1844.-] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL 



365 



over a rough gravel path more easily by pulling the handle than by 

 pulling a long rope fastened to the handle. This last illustration sug- 

 gests an experiment worth making, and easily made, by which the 

 subject would be elucidated far more clearly than by written explana- 

 tion. 



The alternate retardation and acceleration of the train will have 

 another effect which is due to the elasticity and weight of the rope, 

 namely, that at each retardation the tension of the rope will be slightly 

 increased, and at each acceleration diminished ; the consequent 

 stretching and unstretching is maintained by force, which contributes 

 nothing to the motion of the train. 



II. In considering the application of steam power by atmospheric 

 pressure, it will be necessary to remove a very common error which 

 supposes that power is in some way gained by the intervention of the 

 air. Now to refute this notion it seems sufficient to state the general 

 theorem that " power is not gained but only transferred by machinery ;" 

 or taking the most favourable case that could possibly exist, namely, 

 that the exhaustion of air should be perfect, and effected by apparatus 

 perfectly air-tight, and without friction, it may be seen that whatever 

 pressure exists on that end of the locomotive piston open to the air 

 can only arise from, and will be exactly equivalent to, the power ex- 

 erted in removing a corresponding pressure from the other end of the 

 piston, so that even in this hypothetical case, power would not be 

 gained but merely transferred. 



But it will be shown that in practice the amount of power actually 

 transferred is much less than that expended. The causes of the los,s 

 are many ; among them are the friction and leakage of the locomotive 

 piston in traversing the whole length of the tube, and the friction and 

 leakage of the air-pumps. But these are trivial compared with the 

 enormous waste owing to leakage in the fissure extending along the 

 top of the tube ; and this cause will operate after every precaution 

 has been employed. The apparatus also for closing this fissure will 

 require and abstract additional power, which contributes nothing to 

 the motion of the train. 



There is another cause of power being lost which, as I have never 

 seen it noticed, I shall discuss at some length, namely, that arising 

 from the elasticity of the air and analogous to the effect alreadv alluded 

 to, of the elasticity of a rope, where that means of traction is em- 

 ployed. 



Suppose first for sake of explanation that the power of the engine 

 is transferred to the train by compressing instead of rarefying the air. 

 Taking the simplest case, let A, a, be two pistons moving air-tight in 



a horizontal tube. If the piston A were advanced to B, the effect 

 would not be that a would advance an equal distance to b, it would not 

 move so far, and part of the force used in advancing A to B would be 

 absorbed in condensing the air between the two pistons into a smaller 

 space. 



Similarly suppose that A receded to C, a would not therefore re- 

 cede an equal distance to c ; part of the force used in moving A would 

 be absorbed in rarefying the air between the two pistons. Now this 

 is precisely the case of the Atmospheric Railway. 



Or the matter may be simplified thus— drawing an analogy between 

 the traction by a rope and that by atmospheric pressure, we may 

 state that in the one case the power is transferred by a rope of com- 

 paratively inelastic material, iron wire or hemp, and in the latter case 

 by a rope of the most elastic substance — air. 



Papin, the inventor of the well known machine, called "Papin's 

 Digester," proposed to pump water out of a mine by aid of a stream 

 moving a water-wheel, two miles distant; his plan was to use the 

 water-wheel to work two pistons moving air-tight in a tube which 

 •was continued from the stream to the mouth of the mine, where two 

 similar pistons were placed. He imagined that the air would communi- 

 cate the reciprocating motion of the first pair of pistons to the second, 

 though they were two miles apart. Owing however to the elasticity 

 of the air, he found that no effect could be produced without giving 

 the first pair of pistons an extent of motion altogether preposterous. 



Sir Walter Scott had a scheme at Abbotsford for superseding beil- 

 wires by air-tubes, at the ends of which next the bells, solid pistons 

 were placed which were to set the bells in motion ; at the other ends 

 similar pistons could be worked by hand. The apparatus proved 

 altogether ineffectual. 



To determine more precisely the nature of the waste of force in 

 atmosplieric railways from the cause under consideration, we will 

 imagine an atmospheric pressure of (suppose) 10 lb. to the square 

 inch on the locomotive piston necessary to overcome the inertia of 



the train, and set it in motion with the requisite velocity. "The 

 elastic force of air at a constant temperature varies inversely as the 

 space It occupies;" or, in other words, the pressure lessens in 

 proportion as the air is rarefied, and increases in proportion as the 

 air IS condensed. Now to produce a pressure of 101b. to the square 

 inch on one end of the moving piston, we must (taking the ordinary 

 atmospheric pressure at 151b.) diminish the elastic pressure in the 

 tube of rarefied air till it amount to only 51b. on the square inch: that 

 IS, the air in a tube some three miles long, must be rarefied 5-15ths 

 or one-third its original density before the train can be put in motion. 

