444 DR. LARDNER'S LECTURES ON MECHANICS. small gravel, so as to deepen the bed" yet that this lowering of the bed would "seriously affect" the foundations of some of the other bridgesthose of Blackfriars', Waterloo, and Westminster, in particular; cause settlements of the wharfs and houses on the banks of the river; walls to be undermined, &c. And, 5. That "all the river above bridge"-" all the banks and low-grounds on each side from Westminster to Teddington"-will when the dam is removed be more liable to be overflowed by high tides, and be "exposed to the influx of heavier waves driven from the Nore with storms from the northward, which have hitherto been checked by the almost solid mass of the upper part of London Bridge." There was, thirdly, the corroborative evidence of Dr. Olinthus Gregory, who to great knowledge and much sagacity, adds a peculiar acquaintance with every thing relating to the River Thames and its banks-an acquaintance more extensive and circumstantial, we believe, than is possessed by any other individual of the present day. The opinion of Dr. Gregory, as stated by our intelligent correspondent, O. C. F., in our 335th Number, was to this decided effect-that "after the removal of the old bridge the bed of the river between its site and Westminster Bridge would often at and near low-water be dry, and the navigation completely at a stand," Many similar opinions by individuals, only second in weight to those we have named, might be quoted; but is not the fact, that the warnings of such men as Smeaton, Telford, and Gregory, should have been passed over wholly unregarded-that they should not have induced even the slightest precautionary measure quite sufficient to show, that had there been a body of similar evidence as bulky as the old bridge itself, it would have been all to no purpose? A new bridge was to be built at all events, and only those portions of the evidence which favoured that project-no matter how slender or how equivocal they might be were to have any regard paid to them. The evidence of the lowest waterman on the river who could swear that a fraction of a man per annum and a fraction of a pound per day were lost by accidents at the old bridge, was as a matter of course to be treated as decisive of the fate of that ancient structure: while all that the first engineers and philosophers of their time could say of the thousands of individuals and millions of property dependent for subsist ence or preservation on the continuance of the existing state of the river, was to go for nothing. ་. But what was there in the preservation of the dam caused by the old bridge which made it inconsistent with the project of a new one? Strictly speaking, nothing at all. Dr. Gregory, while he represented the great evils that might result from the removal of the old bridge, pointed out at the same time how they might be effectually obviated in the erection of a new oue (see " Mec. Mag." No. 335, p. 339). Inconsistency in the case there was none; it was convenient to keep the utility of the dam out of sight, and that was all. It would doubtless have been as good a job to build a new bridge with sluicegates in the way proposed by Dr. Gregory as without them; but so weak was the case for taking down the old bridge, so slight the testimony on which its "dangerous and destructive" character rested, that to have invited or encouraged attention to the good it did, might have endangered the job altogether. (To be concluded in our next.) NOTES OF DR. LARDNER'S LECTURES UNIVERSITY. (Continued from page 429.) 's Wheels are classed into three kinds, according to their position; as, when the teeth are on the edge they are called spur-wheels, or spur-gear (gear being a general term for all wheelwork); when they are perpendicular to the wheel they are called crownwheels, and they are bevelled-gear when the teeth are placed obliquely to the wheel. The second class of elementary machines (viz. the cord) is now to be considered. It is this which has been generally called the pulley, although the cord is a better term for it, as the mechanical virtue does not depend on the pulley, but on the cord. The general principles are these:-A cord is supposed, in mechanics, to be perfectly flexible. If two forces that are equal act in opposite directions on the same point, they will keep each other in equilibrium, and produce no effect, whatever the nature of the point, whe ther solid, fluid, or even gaseous; but if DR. LARDNER'S LECTURES ON MECHANICS, they do not act on the same point, but at distant points of the same body, they will or will not neutralise each other according to the circumstances. If the body be solid they will do so, in whatever direction they act, whether in the directions of any of the arrows in fig. 1; for by the definition Fig. 4. Fig. 5. B M PO P E 445 before given of a solid, it is incapable of either compression, extension, or flexure. If the body be a rope they will do so, if the forces act in the directions