108 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[April, 



feet diameter, would be required to be 75 feet long. Of course it would 

 be preposterous to carry with the engine a vessel of this magnitude. 



In the first place, no power is f;uinid by using compressed air, because 

 as much force must be employed in condensing the air into the receivers, 

 as the condensed air can exert when brouglit iuio action. Next let us sec 

 what size of magazines or cases would be required for a railway locomotive 

 worked with compressed air, for a thirty mile stage. 



" The cylinders of a modern locomotive are about 14 inches diameter, that 

 is, the pistons have each an area of about one foot; the stroke is usually 

 about IG to 18 inches, and the circumference of the driving wheels is almut 

 17 feet ; they will consequently make about 310 revoUilions in a mile ; the 

 pressure in the pistons is about 50lb. on the inch. Then, assuming that 

 the air is compressed toa pressure of about 5000 lb. on the inch, we have 

 the elements for calculating what size of magazines or cases would be re- 

 quired." 



"As the wheels would make 310x30 = 9300 revolutions in 30 miles, and 

 as the two cylinders would each be filled twice during each revolution, 

 there would be 9300 X J = 37.200 cylinders full of compressed air required 

 to carry on a locomotive 30 miles ! Assume that the air was worked ex- 

 pansively in the cylinders, and that only a cubic foot was admitted at each 

 half stroke, the quantity of air compressed to 50 lb. on the inch, would be 

 37 200 cubic feet ; but as the air is supposed to be compressed to 500 lb. 

 on 'the inch in the portable magazine, its cubic contents would still require 

 to be 3,720 cubic feet ! To hold this would require a cylindrical magazme 

 of abou't 8 feet diameter, and 75 feel long ! Kalhcr a bulky case to move 

 about, or carry along a line.''* 



We have only one remark to make in support of these conclusions, 

 and that is, that not only would there be no gain of power by the 

 above arrangement, but many sources of absolute loss. lu the liist 

 place there would be the friction of the engine pumping the air into the 

 magazine, and in addition the friction of the locom.itive engine worked by 

 the compressed air. So that comparing Mr. I'arsey's system with the pre- 

 sent locomotive system, there would be for every journey the friction of 

 two engines instead of one. Another source of loss would arise from the 

 fact that all elastic fluids when compressed develop their latent heat. Now 

 as the elasticity of air is greatly increased by an increase of heat, it is 

 clear that the development of latent heat would in the present cnse greatly 

 increase the labour of pumping. This increased elasticity by the genera- 

 tion of heat would hovve.er be all lost, for the magazine would be rapidly 

 cooled by the radiation of its metallic surface. Another loss would arise 

 from the refrigeration of the air by its dilation when passing from the 

 magazine to the cylinder. 



It may be said that air could be pumped into the magazine so slowly 

 that the development of heat would not be apparent to the senses. But 

 this is only concealing the evil instead of removing it. It is true that the 

 heat might be generated so slowly that the radiation of the cylinder would 

 carry it°off as fast as it was produced, but this would simply render the 

 evil non npjinrent. 



Contrasted with the previous quotation which avoids all diBiculties 

 arising from the variation of the pressure in the reservoir, we have a letter 

 addressed to the Mining- Journal in favour of the new invention. We wish 

 to draw attention to one error in it, because it is one very likely to be com- 

 mitted by a person not familiar with the theory of pneumaiics, and as it 

 entirely vitiates the calculations. The writer calculates " that to draw a 

 train CO miles with a tractive f.irce of 3000 lb. the work done must be 

 1,188,000,000 lb. moved through one foot," and the letter concludes in the 



following manner. 



" Let it be propo'jcd.to compress the air to 1000 lb. pressure, which will 

 give a medium working pressure of 500 lb. per square inch ; 1000 lb. pres- 

 sure per square inch is equal to CC atmospheres-consequemly, a column 

 of a,r compressed into 60 times its density-«u> foot iiigh, and inch 

 IZ at"lu. base-will lift 500 lb. GO feet high, or 33,000 lb. 1 foot high ; 

 consequently, a column of compressed air of (iG at.nospheres, being 1 foot 

 higraml 1 f^ot square at the base, will lift 33,000 X 141 lb. 1 foot high, 

 or 4,752,000 lb. I tout high. Then, as 4,752,000 lb. "'H ■■"qun.-e one cubic 

 fool what v^ill l,llS,000,UOOIb.r..quire?-Auswer 2.(7 cubic feet. In 

 iL' manner, if the air were compressed to 2000 lb., the contents of the 

 magazine required would be 60 feet. A magazine of 3 feet diameter J 

 feet lon<f and 1 inch thick, would, therefore, be amply sufficient ; the 

 weight of such a magazine would be4000lb.-AN tNGiNEEa: London, 

 Feb. 18." . ^ , . , ., 



The chief error in the above paragraph is the assumption with which it 

 starts, that if the air be at 1000 lb. pressure at the first, and at 15 lb. pres- 

 sure at the last, the average pre ssure will be about half way between th ese 



'. or course if tlic prB8»uie be lOCil) lb. to the inch ia the reservoir, llie size of it will 

 be reduced ooe-balf. 



two pressures, or equal to 5001b. Now we want to show that the average 

 will not be nearly so much as this, and the explanation is worth attending 

 to, because it shows the danger of "jumping" at conclusions. 