 And the force requisite for this purpose contributes nothing, be it 

 remembered, to the subsequent motion of the train, since to maintain 

 Its motion the pumps must continue to be worked exactly as if this 

 preliminary exhaustion had not been effected, for otherwise the advance 

 of the piston would soon condense the air again. 



We must now recur to the experiments illustrated by the preceding 

 diagram. In these experiments we have tacitly assumed the existence 

 oi friction or some other resistence to the motion of the piston a. Did 

 no such cause operate, the piston A would not by its advance or re- 

 treat condense or rarefy the air between it and a ; the pressure of air 

 on both sides of a would ultimately be balanced— that is, the air be- 

 tween the pistons would become of equal density with the external 

 air; consequently the extent of motion of both pistons would be the 

 same when not resisted by friction or otherwise. 



When however resistances exist, the motion of the first piston is 

 greater than that of the second. It must not however be hastily con- 

 cluded that the loss of power, because called into existence by the 

 friction, IS therefore equal to it. If such were the case, we should in 

 the preceding paragraph have been allowing for the friction twice 

 over. This, however, is not the case, for if the loss of power now 

 under consideration were equal to the friction, its amount would 

 clearly be determined by the friction only, whereas that amount de- 

 pends also on the length of the tube. And from principles already 

 laid down It will be readily seen that, cceteris paribus, the loss of 

 power will only be half so much in a tube a mile long, as in one twice 

 the length. For instance, suppose a force of 5 lb. to the inch were 

 required to overcome the resistance of the piston, the pressure in the 

 tube of rarefied air must be made = 15-5, that is 10 lb. ; consequently 

 the air must be rarefied to 10-]5tbs its original density. Now for 

 tliis purpose twice as much air must be pumped out of an air-tube 

 two miles long, as out of one, half the length. 



It may be considered also that we have over-estimated the loss of 

 power 111 stating that "the preliminary exhaustion contributes nothing 

 to the subsequent motion of the train." It may be argued that the 

 amount of pressure necessary to merely put the train in motion is 

 much less than that necessary to maintain its full velocity. In prac- 

 tice, however, the train is never started till a great proportion of the 

 exhaustion has been effected, and before the train has performed but 

 a very small part of its journey the maximum exhaustion is effected. 

 Moreover, up to that point the waste of power will continue to ope- 

 rate—though of course not in so great a degree as when the train is 

 at rest and diminishing as the velocity increases— for this reason, that 

 until the full speed is attained, the vacuum increases in degree and is 

 therefore carried on with greater rapidity than corresponds to the 

 mere progression of the train. 



We must explain what is meant by " rapidity of exhaustion cor- 

 responding to the velocity of the train." When the rarefaction has 

 reached that degree which is to be maintained without increase or 

 diminution throughout the journey, the train will also reach its full 

 speed. It will follow, therefore, that while the degree of rarefaction 

 remains unaltered, for every foot which the motive piston advances 

 along the air-tube a quantity of air equal to that contained in one foot 

 of the air-tube will be pumped out by the engine. If this exact cor- 

 respondence in the rate of pumping the air and of the motion of the 

 train were not maintained the degree of rarefaction would not remain 

 unvaried. If the air were pumped out more slowly than the motion 

 of the propelling piston required, the air would tend to condense, and 

 vice versd. Of course in this explanation the supposition of leakage 

 is excluded. ^ 



The elasticity of the air affords a reservoir of force which towards • 

 the end of the journey would keep the train in motion for some little 

 time alter the air-pumps ceased to be worked. This circumstance 

 might be considered another offset against our estimate, but that the 

 tram is never in practice allowed to come to rest gradually but is 

 stopped by the external force of breaks. On the whole, therefore, the 

 amount of loss must be considered to be almost exactly that above 

 estimated. The motive piston successively occupies every part of 

 tha air-tube, consequently, supposing no leakage, the air-pumps must 

 before the journey can be completed, pump out a volume of air equal 

 to the solid content of the tube. Now we have shewn that where the 



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