IS4.8."1 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



237. 



always remain in a state of saturation durinp: the whole period of 

 the expansion ; the pressures of the steam will vary in the inverse 

 ratio of its volumes, and they will constantly |)resent the relations 

 to the temperatures, which connect the temperatures of saturated 

 steam with its elastic forces. 



Second case. — The total heat of the steam increases in propor- 

 tion as its elastic force is greater. As we suppose that the steam 

 is not subjected to any external cooling influence, it is evident 

 that, in proportion as the steam dilates into a larger space, it will 

 require a smaller quantity of total heat to keep it in the state of 

 vapour. Conse<iueiitly, during the dilatation, there will be a dis- 

 engagement of a certain q-aantity of latent heat, which will 

 become sensible to the thermometer, and will raise the temperature 

 of the steam above tlie point whicli corresponds to its saturation. 

 The temperature of the steam will then be more slowly reduced 

 than in the former case ; the steam will be found overheated 

 during the expansion, and the pressure of the steam upon the 

 piston will diminish more slowly than it would according to the 

 law of Mariotte. 



Third case. — The total heat of steam is less in proportion as its 

 elastic force is greater. If this law were true, there would be a 

 precipitation of liquid water during the expansion, the steam 

 would remain constantly saturated, but the elastic force would de- 

 crease more rapidly than according to the law of Mariotte. 



In the absence of decisive experiments to show the accuracy of 

 one of these three hypotheses, mechanicians have generally 

 adopted the first, which is at the same time the most sim])le and 

 the most precise. This hypothesis assimilates the expansion of 

 steam to that of a permanent gas, dilating in a variable space, 

 whose walls constantly restore to the gas the quantity of heat 

 which is absorbed in tlie latent state during its expansion, so that 

 its temperature remains invariable. 



The work developed during the expansion is then calculated in 

 the following manner : — Let v be the volume of the steam, and /) 

 its pressure at a given moment ; dx tlie space described by the 

 piston wliile tlie volume becomes t; + rfti; the element of work 

 produced will be padx^^pdv. At the commencement of the 

 expansion, the volume is V, and the pressure P, and as we admit 

 the law of Maiiotte between the volume of the steam and its 

 elastic force during expansion, we shall have 



p = — , ^ pdv = VY — ; 



V V 



and the whole work produced, while the volume of the vapour 



passes from V to V, is /*^ p v — ;= P V log. yr = P V log. -, 

 ^ V u V r 



This is the expression for the work produced during the period 

 of the expansion. The total quantity produced during a complete 

 stroke of the piston, is then 



PV 



+ log.|,). 



We have heretofore attended only to the pressure which is ex- 

 erted upon one of the faces of the piston, but the other face is 

 constantly submitted to the pressure which exists in the con- 

 denser. We will suppose this latter pressure to be constant during 

 the stroke of the piston, and represent it by f. The amount of 

 resistance which it will have produced during the stroke of the 



VP 



piston, will he/V, =f-~. So that the moving power will be 



* 1 



expressed by P V ( 1 + log. ^ — p ) • 



5f n represents the number of strokes of the piston per minute, 

 the power developed during this unit of time, will be expressed by 



But the accuracy of the formula depends upon the accuracy of 

 the hypothesis which we have admitted, and it is necessary to de- 

 termine by direct experiments — 



II. The quantities of heat which must be given to a kilogramme of 

 wa'er, at 0°, to vapourize it, under different pressures. 



These quantities of heat are composed of two distinct parts — 

 the heat necessary to raise the temperature of the liquid water 

 from 0° to the point at which the change of state takes place, and 

 the latent heat of vaporization. If we wish to distinguish these 

 two parts of the total heat of steam, we must determine by ex- 

 periment — 



III. Tlie capacity for heat of loater at different temperatures. 

 Finally, if the total heat of steam is not constant under all 



pressures, in order to calculate the effect of expansion, we must 

 still learn — • 



IV. The specific heat of the vapour of water in different states of 

 density, and at different temperatures. 



The theoretic power of a steam-engine may be estimated, by 

 stating the amount of power which it is capable of giving for each 

 kilogramme of steam consumed. 



To do this, let w be the weight of a cubic metre of steam under 

 the pressure P, and at the temperature T ; ir the weight of steam 

 consumed by the machine in one minute. We shall have 



n V = -, and consequently the power given by the machine, from 



a kilogramme of steam, will be expressed by 



But in order to calculate, under all circumstances, the value of 

 w, we must know — 



V. The law according to v^hich the density of saturated vapour of 

 water varies under different pressures. 



VI. The co-efficient of dilatation of the vapour of water, in its dif- 

 fferent states of density. 



Mechanical philosophers generally admit that the weight (oi) of 

 a cubic metre of steam, under the pressure P, and at the tem- 

 perature T, may be calculated by applying to saturated steam the 

 law of Mariotte, and the law of tlie uniform dilatation of gases. 

 Now, these laws are not even rigorously exact for tlie permanent 

 gases, and it is to be feared that tliey are completely false for 

 saturated vapours. Finally, the method most generally adopted 

 to compare steam-engines, consists in stating the work which they 

 perform for each kilogramme of fuel consumed. To do this, we 

 must know the weight (K) of steam under the pressure P, which 

 a kilogramme of fuel can develope under the circumstances in 

 which it is employed ; and we then have, for the work performed 



(p f ^ 



1 -\- log. p p~ )■ 



The quantity K, depends upon a variety of circumstances which 

 we cannot now discuss, such as the quality of the fuel, the nature 

 of the furnace, the arrangements of the boiler, &c. 



To sum up then, the theoretic calculation of steam-engines re- 

 quires the knowledge of the following laws and data : — 



I. The law which connects the temperatures and elastic forces 

 of saturated steam. 



II. The quantities of heat which one kilogramme of liquid 

 water at 0° absorbs, in being converted into saturated steam, under 

 different pressures. 



III. The quantities of heat which one kilogramme of liquid 

 water at 0° requires to elevate its temperature to that at which it 

 assumes the state of steam, under different pressures. 



IV. Tlie specific heat of aqueous vapour, in difl'erent states of 

 densitv, and at different temperatures. 



V. The law acctu-ding to which the density of saturated steam 

 varies, under different pressures. 



VI. The co-efKcients of dilatation of steam, at different densi- 

 ties. 



Before commencing the search for these different laws,_ it was 

 necessary to treat several preliminary questions, so as to fix with 

 certainty the indispensable auxiliary data, and, above all, 

 to define clearly the conditions which must be fulfilled by the 

 thermometers, by means of which we measure the temperatures, 

 in order tliat these instruments may be rigorously comparable. 



These preliminary researches obliged me to undertake succes- 

 sively, long series of experiments, the necessity of which I was 

 far from foreseeing when I undertook the work. I was in fact 

 obliged to undertake the re-determination of a great number of 

 data, which, for the most part, appeared to be fixed with complete 

 certainty by the researclies of my predecessors, and as to which 

 physical philosophers entertained no doubts whatever. 



The whole of these researches will be published in a series of 

 detached memoirs. I intend, at the end of my labours, to sum 

 them up in a report, which will be addressed to the Minister of 

 Public AVorks, in which the results will be presented under a form 

 suitable to the especial view witli which the work was undertaken 

 — that is, the theoretic calculation of steam-engines. 



My experiments frequently required the assistance of a great 

 number of observers. I was' frequently obliged to a\'ail myself of 

 the kindness of several of my students, among whom it gratifies me 

 to cite especially MM. Berlin, Grassi, Bertrand, Lissajoux, and 

 Silberman. Let me be permitted to return to them, thus publicly, 

 my thanks. 



