228 



THE CIVIL ENGINEER AD ARCHITECTS JOURNAL. 



[July 



be clearly expressed by the difference of the corresponding numbers in this 

 column. 



Tart of the remainder of the paper was devoted to showing, that whilst the 

 performanre of engines coulil not possibly be expected to exceed the results 

 ascertained as above, it should not fall far short of thera in the case of en- 

 gines of good construction. In conclusion, a simple method was suggested 

 of ascertaining the magnitude of all the forces in action during the working 

 of the Cornish engine, independently of the indicator. 



In the course of the paper, the fallacy of the theory of what had been 

 termed the "percussive action" of steam was ably exposed ; and although, 

 from the paper being full of mathematical formula, it was not well adapted 

 for being read at a public meeting, it evidently possessed great merit as an 

 investigation of an important subject. 



" On the E.vpansive Jetton of Steam." By Mr. Tate, mathematical mas- 

 ter of the Training College, Battersea. 



The object of this paper was to demonstrate and apply a formula some 

 time since discovered by the author, expressing the law of the expansion of 

 steam, and at the same time to establish certain general equations relative 

 to the work of steam, applicable to all formula: professing to give the law of 

 volume and pressure. It also examined and corrected Pole's formula, which, 

 although a decided improvement upon Panibour's, was stated to be not suf- 

 ficiently accurate for pressures above 701b., or below IG lb. 



M. PiAROET exhibited in the library, after the meeting, specimens of his 

 improvements in producing ornamental metal surfaces, formed by the deposi- 

 tion of metals during the electrotype process, which is conducted in a pecu- 

 liar manner, with mixtures adapted to the effect desired to be attained. The 

 form also of the bath is peculiar, and when the plate is taken out of it, and 

 otrthe model, it exhibits a burnished polish, or a dead appearance, according 

 to the preparation used. The metal thus produced is stated to be of a mucli 

 better description than metals which liave not undergone such process, as it 

 is more flexible, and is capable of withstanding the action of heat without 

 destroying the form or the copper, and the surface will not tarnish when ex- 

 posed to the air. Portions of any pattern can also be silvered by a similar 

 process ; and the general expense is about one-third of that of engraving or 

 chasing, while the boldest or most minute patterns can be equally well pro- 

 duced. 



Jnne 15. — " On the Law which Governs the Discharge of Elastic Fluids 

 under Pressure, tlirough short Tubes and Orifices." By M'. Froude, M. 

 Inst. C.E. 



The law proposed was a modification of that which has been usually 

 assumed — viz. : a simple application of that which holds good with respect 

 to non-elastic fluids; this law is, generally, that the velocity of issue is 

 directly as the square root of the pressure, .ind inversely as the square root 

 of the density ; liut this law neglects wholly the reaction that must arise 

 from the expansion necessarily taking place in the course of issue. The 

 nature of the action was illustrated by the following example : — If a balance 

 lie supposed, with an equal weight in each scale, one of the weights being 

 a spiral spring, like that of a S|)ring balance compressed lengthwise with 

 its axis vertical, and held in a slate of compression by a cord. Now let 

 the cord hv siHl<lenly reversed, so that the spring is enabled to extend itself 

 vertically ; tlie scale in wliich it stands will obvinuslj be depressed, the 

 i^liring reacting on it as it expands upwards, and continuing to press till 

 wholly relaxed ; or if the scale in which it stands were ascenduig by a 

 preponderance given to the other scale, the rate of ascent would lie in the 

 .same way retarded. The amount of the retardation would depend on the 

 strength and the weight of the spring, and on the lengtli to which it wnuld 

 entend itself when released. Now in the discharge of an clastic fluid, 

 there is an action, strictly analogous, operating coatinuously, however, in- 

 .stead eii pa- siiltum, the strength and weight of the spnn;; bi-ing representeil 

 by the i-Uislicily and density of the fluid, and the length ti> which it would 

 extend itself by the degree of expansion, in the course of issue. The re- 

 duction in quantity of discharge, due to the action, was to be measured by 

 (he velocity imparled by expansion, to each panicle of the clastic fluid in 

 course of issue, the velocity of each particle after expansion, would be its 

 velocity before expansion, multiplied into the rate of expansion, and the 

 primary force must he subdivided in generating each additional unit of ve- 

 locity, so that the portion applicable to tlie generation of velocity before 

 expansion, would be the whole force <livided by ihe rate of expansion; 

 thus, the velocity before expansion would be divided by the square root of 

 that rate. For inttance, an elastic fluid expanding four limes in course of 

 issue, would be discharged with only half the velocity of a non-cIastic fluid, 

 under the siime circumstances of pressure and density. This inodilication 

 was shown to fulfil the general djnaniical law "that a given force, acting 

 for u given lime, will produce a given nnnnentum, vvhalever be the weight 

 of the mass acted upou." This ^eelned to be the essence of the law for 

 non-elastic fluids, hut il was disregarded by the unmodified application of 

 that law to elastic fluids, in which there would be a great accession of ve- 

 locity, of particles issuing under a given pressure, without any reduction 

 of quantity discharged in a given lime ; if, however, the quantity be re- 

 duced as proposed, iu the ratio of the square foot of the den^ity, and the 

 velocity be accelerated in the same ratio — Ihe final momentuin would be 

 llie true equivalent of the pressure. This, in its practical application, ex- 

 plained what was inexplicable by the ordinary theory. 



