IS45.1 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



NOTES 



ON THE PHILOSOPHY OF ENGINEERING. 

 I. 



On the Lead of the Slide. 



Tlie sitIps of notes on the philosopliy of engineering wliioli I pro- 

 pose to coiiliime from time to time in tliis Journal will be commenced 

 with a somewhat bold design— which is no le>s than to call into ques- 

 tion certain of the views of the Comte de Pambour on the theory of 

 the steam engine. The extraordinary perspicuity of his investiga- 

 tions, the admirable arrangement of liis experiments, and the beauti- 

 ful simpliritv of his physical conceptions, have procured for him so 

 just a reputation an;ongsl those whose applause is really worth hav- 

 ing,!!!.^! almost despair of being able to overcome the prejudice which 

 will exist against any attack upon his doctrines. Nevertheless, the 

 foUowing tenets respecting the lead of the slide, appear to ine, after 

 careful consideriition, so essentially erroneous, that I think that lie 

 himself, on reconsideration, would hardly be prepared to defend them. 



"We have already mentioned the advantages arising from tlie lead 

 of the slide, with regard to the play and conservation <;f the engine ; 

 but there is another advantage uo less important, resulling from this 

 disposition, namely, that of obtaining a greater velocity, and conse- 

 quontlv a greater useful effect of the engine with a given load. 



"This effect is easy to comprehend; for if the suppression of the 

 steam from the boiler, instead of being made precisely at the end of 

 the stroke of the piston, takes place, for instance, at the moment when 

 the piston is yet an inch from the bottom of tlie cylimler, from that 

 moment steam ceases to flow into the cylinder. Thus, with regard to 

 the quantity of steam admitted into cylinder or expended at each 

 stroke of the piston, the length of the stroke is really diminished an 

 inch. Now it is the quantity of steam produced by the boiler which 

 regulat> s and limits the velocity of the engine. Suppose that such 

 producti' n furnished m cylinders-full of steam per minute, when the 

 total length / of the stroke was tilled with steam : now no more than 

 he length / - a is filled with steam ; the same production then will fill 



per minute a number of cylinders expressed by »s X •. Hencei 



in fine, the velocity of the engine will be increased in the inverse 

 ratio of the lengths of the cylinder which are filled with steam." 

 Trtalist, on Locomotive Engines, Chap. IG, sec. 2. 



The error in this passage appears to me to be this, that M. de Pam- 

 bour in comparing the two cases, supposes that the density of the 

 sleam in th'' cylinder is the same in eillier instance. Now were this 

 so, we should arrive at this strange conclusion — that if the same mo- 

 tive fore, which in the first instance acted through a distance I, be 

 made to act through a shorter distance I — a, it will move its load with 

 greater velocity. This appears to me perfectly inadmissible, and I 

 shall show that the motive force is in the second case so altered that 

 though it act through a shorter distance, it does the same work that 

 the original motive force does in acting through the whole length of 

 the cylimler. 



It need scarcely be said that I here assume the truth of Boyle or 

 Mariotte's law ; it is ascertained from M. de Pambour's experiments 

 that this law is really true for the steam in high pressure engines, 

 when the densities are not greatly varied. 



It is also presupposed that the reader is aware that when an engine 

 is ill motion, the density of sleam in the cylinder may vary consider- 

 ably from that in the boiler. For if the boiler generate such and such 

 11 number of cubic feet of steam per minute of a given pressure, and if 

 that sleam have, owing to the rapidity of the stroke, to occupy twice 

 as manv cubic feet in the cylinder, by Mariotte's law the cylinder- 

 pressure Would he only half the boiler-pressure. 



B fore however examining w4a/ the cylinder-pressure must be, that 

 as much work may be done where there is, as where there is not, a 

 lead of till- slide, 1 must draw attention to another passage from M. 

 de Pambour's treatise. 



" At the nioioent when the piston reaches the point which cor- 

 responds to the lead of tlie slide Jur the suppression of the steam, the 

 motive force is siipprtsstd ; and lohen the piston, continuing its stroke in 

 virtue if its aci/uired relocily, arrives at the point which corresponds 

 to the lead for the admission of the steam, it not only receives no fur- 

 ther impulse in the direction of the motion, but suffers an opposition 

 from the motive force itself, then let in against it." 