Suppose, for simplicity, the case taken in the extract, of the air in a tube 

 60 feet Ion;;, and of uniform diameter, being compressed so as to occupy 

 only one foot of the tube at its end : what we want to find is the work 

 done by this compressed air (or the number of pounds moved one foot by 

 it), while being dilated back to its ordinary density. Tracing its progress 

 foot by foot from the first foot to the sixty-sixth, we find that at the second 

 foot it occupies twice as much space as at first, at the fourth foot, four 

 times as much space, at the eighth, eight times as much, he. Consequently 

 the pressures at the 1st, 2nd, 4th, 8th, & c, feet are respectively 1000, 500, 

 250 125 6tc. Now the mere consideration that at the second foot the, 

 density is reduced to 500, shows how terribly the average has been over- 

 rated in the above extract, where the rapid decrease of pressure is ne-' 

 glected, and the air is supposed to act with the same average force through- 

 out the CO feet, which in fact it exerts only from the first to the second 



foot. 



We could not without a few mathematical symbols calculate the exact 

 amount of work done in the present case, still we can give an approximate 

 method readily intelligible to any one acquainted with the first four rules 

 of arithmetic. Let us consider what would be the pressure of the air at 

 the first, second, fourth, eighth, &c. feet, and let tis suppose that it passes 

 from each one of these stages to the next without a diminution in pressure. 

 This supposition of course exaggerates the amount of work done. Then 

 from the first foot to the second it moves 1001) lb. through one foot; from 

 the second foot to the fourth it moves the half of 1000 lb. through two feet 

 (= 1000 lb. through one foot) ; from the fourth foot to the eighth it moves 

 the fourth of 1000 lb. through four feet (= 1000 lb. through one foot, See.) 



Arranging the results in the form of a table, we have- 

 Work done or number 

 of lb. moved one toot. 

 1st to2nrtfoot, 1000 lb. through 1 foot - lOllO 



2n.lto4th, halfof lOOOlb. tlirough a feet - liiOl) 



4tli to Sth, quarter of loonlb. througll 4 feet - lOOO 



8tb to llilb, oneeighth of ISiiO lb. through 8 feet = 1000 



Killi to 32nd, one-sixteenth of loriO lb. through 10 feet = 1000 



.i2nd to64ih, one-thirty-sccOBaof KlOO lb. through a2 feet •= 1000 

 This gives the total work up to the G4th foot ; for the remaining two 

 feet add' two sixty-fourths of 1000 lb. (about 31 lb.), and we find finally for 

 the total work done, that according to the above calculation (which is a 

 very favourable one) the number of lb. moved one foot is 6031. The " En- 

 gineer" makes the number 33,000, or more than five times as much 1 



The following method gives the true result much more accurately. If 

 the pressure at a distance of 1 foot from the end of the tube be 10001b., at 



any increased distance .t the pressure will be 



the work done through a short distance dx, 



1000 100 



1 and dx will be 



. • . the whole work done 



will be 1000 



/dx 



between limits 65 feet and 1 foot = 1000 x log, 66 



= 1000X 11S9I1 = 4189-G. 



The amount of work then really done is equivalent to 41891b. moved 

 through one foot. Comparing this with the quantity calculated by the 

 "Engineer," (namely, 33,000 lb.), we find that he has made it between 

 seven and eight times ii-ltnt it ought to be. 



It is really lamentable to see people deluding themselves and others in 

 this manner. The newspapers state that Prince Albert saw the model of 

 Ihe air engine, and expressed his approval. It is not however stated that 

 he made any calculations, or that his royal power extended to a suspen- 

 sion of the laws of elastic fluids. 



AVe had almost forgotten to mention that the pressure in the reservoir 

 supposed to be 1000 lb. to the square inch, is more than ten times as much 

 as the very extreme pressure which is considered safe in the boiler of a 

 locomotive engine. 



DnrDGiNG Machinery for Ecvpt.-M. Cav^, of Paris, who contracted 

 for the building of the Chaptal, iron steamer, with all her machinery com- 

 plete, which is about leaving France, is now busdy engaged at Uoiien, 

 ft sb ppiug oirto Alexandria, in Egypt, the ddlerent materials to complete 

 I e U-'e dredging machine, for which he has contracted with the Pacha, 

 Mehen^^l-Ali, for the purpose of dredging the Nile, so as to render it per- 

 fectlv navi<rable. This is only a preliminary step towards the cutting of a 

 navigable ship canal across the Isthmus of .Suez to j,,m the lied Sea with 

 Uie MedUcnanean-one of the grand projects of the Emperor Napoleon. 