The dilhculty experienced from the back pressure of the waste steam in 

 locomotive engines was exhibited, showing, that at tiO miles per 



hour, this would he at the least equivalent to 8 lb. per inch throughout the 

 slioke, thus showing a loss of nearly 50 h.p. As applied to the case of air, 

 discharged into an exhausted receiver, the result was highly curious. The 

 rate of discharge, instead of increasing throughout as Ihe degree of vacuum 

 was increased, would be maximum at 15 inches of vacuum, although nearly 

 uniform for many inches above and below that point ; it would, however, 

 progressively decrease above that point, because the expansion would in- 

 crea>e in a higher ratio than the pressure, and ultimately, at the point of 

 perfect vacuum, it would be at a minimum (indeed stationary, were air 

 perfectly elastic), because at that point the expansion would be iufinile, but 

 the pressure only finite — viz.: 30 inches of mercury. Experiments made, 

 by permission of Mr. Brunei, with the South Devon Railway atmospheric 

 apparatus, confirmed the theory. The line traced by an indicator appara- 

 tus was shown to accord very closely with one traced by this theory, whilst 

 it was widely at variance with the result of the ordinary theory. 



[Me must caution our readers against placing any confidence in the new 

 law of the motion of elastic fluids, enunciated by Mr. Fronde, which 

 seems to us to be directly opposed to the fundamental laws of dynamics. 

 If we suppose any number of particles acted on by external impressed 

 moving forces, all in the same direction, the motion of the centre of gravity 

 of the particles in that direction will be the same as the motion of the cen- 

 tre of gravity of a solid body of which the mass is equal to the sum of the 

 masses of all the particles, and the moving force the sum of the moving 

 forces acting on all the particles ; and Ihis law is true wbateier be the na- 

 ture of the connection between the particles or the mutual internal forces 

 which they exert on each other. In the case of the motion of particles of 

 fluid from an orifice— if the pressure at the orifice is constant, we confess 

 we can see no reason why the quantity discharged in a given time should 

 not be the same, whether the fluid be elastic or not — the question of elasti- 

 city or non-elasticity involving merely the internal or molecular connection 

 of the discharged particles. Vie wish, instead of the brief and not very in- 

 telligible abstract inserted above, we had been favoured with Mr. Fronde's 

 unabridged analysis. If his views be correctly reported, it seems to us that 

 he has confounded mass with volume ; at all events, his results lead to an 

 evident absurdity — viz., that if air were perfectly elastic (as indeed it is 

 very nearly), and the vacuum in an air-pump were perfect, on opening the 

 cock of the receiver no air would flow in. We think that if Blr. Froude 

 repeats his experiments with a well constructed air-pump, he will be con- 

 vinced that he is mistaken. Let him take an exhausted receiver, with a 

 mercurial gauge, and havingopened the cock, note the times of the mercury 

 rising from to 5 inches, 5 to 10 inches, 10 to 15 inches, respectively ; 

 — why our ear at once detects the absurdity, Mho has not noticed how 

 the hissing of the air, as it rushes through a small orifice into a vacuum, 

 changes from a shrill to a hoarse note ? There is no doubt that the law of 

 theory is not fulfilled in practice, but that is owing to the friction — or rather 

 resistance — arising from the particles of air striking, with enormous velo- 

 city, against the inequalities of the small lube. Neither is it possible — at 

 least in the present stale of analysis — to estimate exactly the pressure at 

 the orifice. But the same difficulty holds in the case of inelastic fluids, — 

 for llie motion of which, we refer the reader to a paper in the Journal for 

 April ; one or two errors which escaped us at the lime, in the proof, will 

 be found corrected iu the Number for June. For the "backpressure," 

 we recommend our readers to turn to the Count de Pambour's valuable 

 work on the steam engine. — Editor.] 



Jnne Tl. — " An Accnvnt of the Plans that have been Proposed /or Con- 

 necting the Atlaiilic and Pacific Oceans liy a Sarigable Canal." By Mr. 

 JosEi'H GLV^N, M.Iust. C. E. 



The author took a review of these projects from the time of Corlez, who 

 proposed to cross the Isthmus of Tehuantepec by joining the waters of Ihe 

 River Coatzoccoalers, which flows into the Gulf of Mexico, with those of 

 the River Chicapa, flowing into the Pacific, by the Bay of Tehuantepec ; a. 

 plan which has lately beeu revived by Don Jos^ de Garay, who, with the 

 assistance of Siguor Moro, surveyed the country from sea to sea, and 

 showed that the chain of mountain is there broken for about 35 miles, 

 giving place to an eleviiled plain or table land, called the Mesa de 

 Tarifa, where both these rivers originate, and where their junction could be 

 easily effected. The objections to this plan are, the length of the river 

 navigation, about 200 miles, and the ascent of the stream to the Mesa de 

 Tarila, about 200 ineties, or C56 feet above ihe ocean. The survey was 

 made under ihe patronage of the Mexican President, General Santa Anna, 

 who professed lo grant many important privileges to the promoters. The 

 Isthmus of Nicaragua was next examined, and after that the course of 

 the River .St. Johu to the lake, which is a little more than 15 miles distant 

 from the Pacific Ocean, and about 130 feet above its level. The dis- 

 tances and the levels were accurately taken by Mr. Bailey, an olficer in 

 the Royal Marines, by desire of General Marazon, President of the Cen- 

 tral American Republic. The ridge of hills intervening between the lake 

 and the ocean, and the uncertainty of the waters in the River St. John, 

 alternately swollen by the rains, or dried up by the heat of a tropical sua, 



