]56 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[Mat, 



of Saint Antony, at Padua ; as Simon Andreozzi did in the side elevations 

 of the AraCccli. at Rome ; and as many other Italian artists contemporary 

 with the Fiiinted-arch period have done, hut in general very imperfectly, in 

 numerous edifices scattered about Italy, from Venice to the kingdom of 

 Naples." 



The last number contains the title-page and index of the volume. The 

 third volume will be published in December. 



NEW LAW OF COMPOUND MOTION. 



At the last soirt'e of the Slarquis of Northampton there was exhibited 

 an instrument by Mr. I'erigal for developing a peculiar law of com- 

 pound circular motion ; the following description we extract fnom the 

 Literary (iazette. It is an instrument for " generating rclrugressive or 

 recurrent curves, by which the moving body, when it has reached the 

 extreme points of the curve, retrogrades or returns back in exactly the 

 same line along which it advanced ; constantly moving forward and back- 

 ward from one extremity to the other; and always tracing and retracing 

 the same line as it alternately advances and recedes." 



These curves were produced by a complicated system of wheel-work, 

 which Mr. Perigal stated lo be capable of generating numberless varieties 

 of curves dependent upon the ratio of the velocities of the movements ; but 

 the instrument was, on this occasion, adjusted for the production of para- 

 bolas or hyperbolas, and a sort of figure of 8 curve, resembling a lemnis- 

 cate, which he showed to be different forms of one and the same curve, 

 just as circles and right lines are (limits or) varieties of ellipses. M'hen 

 the tracing- point passed through the centre, the curve was at one of its 

 extremes or limits ; and the two ovals of the figure of 8 were opened to 

 their fullest extent of roundness; but alterations in the angular adjustment 

 of the movements caused these ovals to become more and more flattened, 

 till they ultimately converged or collapsed, and became in appearance a 

 single line, terminating in points, with the form of a parabola or hyperbola ; 

 and the tracing-point travelled forward and backward from one extremity 

 of the cur\e to the other repeatedly, without in the least degree thickening 

 the line in one part more than in another ; evidencing that it advanced and 

 receded in exactly the very same path ! In fact, the line of return might 

 be considered as superposed upon the liue of advance; as Mr. Perigal 

 remarked, in reply to a very eminent mathematician, who objected that 

 the figure of 8 cui-ve was a liue of the fourth order, inasmuch as it could 

 be cut by a straight line iu four places, while the parabola was a line of 

 the second order, because it could be so cut only in two places; but the 

 suggestion of its being a double line superposed seems to remove the 

 difficulty. 



Mr. Perigal informed us that one of his objects was to exhibit the para- 

 bola in the novel character of a retrogressive or recurrent curve of definite 

 range ; whence he inferred, that (/' a comet mored in that curve (as most of 

 them are said to do) it might return after it had performed its allotted 

 journey, and continue to visit us periodicalli/, as several do, which are 

 therefore supposed to travel in very elongateii ellipses, although their ap- 

 parent path more resembles a parabola. 



We do not take upon ourselves to decide that this " retrogressive" curve 

 of Mr. Perigal is or is not identical with the parabola of Apollonius ; but 

 we can bear testimony to its striking resemblance to the conic section; 

 and atlording at least primafacie evidence of its relationship, however 

 much its newly discovered properly of " periodicitij" may shock the pre- 

 judices of those who have hitherto thought themselves learned in such 

 matters. Besides, it is well known that reciprocating straight lines can 

 be produced by combinations of circular motions ; and, therefore, we can- 

 not see why it should have been deemed impossible so to produce para- 

 bolas and hyperbolas, which, being curved lines, would even appear the 

 less unlikely. Of the importance of the discovery in reference to the 

 cometary theory, our scientific readers can judge for themselves ; and such 

 of them as are mathematicians can, for their own satisfaction, put the 

 question to the proof by submitting the problem to analytical investigation. 



POWER TO OVERCOME INERTIA OF RAILAVAY TRAINS. 



Paper read at the Royal Society, on the Investignlion of the Power con- 

 sumed in Overcoming the Inertia of Railway Trains, and of the Resistance 

 of the Air to the Motion of Railway Trains at high velocities, by P. \V . 

 Barlow, Esq. — The object of the author iu this enquiry is to obtain a 

 more correct knowledge than has hitherto been possessed of the resistance 

 which the air opposes to the motion of locomotive engines at high veloci- 

 ties, and of the loss of force arising from increased back pressure, and the 

 imperfect action of steam. For this purpose he inslitutes a comparison 

 between tie velocities actually acquired by railway trains with those 

 which the theory of accelerated motion would have assigned ; and his ex- 

 periments are made not only ou trains pro|)elled by a locomotive engine, 

 but also on those moving on the atmospheric railway, which latter afford 

 valuable results, inasmuch as the tractive force is not subject to the losses 

 at high velocities necessarily mcident to locomotive engines. A table is 



given of the theoretical velocities resulting from calculations founded on 

 the dynamical law of constant accelerating forces, in the case of trains of 

 various weights, impelled by different tractive forces, moving from a state 

 of rest, and is followed by another table of the observed velocities in Mr. 