The passages which I have marked by italics, I may unhesitatingly 

 atliini to be erroneous. The motive force is not suppressed when the 

 steam is cut otf, for it continues to act expansively ; the piston does 

 not continue its motion in virtue of its required velocity merely, hut 

 dues receive " further impulse in the direction of the motion." 



The last clause of the quotation refers to the lead of admission, but 

 I shall in the following investigation consider the effi'cts of the lead 

 of suppression alone, as being the most important, and bec.iiise I do 

 not wish to complicate the question with effects which are of such a 

 nature that they may be consitlered separately. 



In estimating the work done by steam of a given pressure n in a 

 cylinder of given length a fur a given lead of the slide, I will take the 

 usual measure of the " travail" or " work done," namely, the pressure 

 multiplied by the space through which it is exerted. 



Suppose the piston has risen to a height h in the cylinder at the 

 moment when the steam is cut off, then up to that moment the full 

 pressure n has been exerted through a distance h, or the work done = 

 nh. 



Let 3 he a point to which the piston lias risen after the suppression 

 of the steam, the pressure is now decreased in the inverse proportion 

 of the 3|>aces occupied, or of j- ; h, ar.d if we suppose this pressure 

 constant for a distance d Jc, the work done at this point is 



- ndT. 



X 



And the whole work done after the steam is cut off is determined 

 by integrating this expression between the limits h, the point of sup- 

 pression, and a the height of the cylinder. Effecting this integration 

 and adding the work done before suppression, we have for the whole 

 amount of work done, 



nA+nAlog a — nAlog h 



(A.) 



I will just pause here for a moment to observe that the expression 

 which 1 have marked (A) vanishes (as it ought) when A is put = 0, or 

 when the steam is wholly suppressed. The first two members of (A) 

 obviously vanish when A is zero : the last one however becomes 

 n logo, which is an illusive expression ; but if for log h we use Us 

 expansion 



(A — l)-i (A— l)^-Fi(A-ir - 



and multiply this by A, it is seen the whole vanishes when A ^U. 



Suppose that when the engine is working at uniform velocity, that 

 is, is at its normal state of motion, the resistance offered to the pistun 

 by the work to be done is J9 lb. to the square inch, then of cunrse the 

 work to be done in each stroke =;; «, if a be the height of the cylin- 

 der; and if steam be admitted during the whole stroke it is clear that 

 the pressure of steam in the cylinder also must be;^ lb. to the squ are 

 inch. If however steam be admitted during part only of the stroke, 

 the pressure must be so much increased that the work done by the 

 steam may still be the same. We have then to equate our exprcssio:), 

 obtained above, with p a. Hence 



^ a = n A (1 + log a — log A). 



Here then nothing is more easy than to compare the pressures in 

 the two cases where there is, and where there is not, a lead of the 

 slide; for the equation gives at once 



(B.) 



A (1 + log a — log A) 



This then must be the pressure of the steam supplied to the cylin- 

 der in order that when cut off at a height A, it may do the same work 

 that steam of pressure/) would if acting through the whole length of 

 the cylinder. By examining equation B it will be seen tli.m when 

 A^U, or the steam is totally suppressed, the expression for the cor- 

 responding pressure becomes = cc, as it ought. But it is carefully 

 to be noted that the real limit to the value of this pressure arises from 

 the consideration that it can never be greater than in the boiler. We 

 must therefore never give a value which would make the va:ue of n 

 greater than the boiler-pressure. If we did the engine would no longer 

 be able to do the work we have assigned to it. 



I will now resume the expression (A) and employ it for the purpose 

 of comparing a steam engine which h.is, with a steam engine which 

 has not, a lead of the slide. I think the following will be a very con- 

 venient way of instituting this comparison. There are four principal 

 conditions under which the problem of the steam engine is varied. 



I. The degree of pressure in the boiler. 



II. The rapidity of evaporation. 



III. The load moved. 



IV. The velocity with which the load is moved. 



The reader will see that of these conditions the first two are )f the 

 nature of causes, the last two are effects. Now the way in which I 

 propose to examine the result of introducing a lead of the s.iile into 

 an engine which was before worked at full pressure is this; to see 

 what change it would produce in tucA of the above two effects, sup- 

 posing the other three conditions to remain unaltered. That is, to 

 see 