Aa or Bb, for a rope is supposed to be incapable of extension; but if they act in the opposite directions the rope will be compressed, and the forces will not neutralise each other's effects. Another principle is its perfect capability of transmitting force in the direction of its length and from its ends. A form in which the rope is applied is the pulley, which is composed of a hollow shell, called a block, with a grooved wheel acting inside, and called the sheaf. In the simple pulley, as fig. 2, a string is passed over Fig. 2. Fig. 3. W this sheaf; to one end of which is suspended the power P, and to the other the weight W. Pulleys are divided into two sorts; viz. fixed (fig. 2) and moveable (fig. 3): the names of which will sufficiently indicate their nature. In the fixed pulley, the power and weight must be equal; for from the definition of the rope before given, each part of the string will be equally stretched by the power, and also by the weight, consequently they must be equal. It may be asked, of what use is this pulley? Its object is principally to change the direction of the force, which is often of material consequence. Thus, if a weight were required to be raised, a person acts to considerable disadvantage when raising any weight; but by means of a fixed pulley, a force applied in a downward direction (which is most effective) will raise the weight. Thus the object of a fixed pulley is merely to change the direction of a force, and no other mechanical advantage is gained by it. In a moveable pulley, however, there is a power gained; fig. 4 is a view of one. It will be seen that one end of the cord is fixed to the point A, and is continued round the moveable pulley M; thence over the fixed pulley F. The power being suspended at the end P, the weight W is suspended to the moveable pulley M. It is evident that the pulley M must move upwards with the weight, on the power being drawn downwards. Now, by the definition of a cord, the tension of all the parts will be the same. As the weight is supported by the two cords (for they may be supposed to be unconnected) AM and FM, and each cord supports the same weight they must each support W; and as the power and weight are both equal when they are supported by a fixed pulley, the cord FP is also stretched with the same tension as FM; consequently P must be equal or the power is equal to half the to W 7' weight. It has been asserted by some that 446 DR. LARDNER'S LECTURES ON MECHANICS. the pulley depends, for its principles, upon the lever; but this can be proved to the contrary: for the same principles will be true, even if a point be supposed to be the pulley, and there can be no lever in that case. In the last case, the strings were supposed to be parallel: the next proposition for consideration is, when they are not so. Let fig. 5 be the pulley, and let AE and FE be the two directions of the strings: draw the parallelogram BECD; and if the sides BE and CE represent the tensions of the strings, the diagonal DE will represent the power. It is evident from the foregoing cases, that in a single pulley the proportion between the power and weight can never exceed 1 to 2; but by combining a number of wheels in the same block, a very great degree of power can be gained. Let fig. 6 be Fig. 6. end of it is fastened to the pulley C, and is passed under D; up again over C, under E; up again over B, from thence it proceeds under F, then over A; and on the other end is suspended the power P. Now the weight is suspended by six strings; and as they are each stretched with the same tension, each string will be stretched with a tension equal to one-sixth of the weight: therefore the weight will be equal to six times the power. In general, the power is to the weight as the number of wheels in both blocks is to unity. One objection to these machines is the friction, which is very great; every wheel having a separate axle, which must be taken into account. The same observations apply to this machine as were before mentioned. A small force appears to balance a great weight: the weight and power are both thrown upon fixed points, which support them both. În the case of lifting-1 lb. weight raised 20 feet, requires the same force as 20lbs. raised 1 foot, which is exactly the same thing that is effected by the pulley: it effects by gradual efforts Fig. 7. EXTRACTS FROM MY NOTE-BOOK. what could not be done by a single exertion. In the last cases there was but one string: now let there be more than one. Let fig. 7 be a system of pulleys, consisting of three moveable (A, B, and C,) and one fixed (D). Now, if the weight be supposed to be 8 lbs., it is plain that it is supported by the two ropes EA and BA; consequently they each support half that weight, or 4 lbs.: but the 4 lbs. supported by BA is also divided between the lines CB and FB, therefore they each bear a tension equal to 2 lbs.; and in like manner it can be shown, that the string DC bears a tension of 1 lb., and by means of