 Stephenson's experiments on the Dalkey line ; the resultof the comparison 

 being that, in a distance of a mile and a quarter, the loss of velocity is 

 about one-half of the observed velocity. A series of experiments ou lo- 

 comotive lines is next related ; but the comparison is less satisfactory than 

 in the former case, because the tractive force cannot be so accurately estij 

 mated ; it is, however, sulliciently so to establish the fact, that the power 

 lost by the locomotive engine below the speed of thirty miles per hour, is 

 so small as lo be scarcely appreciable; and that the time and power vshich 

 are absorbed in putting a railway train in motion are almost entirely re- 

 quired to overcome the inertia of the train, and do not arise from any loss 

 or imperfection of the engine. It appears from these experiments _lhat 

 above one-fifth of the whole power exerted is consumed in putting the 

 train in motion at the observed velocity. In the atmospheric railway the 

 author finds that the tractive force of a Dfteen-inch-pipe is so small (being 

 less than half that of a locomotive engine) that the time of overcoming the 

 inertia must limit the amount of traflic on a single line, especially with 

 numerous stations. When a great velocity is obtained, the tractive force 

 of the locomotive is much reduced, and, therefore, a much greater velocity 

 can be attained on an atmospheric railway. The inquiries of the author 

 into the amount ol resistance exerted by the air on railway trains, lead him 

 to the conclusion that on the atmospheric railway the loss of the tractive 

 power of the piston from friction, itc, is very inconsiderable, and that the 

 resistance of the air is less than had been hitherto estimated, not exceed- 

 ing, on an average, ten pounds per ton on the average weight of trains. A 

 tabular statement is then given of the results of the experiments made by 

 the British Association for the purpose of comparison with those obtained 

 by the author. The general conclusion which he arrives at is, that the 

 resistance of the air in a quiescent state is less than had been previously 

 estimated, and that the ordinary atmospheric resistance in railway pro- 

 gression arises from the air being generally itself iu motion, and, as the 

 direction of the current is not always oblique, from its producing increased 

 friction in the carriages. This kind of resistance will not increase as the 

 square of the velocity ; and as it is the principal one, it follows that the 

 resistance to railwaj trains increases in a ratio not much higher than the 

 velocity, and that the practical limit to the speed of railway travelling is 

 a question, not of force, but of safety. 



FROCBSDINGS OF SCIENTIFIC SOCIETIES. 



ROYAL SCOTTISH SOCIETY OF ARTS. 

 March 23. — John Clerk Maxwell, Esq., F.R.S.E., in the Chair. 



The following communications were made : — 



1. Description of a Water wheel with Vertical Axle, on the plan of the 

 Turbine of Fourneyron, erected at Balgonie Mills, Fifeshire. By Joseph 

 Gordon Stimrt, Esq. The paper gave an interesting description of a 

 Wheel on tliis principle recently erected by him at his tlax-spinning works 

 at Balgonie, in Fife, and a summary of its general advantages. The Turbine 

 is, in general appearance, like an overshot wheel, laid on its side, and wrought 

 at the bottom of the fall. The water enters it from the inner circumference 

 of the crown, and quits it at the outer circumference, impinging on every 

 bucket of the one, and flowing from every part of the other, at the same 

 instant of time. The water is supplied from a reservoir rising above the 

 wheel, in which it stands to the full height of the fall, and is discharged 

 from the bottom of this reservoir tlirough a cylindrical sluice, so as to be 

 delivered not only on every bucket or curve of the wheel at the same time, 

 but also with the full velocity due to its head. The problem sought to be 

 solved in the construction of the curves is, that the water, which has entered 

 without shock, should quit without velocity. On the nicety of this con- 

 struction will depend the economy of power, but in general the useful etfect 

 obtained will be equal to that of the best constructed overshot wheel. The 

 turbine has the advantage of the overshot wheel in being adaptable to any 

 height of fall (such wheels are working on the continent on falls from 332 

 feet to 13 inches), in being generally cheaper in constrnction, and always 

 much cbeai>er in maintenance, — in being little disturbed in its economical 

 arrangement citheir by changes in the quantity of water supplied, or by 

 being thrown in back water — and in going at such speed as greatly to eco- 

 nomise the necessary connecting gearing for factory work. Mr. Stuart's 

 paper, with the illustrative drawings and model, was remitted to a committee 

 of the Society that they may report fully on the merits of that (in this 

 countrj) novel mode of economising water power. M'hen that committee 

 have made their report it may be expected that the result will he laid more 

 fully before the public, especially if it be such as to justify the expectations 

 entertained by Mr. Stuart, of this being a most valuable improvement upon 

 any water wheel hitherto in use. 



2. Xotice of a Double Bell- Jar, — or Receiver, — for the Air Pump. By 

 James Ton, Esq., W.S., .Sec. On a late occasion, in treating of his experi- 

 ments on the relative capabilities of different gases to convey sounda. Dr. 

 M'ilson having stated that he had constructed the plate on which the bell-jat 



