222 DR. LARDNER'S LECTURES ON MECHANICS. and B, let them be 32 lbs. each, and acting at a distance of 4 inches from each other. Now the rotative effect, which is produced by A and B, will be equal to their weight multiplied by the distance between them, or 16x8=128, and that produced_by C and D will be 32x4=128. But their effects are equal; consequently they neutralize each other's effects, and are in equilibrium. Whence is deduced this rule." If the effect produced by one couple of forces be equal to that produced by another, they will be in equilibrium." It is beautiful to see in this rule the wonderful harmony with which all these different combinations agree, there being still the same manner observed of multiplying the weight by the distance. In the last cases the forces have been all considered as parallel, whereas the same rules will hold good if the parallelism be not preserved. Fig. 3. that the preceding rules must be founded on actual fictions, or on the supposition that there exists a body which has no existence: consequently, there is another set of rules to be learnt, and which are called corrections, which are compensations for the fictions obliged to be used in the last case. It now remains to be considered, what will be the effect produced on a solid by several forces acting together in different directions: it may be supposed to be moveable on a single point (round a centre), or on a line (round an axis). When it is moveable on a centre, the single force to keep it in equilibrium has been shown: therefore, it is only required to find the effect produced when moveable on an axis. The most simple example of this case may be shown in a wheel. Fig. 4. Let A and B (fig. 3.) be 'one couple of forces of 9 lbs. weight each, acting in opposite directions, at the distance of 8 inches, and let C and D be another couple acting in opposite directions, but not parallel to the former couple, and at the distance of 6 inches, with two weights of 12 lbs. each. Yet these forces will be in equilibrium, if the momentum of the couples be equal; and they are so, because 9x8 72, and also 12×6=72. Again, it is not necessary that they be on the same plane, provided the different planes are parallel to each other, although this can only be shown by experiment. In the last cases the body on which the forces acted was supposed to be perfectly inflexible, but which is never the case, as no such body exists. But such is the imperfection of science, B Β ́ Let A be the fixed axis (incapable of any motion) of a wheel, FGH; and let B be any weight acting on the point C, in the direction CB. Now it is evident that if the wheel be turned, the weight will then be exerted on the point C', in the direction of C'B'; and if again turned, it will act on the point C", in the direction of C" B": therefore it does not signify in what directions the forces act, so long as they tend to force the wheel round the same way; consequently, its equilibrium cannot depend on the direction alone. Now suppose a weight E to be applied on the point D, in the direction of DE. If this weight E be equal to the other one B, the wheel will be in equilibrium: for the tendency which one PROGRESS OF THE RAILWAY SYSTEM. has to produce rotation in one direction, will be counterbalanced by the other one; but if the weights be unequal, it will be in equilibrium if one weight be in inverse proportion to the other, as their distances from the centre. It has been proved that two unequal weights, when acting at distances in this proportion, will be equal in effect to a weight equal to their sum acting on this point; consequently these weights will not produce rotation, they will only press on the axis of the wheel, and that with a force equal to the sum of the weights. The equilibrium will not, therefore, depend either on the forces or the direction alone-but on what does it depend? The rule is this-"Multiply each weight separately, by the distance of the points on which they act, from the centre, and if the products be equal the wheel will be at rest.” Fig. 5. Let C (fig.5.) be the centre of a circle D, E, F, and let A and B be two unequal weights acting on points at the distances of a and b from C. Now if Aa Bb, the wheel will be at rest. Let A 8 and B=12, and the distance a 9 and b=6; but 9×8= 6×12: therefore the wheel will be kept at rest by the unequal forces A and B. The next case is, supposing that several forces acting in different directions tend to produce rotation in opposite ways; required the conditions of equilibrium. The rule is→→ "Multiply each weight by the distance from the centre of the point on which it acts, and if the sum of the products of those forces tending to produce ro 223 Let O(fig. 6.) be the centre of a circle, G, H, I; and let A, B and C be three weights acting in one direction, and D, E and F be three weights in another direction, and let them act at the several distances from the centre of a, b, c, d, e, and f. Then if Aa+ Bb+Cc Dd+Ee+Ff, the wheel will be in equilibrium. Suppose the weights to be A=3, B=6, C=8, D=5, E=4, and F=2, and the distances to be a=7, b=3, c=2, d=3, e=6, and f=8, then the several products will be, 3x7-21 and 5 x3=15 224 PROGRESS OF THE RAILWAY SYSTEM. the grand centre to which all the other rail-roads will tend. The Directors of the Liverpool and Manchester Railway Company have commenced the construction of warehouses two or three stories high, over the road at the west end of the Tunnel, next to Wapping; but it is evident, that the space at present in the possession of the Company, between Crosbie and Sparling streets, will be far too narrow for the accommodation of the parties who will carry merchandise, coal, &c. on the rail-road. We should not be surprised, if, when the line is completed, and the business of carrying has actually commenced, the offices, yards, warehouses, coal depots, &c. should occupy all the ground on the north side of Crosbie-street, from the mouth of the Tunnel to the back of the houses in Sparling-street, and so down to Wapping. We hear that the Directors hope to commence carrying, on part of the line, early in the next year. Coal, from the collieries of St. Helen's, Prescot, &c. will be the first article that may be expected to be brought from Liverpool on the rail road." The "Notices" mentioned in the preceding quotation are, 1. For the Wigan Railway, mentioned in our 325th No. and of which Mr. Vignolles is engineer. 