3:36* 



THE CIVIL ENGINELR AND ARCHITECT'S JOURNAL. [Noykmbkr, 



A = 134 65 cubic feet 

 B=I76;-76 cubic feet 

 C = 8771-33 cubic feet 

 C + C 

 TbeaR = - 



o = 66 inches = 55 feet 

 *= 3421-2 square inches 



V = 79 nearly, log R = 0'0043. 



A + I3 + C 10073-74 

 S-A B-i-C 

 A ~ A ~ 134-65 

 To determine («) suppose the exhaustion carried on until the pressure of 

 tlie air in the main is reduced to 5 lb. per inch, then we have 



R" = ;J .■.raxO-0043 = -4771 .-. n=lll nearly. 

 Substituting in (A) we find, after some troublesome arithmetic, the work 

 done to be equivalent to 15,947,068. (4) 



After the train piston has slatted, it is clear that in order to preserve the 

 rarefaction obtained by the preliminary exhaustion we must have 

 lts = k's' (5) 



Where s, s' are distances simultaneously described by, and i. A' the areas 

 of, the pump and train pistons respectively. So that if m be the number of 

 ttrokes made by pump while the train piston travels over a distance s', and 

 a, i% before, the stroke of the pump, we have 



m a = s=—r- .•.»! = — r (b) 



K a k 



In this case the pressure in the direction of M's motion is constant, and 

 equal to 5 lb. per inch. The pressure against M varies until the valve which 

 comunicates with the atmosphere opens, after which it remains constant. 

 We have — 



Pressure against M : Pressure at beginning of stroke ( = 5 ilb.) 

 ■.■.AB:AU::a:x 



.•. Pressure against M = 5A-lb. 



Supposing C to open when M arrives at H, where A H = 'v,then i = 5 a. 

 The work done in any stroke when the train is in motion is therefore — 



/» dx 



*/-v 



= 5 * log 3 



The woi k done while the train piston travels over a distance s' is there- 

 fore — 



&' s' 

 W = 5 a»>*Iog3 = 5 «*— -r log 3 by (6) = 5 k' s' log 3. 



Suppose, for example, that A' = 176-7 square inches and s =7147-5 feet — 



Then W = 5 x 1767 x 7147-5 x 0-477 nearly = 3,012,167. (7) 



From (4) and (7) we see that the whole work done in order to enable (he 

 piston to travel through a distance of 7147 5 feet is equivalent to 



18,059,235 (8) 



The work done by the piston in travelling over 7147-5 feet is equivalent to 



10 X 176-7 X 7147-5 = 12,678,225 nearly. (9) 



From (8) and (9) we have the power lost = 18,959,235 - 12,678,225 

 Beariy = 0,281,010 nearly. 



Hence the proportion of the work done to the useful effect obtained is 

 about 3 : 2| so that about ^rd of the power of the engine are thrown away 

 without producing any useful effect. In other words, the power lost is more 

 than 33 per cent, of the whole power expended, and this loss is independent 

 of friction and leakage. 



NOTES 



ON THE PHILOSOPHY OF ENGINEERING. 

 II. 



Loss OF Power on At.mosphepic Railways. 



It is now about twelve montlis since I ventured to publish in this 

 Journal some obsfrvalions on an objection to atmospheric traction 

 which seemed to have been previously overlooked. The observa- 

 tions which I have offered from time to time on the subject, have ex- 

 cited an opposition due rather to the important nature of the con- 

 clusions arrived at than to their invalidity. 



The present paper will be preceded by one which may be confi- 

 dently ranked among the most valuable that have ever appeared in 

 this v\'ork. The conclusion of Mr. Haydoii's paper on Atmospheric 

 Traction deserves the most attentive consideration — " Hence tlie pro- 

 portion of the work done to the useful eflert obtained is about 3:2; 

 so that about one-third of the power of the engine are thrown away with- 

 out producing any uselul effect. In other words, the power lost is 

 more than 33 per cent, of tlie whole power expended, and this LOSS 



IS INDKPeNDENT OF FRICTION AND LEAKAGE." 



The calculations, from which these grave results are deduced, are 

 founded on data exactly according with actual practice. The reader 



mu!t carefully consider that the investigation, though necessarily pre- 

 sented in a ma'hematical form, is not an abstract theory but really and 

 practically true. The dimensions of the air pumps have been sup- 

 posed in calculation the same as the actual dimensions of the air 

 pumps on the Dalkey Railway, the dimensions of the main pipe and 

 connecting tube have been supposed the same, the pump has been 

 supposed to be of the same construction as that of the Dalkey line, 

 namely, double-acting; the working pressure has been taken at 101b. 

 per inch, and where numerical calculations have appeared they have 

 been carried to several places of decimals. 



