IS45.1 



THE CIVIL ENGIxXEER AND ARCHITECT'S JOURNAL. 



207 



tbe above quotation tliat tlie pressure is somotimi's as mucli as 60 lb. 

 to the square incli, anil sometimes no more tlian two or three ; so that 

 while the engineers of the (iovernment steamers imagine that by con- 

 densing steam of three or four pounds pressure' the ctlVctive pressure 

 becomes 15 or Hi pounds, they in reality command no greater working 

 pressure than four to six pounds. 



It will be observed that in the experiment suggested in the quota- 

 tion above, the piston is supposed to return through the same space 

 as it advanced, — so that, if a steam pressure of liu lb. would act on it 

 through two feet as it advanced, an air pressure of UO lb. would act on 

 it through two feet as it returned ! Or, as we said, the same quaiilily 

 of nattr producing the same effect by eilhcr kind of action, the effect 

 is doubled if it act by both at once'. By the onlinary method, how- 

 ever, of viewing the 'subjfct, there is only one owe degree of steam 

 pressure for which it could be true, namely, for that which equals the 

 atmospheric pressure. 



On the theory laid down above, the writer proceeds to certain ana- 

 lytical investigations of the power of condensing engines. From these 

 we make the following extract. 



Ilencc, neglecting the waste and the friction of the piston rod, we have 

 for the mechanical ctfect of one cubic foot of water, as developed by con- 

 densation, 



5354 (459). {l-^}= ^^^^(^^^y>^^-^-^ 



!I)S. raised one foot. Before leaving this, we may also estimate the loss re- 

 sulting from friction of the piston rod. Let ./„ denote ttie friction of the 

 piston rod, wliich friction we suppose constant. It is obvious that this fric- 

 tion operates in exactly the same manner as the uncondensed steam. The 

 mechanical loss resulting from it will therefore be represented by 

 5354 (459 + /a 



7 

 lbs. raised one foot. 



We are not going to discuss the equations which we have quoted, 

 but we call the attention of the reader to tlie meaning of the symbol t 

 which appears in both of them. This /, on looking bank, we find to 

 be the temperature of the steam before condensation. So that we 

 conclude from the lirst equation that the force of a single acting engine 

 after condensation is in some way dependent on the heat of the steam 

 before condensation, and that, ol all things in the world, the friction 

 of the piiton depends on the same cause ! The resistance to the piston 

 at anv time is determined by the heat of the steam which was in the 

 cylinder some time previously ! A nice notion the writer must have 

 of steam engines. 



If the reader examine the same subject in M. le Comte de Pam- 

 bour's admirable work The Theory of the Steam Engine, he will find 

 the beautiful simplicity of M. de Fambour's views to be only equalled 

 by the perspicuity with wliich they are expressed. 



In the treatise of the "Artizan Club" we have, immediately after 

 the passages quoted, some peculiar notions on the employment of 

 steam expansively. 



In order that the piston rod should remain at rest, it is necessary that the 

 pressure upon the piston should equal the elastic force of the steam. If the 

 load upon the piston be in the smallest degree below this, the piston will be 

 forced up till the increased expansion has so diminished the elastic force of 

 the steam as not to move it higher. * * * * 'j'lie mechanical effect 

 gained by removing at once the load necessary to allow the piston to take 

 the position, is smaller than what would be gained by taking the load off 

 gradually. 



We wish to direct tbe reader's attention to the last sentence. The 

 statement is this, that if the load on the piston be diminished gra- 

 dually the effect of the steam will be greater than if part of the 

 load be taken off suddenly. This proposition, even were it true, is by 

 no means clear enough to be staled axiomatically, without a demon- 

 stration. But there are many re.isons for pronouncing it untrue. In 

 the first place, it would lead to this conclusion — that the amount of 

 a force is regulated by the external resistance opposfd to it. The 

 problem is essentially a dynamical one, and by all the laws of dynamics 

 the effect of a given force of any nature whatever is the same w hetlier 

 a great or a small resistance be opposed to it. In the first case a 

 small, and in the second a great velocity would be produced. To take 

 an illustniticn ; the elastic force of a buw would be accurately mea- 

 sured by the motion it produced whether it acted on a large arrow or 

 a small one. Lft us suppose the law of elastic force the same for the 

 bow as for steam, proportionil to the compression, then we have a 

 case exactly in point. But as the size of the arrow does not alter the 

 elastic force of the bow, we cannot imagine that there would be any 

 gain of force were it possible to diminish the arrow while the bow 

 was acting on it, and in the same way the effect of the steam cannot 

 be altered by altering the mass of the piston. 