2. For " a railway and branches from the collieries at St. Helen's and its vicinity, having a communication with the main line of the Liverpool and Manchester Railway, but also proceeding across the same, and terminating at Runcorn Gap ;" of which line Mr. E. Vignolles has been also appointed engineer. And, 3. for "a railway from the Warrington and Newton Railway, to the Grand Trunk Canal, at or near Roughwood Salt Works; with a branch railway from the same to the town of Middlewich.". The eagerness with which these speculations have been embarked in, may be judged of from the following paragraph, which we insert from the same paper : ST. HELEN'S AND RUNCORN RAILROAD.-On Tuesday last, a meeting was held at Warrington, for the purpose of engaging shares in the St. Helen's and Runcorn Railway. We understand, such was the anxiety of gentlemen to have shares, that they were literally scrambling over each other's shoulders to get to sign their names; if there had been a present of 1007. for each signature, the struggle could not have been greater. One gentleman, who could not get di rectly to the table, went on his knees, crept through another gentleman's legs, and signed in that position, his hand and nose being all that could be observed! MINOR CORRESPONDENCE. Glasing Coarse Pottery.-Sir, Being a reader and constant subscriber of your valuable maga. zine, I take the liberty of requesting you will inform me the title of any work giving information on the best mode of glazing coarse pottery. I am particularly desirous of producing a good black, and also a lead colour; and should be much obliged by any information on the subject, also as to the kind of kiln best adapted for burning pottery. I am, Sir, your very obedient servant, Liverpool. F. F. O. B. [We believe F. F. O. B. will find in Parkes's Chemical Essays all that books can tell him of the potter's art. But probably some of our Staffordshire readers will have the goodness to take the wants of our Liverpool correspondent into their friendly consideration, and favour us with a communication on the subject.-EDIT.] INTERIM NOTICES. We need make no apology for giving a preeedence to the Almanacs over other matters of older date, yet of a less pressing character. They form the most useful portion by far of our annual literature, and are more extensively circulated than almost any other class of publications. Every one has need of au Almanac; aad every one must therefore be anxious to know, as soon as possible, which of the many rivals for his favour is most likely to suit him best. That we may be the better able, however, to complete our notice of these Annuals, and to do justice, at the same time, to the numerous other claims on our attention, we propose next week to publish a double number. But by way of compensating our readers for the extra expense to which they will be thus subjected, we shall take the opportunity of making them a present of an engraving, on a separate sheet, of the "Rocket, "Novelty," and "Sans Pareil," steam-carriages; very beautifully executed on stone by Burton, drawn to the same scale, and with somewhat greater correctness, than our earlier wood-cut sketches. The double number and the engraving, stitched together in a cover. - will cost but 6d. ; the engraving, by itself, will be afterwards sold for 1s. 6d. As but a limited number of the engraving can be printed, early orders will be necessary. We have received Mr. Gray's papers, and shall not fail to do him the justice he claims at our hands. G. A. E. is among our papers for insertion. "Betty's" humorous Epistle to Mr. Hebert only reached us on Thursday night. Communications received from G. S.-Mr. Daniel-Inquisitor- Mr. K. Williams-Mr. Day-Nemo-Blackstone-Ignoramus-Juvenis Mechanicus-C. J.-T. F. M.-Mr. TimesG. J. Y.-Lieut. Brown-W. H. D.-Mr. Hopwood. LONDON: Published for the Proprietor, by M. SALMON, at the Mechanics' Magazine Office, No. 115, Fleet Street; where Commu nications for the Editor (post paid) are requested to be addressed. M. SALMON, Printer, Fleet-street. 226 A BRIDGES OVER THE THAMES. OF THE ARCHITECT. No. 4. Bridge (Continued from p. 100.) From the following statements, it will be seen that Mr. Gwilt augured rather too favourably of the House of Commons, when he rejoiced in the "control over the rebuilding of the bridge" being transferred from the Corporation of London to a Select Committee of that Honse. The first step of that Committee was to award to the plans of three gentlemen the three premiums advertised by the City, but to adopt none of them! The reason alleged was, that upon farther examination they were all found to be inadequate to the proposed situation; and ultimately, certain plans, designed to order by the late John Rennie, Esq., were adopted. Although it is well known that public competition has never been at any time of the purest description; yet circumstances so extraordinary have hitherto had no parallel in the annals of competition. To substantiate these assertions, we need but refer to the Report presented by the Committee to the Court of Common Council, bearing date October 31, 1828, which runs thus: "We, whose names are hereunto subscribed, your Committee for carrying into execution the Act of Parliament for the rebuilding of London Bridge, and for improving and making suitable approaches thereto, who were, by a resolution or order of this Honourable Court of the 21st day of August last, directed to report on the progress, present state, and plans proposed for the completion of the new bridge, and its approaches, and on the actual and proposed expenditure, and to whom it had been previously referred, to consider the allegations in the several memorials of Mr. George Allen and Mr. Peter Jeffery, and also of the inhabitants of the wards of Bridge and Billingsgate, and the petition of the proprietors of stagecoaches running to Gracechurch-street, from a number of places within and without the Bills of Mortality, relative The principal writers on bridge- |