The object of the present paper will be to explain, as far as possi- 

 ble, that which precedes it, in language divested of mathematical sym- 

 bols, so that the general reader may judge of the accuracy of the in- 

 vestigation and ascertain how far he may place reliance on the results 

 obtained. A few word.s may, however, be perhaps admitted to show 

 that no effort has been omitted to ensure accuracy. The obliging 

 offer to furnish the calculation which I had myself intended to attempt 

 was gladly accepted, from a conviction that the task was resigned to 

 one who would give it more value and authority than I myself could 

 possibly command. It was a great satisfaction to find that the sepa- 

 rate steps of the calculation resembled those which I had taken in my 

 own rough notes, except that the investigation assumed a degree of 

 simplicity and elegance which could scarcely have been anticipated 

 from the complexity of the subject. The numerical calculations were 

 repeated _;fl-e or s/:r /(»i£S, and since have been put into my hands I 

 have gone over thetn again by myself, and where there was any dis- 

 crepancy the whole was examined and re-examined until the cause of 

 the difference was ascertained. I am thus minute in giving the liis- 

 tory of the paper that the reader may not imagine it to have been 

 inconsiderately written or hastily published. 



The air pumps used on the Dalkey line are double-acting — that is 

 to siy, the effect of the piston is to pump out the air when moving 

 either forwards or backwards. It is clear that this arrangement is a 

 source of economy ol power. The pump has also valved covers at 

 both ends, so as to be relieved as far as possible from the resistance 

 to its motion from the pressure of the external atmosphere. The 

 eonstiuction of the pump is sufficiently explained by reference to the 

 diagram in the preceding paper. 



In comparing the power expended with the useful effect, we may 

 conveniently classify the former under two heads. 1. The power ex- 

 pended in getting a vacuum before the train is started. 2. The power 

 expended in maintaining the vacuum after the train and train-piston 

 are in motion. 



I. We will consider the power expended in effecting tlie prelimi- 

 nary exhaustion. To do this it will be necessiry to estimate the num- 

 ber of strokes of the pump necessary to rarify the air in the main and 

 branch pipe to ird its original density ; for supposing the atmos|>heric 

 pressure 15 lb. per inch the pressure in the tiilie must be reduced to 

 5 lb. per inch in order to a pieponderating external pressure of 10 lb. 

 per inch. Now it appejrs that on the Dalkey line the capacity of the 

 air pump is about y\1\\ of the capacity of the main and branch pipe 

 together. Let us then suppose tlie pump begins its work. After the 

 first stroke the same air which preiiuusly occupied the main and 

 brand) pipe occupies the additional space of the pump also; that is, 

 its bulk is ^jth more than it was before, and its density is therefore 

 decreased in the same degree, or is now fjtlis of the natural density 

 of the air. After the second stroke the rarified air of the tube suffers 

 a further dilation, ;iii I it will be easily seen that, as in the first stroke, 

 the air w,i» rarified in the proportion 78:71); this rarified air is in 

 the second stroke again rarified in the same proportion: or,as ff ex- 

 pressed the density in the first case, f§ X '| expresses the density 

 in the second case. After the third stroke, likewise, the density will 

 be Tu ^ ':3 ^ fS> '"■ Ciyl"! •'I''' after the fourth stroke the density is 

 expressed by f| multiplied by itself four times, or (ffj". In this 

 way it is found tliat after the llltli stroke the density is (ff)'",and 

 as this fraction is found on calculation by logarithms to be as nearly as 

 possible equal to i, we conclude that to reduce the air to one-third 

 Its original density 111 strokes of the pump are required. 



Having ascerlamed then the number of strokes necessary on pre- 

 liminary exhaustion, the next step is to find how much work is done 

 in making these strokes. For this purpose we must find the power 

 exerted Tor each separate stroke, for it will be observed, th.u the 

 power exerted differs in amount for each stroke; the first strokes re- 

 quiring much less exertion of power than those made when the ex- 

 haustion has been nearly completed. In the first stroke ol all, very 

 little more effort is required than that necessary to overcome the in- 

 ertion and friction of the pump piston. Fur the air in the pump 

 being the same density as that in the main, the moment the piston 

 moves the valve opening to the external air rises (that is to say, if we 

 suppose the friction and weight of the valve neglected;. 



