocity of the piston; and even though M. de Pambour may 

 liave ascertained that these variations are not worth taking account 

 of, it would have been much more satisfactory, if he had mentioned 

 the circumstance, and shewn that the results are not uuiterially affected 

 by omitting to take them into consideration. At the connncneement 

 of the stroke of the piston, when it has no velocity, the steam must 

 have t!\e same elastic force in the ('ylinder as in tlie adjoining pas- 

 sages; but when the piston has acquired a considerable velocity, as at 

 the middle of the stroke Cparticularly in locomotive engines, where 

 the velocity of the piston is excessive), the steam will not flow from 

 the steam-pipe into the cylinder sufficiently fast to follow the piston 

 in its nuiticn, without a certain excess of pressure on the side of the 

 steam in the pipe, which we do not believe to be a negligeable quan- 

 tity. In a locomotive engine, for example, with w heels of five feet 

 diameter, and 18 inches length of stroke, running at a speed of 30 

 miles an hour, with an effective pressure of GSA '6s. on the square 

 inch, we should estimate the difference of pressure between the steam- 

 pipe and the cylinder at one-third of a pound at least on the square 

 inch. We believe this difference to increase nearly in the ratio of 

 the square of the velocity of the piston, all other circumstances re- 

 maining the same, on w hich supposition it would amount, at a speed 

 of 40 miles an hour, to about three-fifths of a poiuid per square inch. 

 If this be true, it will materiallv affect the calculation of the effect of 

 expansive engines, where the steam is cut off at o;(f-Aa//' of the stroke, 

 as the effect during the expansion is determined by the d.ensity of the 

 steam in tlie cylinder at the instant of cutting off. It is evident, in the 

 same manner, that the earlier the steam is cut off, the less the diffe- 

 rence of pressure will be, since the velocity of the piston is then less 

 considerable ; if cut oft' at one-sixth, f(n- example, when the other cir- 

 cumstances are th.e same as in the above case of tlie locomotive 

 engine running at 30 miles an hour, we believe the loss of pressure 

 W(juld be about two-elevenths of a pound. This is, of course, but a 

 rough estimate of the difference of pressure arising from the variations 

 in the velocity of file piston; but perhaps M. de Pambour will give 

 the subject some consideration before the publication of a second 

 edition of his work. 



On the supposition of the invariability of the pressure, the author 