To examine tbe question analytically — let x be the height to which 

 the piston lias ascended at the time / ; M its original mass. As far 

 as may be collected from the quotation, the mass is supposed to varv 

 inversely as the lieight of the piston : M -f- a: is therefore the mass at 



the time /. Let - be tbe steam force, then for the instant succeeding 



the time i the equation of impressed and effective forces is 



Ud'x 



M 



X (it 





But tills equation is identical with the ecjuation for the motion when 

 the mass is unchanged, viz., 



(it- X 



That i«, the ris viva generated is tbe same in both cases. 



It is, however, scarcely necessary to be thus explicit, for the author 

 himself makes a deduction from his theories wliich is certainlv one 

 of the most notable in the whole range of mathematical authorship. 



Suppose the volume of steam before expansion to he to the volume after 

 expansion in the proportion of 1 to k ; in other words let ,< =» 4, then re- 

 membering that, as we have shown previously, 



p 4 = 5354 (459 + 

 we find for the mechanical effect of the expansion E pounds raised one foot 

 high, where 



E = 5354 (459 + 'og "• 



We learn from this that not only is mechanical effect gained hy using expan- 

 sion, hut that there is no limit to this gain other than the inconveniences 

 arising from the too extensive application of this principle in practice. I he 

 above formula will be useful for determining the amount of mechanical effect 

 gained by cutting off the steam at different parts of the stroke. To facilitate 

 the application of this formula we shall just state the values of n when the 

 steam is cut off at different parts of the stroke. If the steam be cut off at 

 2 stroke, then n = 2 ; if the steam he cut off at | stroke, then n= 3 ; and ge- 

 nerally, if steam be cut off at - stroke ; then n = m, or more generally still 

 m 



if the steam be cut off at - stroke, then n=- 

 1 P 



From the equation " for the mechanical effect of the expansion" we 

 learn that this effect increases as log n increases, and consequently is 

 infinitely great when n is infinite : and we are told that there is in 

 theory " no limit to this gain." Putting these two remarks together, 

 we come to the following conclusions. 



First, a limited force may be made to produce an unlimited effect. 



Secondly, putting ?! : 



and cutting off the steam at the — 



00 



stroke, if 710 steam be admitted the power of the engine is infinitely 

 great. 



What, then, is the use of having a boiler ? 



From all which we conclude that the mathematical theories of tbe 

 " Artizan Club," though not irresistibly conclusive, are irresistibly 

 comic. 



H. C. 



ON THE EXPANSION OF BRICKWORK, 



(Considered with Reference to a Chimney Shaft, at Mr. Cubitt's 



WOKKS, AT Pl.MUCO.) 



Paper read at the Institution of British Architects, Jlpril, 1845. 



The chimney to which I propose to direct your attention is an ob- 

 ject of interest, from the proof it affords of the power of heat, in ex- 

 panding materials — in which such expansion is generally overlooked. 

 The shaft is encased in a tower, without being any where in contact 

 with it, or any part of the adjoining buildings : great care having been 

 taken while building, to keep the chimney quite free from all ilic 

 other work. None of the floors or l.indings of the tower were allowed 

 to touch the shaft; the intention being to permit it to move up and 

 down freely, as the heat acted upon it — thus preventing that displace- 

 ment of materials in the tower which would otherwise have happened. 

 This shaft is built of brick, which is perhaps of all materials, the least 

 affected by change of temperature, and yet it is found that the shaft 

 differs in height considerably, even with the change arising from the 

 comparatively slight variation in the height of the smoke and vapours 

 passing through it. This variation is never more than 250" Falir., 

 and yet the shaft at the height of 90 feet alters, or rises, nearly JtU 



27* 