the fixed pulley D, the power of 1 lb. will balance a weight, W, equal to 8 lbs. (To be continued.) EXTRACTS FROM MY NOTE-BOOK. (Concluded from p. 264.) On the Heat evolved from Metals by Percussion. According to the experiments of Bertholet, and others, it appears that by percussion the greatest heat is evolved from copper, the next from silver, and the least from gold. The specific heats of these metals follows the same order. The specific heat of copper, according to Dulong and Petit, is 0.0949; of silver, 0.0557. The heat evolved from copper by percussion was 26-28°; from silver, 13.10°. Hence it appears that the heat evolved from metals by percussion is in the direct proportion of their specific heats. On Atomic Proportions. The determination of the atomic proportions in a compound, the proportionate weights of whose constituents are given, is a problem of frequent occurrence. The rule given for this purpose by Dr. Ure ("Dictionary," art. Equivalent), is long and tedious. For the following simple rule, I am indebted to the polite communication of Dr. Thompson:-" Divide the weights of the constituents' by the atomic weight of each. The quo 447 tient gives the ratios of the atoms, which you can easily reduce to simple terms." On Light and Shadow. The "Philosophical Magazine and Annals of Philosophy" for February, 1829, contains an interesting communication from Joseph Reade, M.D. I had intended to repeat the experiments, but have been prevented by one cause and another. With the hope that some of your readers will do what I have neglected, and communicate the result to your Magazine, I send you two or three condensed extracts. "Experiment 1.-Having placed a table at about ten feet from a welllighted window, I placed on it a candle in a high candlestick. I now held a quire of white paper parallel to the table, and rather close to the blaze, when two shadows were produced by means of a piece of coiled paper held immediately near the quire; the one next to the candle was a bright orange, the other a bright blue. On turning the quire of paper towards the window, so as to cut off the light of the candle, this orange shadow changed to a perfect black; and on turning the paper towards the candle and excluding the light of the sun, the blue shadow likewise changed to a perfect black." In two other experiments, orange and blue were produced; these caused a green by overlapping. By altering the distance of the paper the orange was changed to yellow and brown; the blue to violet and indigo. On these results Dr. Reade observes, "As to the idea that black proceeds from the absorption of the seven rays of compound light, it is completely upset by these experiments; for we cannot suppose that the quire of paper was at one moment an absorbing substance, and at the next a reflecting one; therefore we must admit, contrary to the opinions of Boyle and Newton, that black is as much a reflected and independent colour as blue, red, or any other of the seven." I am, Sir, Yours, &c. H. Horwood. Carmarthen, Jan. 3, 1830. 448 QUESTION PROPOSED FOR AT THE INSTITUTION MISCELLANEOUS NOTICES. DISCUSSION OF CIVIL Is there any substance of less specific gravity than brick, that is equally incombustible, and as applicable for use in fire-proof floors? MINOR CORRESPONDENCE. Thermometric Phenomenon.-Sir, On Sunday, Jan. 10, I observed a phenomenon so rare, as to deserve recording. At mid-day, Fahrenheit's thermometer indicated 360, with a sharp north wind and a clear sky. Now, though the thermometer was 40 below the freezing point, there prevailed a hard black frost; the ice in the puddles was perfectly black, and the road as hard as stone: in short, it was freezing fast at the time. -I have every reason to rely on the correctness of the thermometer, which had a north aspect sheltered from the wind. No doubt, the frost was occasioned by the rapid current of air which swept along the road, and from which current the thermometer was free. Every body knows how much colder a wind is to the feel thau a calm, though the thermometer may indi. cate the same temperature in both cases; but I never yet saw an exemplification of it similar to the one mentioned here-it may be equally new to inany of your readers, whose amusement is the object of, Yours, &c. Camberwell, Jan. 24, 1830. J. B. Jun. Jones' Cylindrical Iron Wheels.-The use of these wheels appears to be now becoming very general in the metropolis, particularly among brewers, distillers, coal merchants, &c. A cor. respondent, at Hull, requests we will suggest to the patentees the propriety of taking some steps to introduce them throughout the country-" the expense of carriage, and the difficulty which may attend the repairing of them at a distance from town, preventing country persons, like himself, from availing themselves of this admirable invention." Jackson's Patent Studs.-(From R. W. 30. K. S.)—" Mr. Editor, As much has been said concerning Jackson's Patent Studs, in your interesting work, allow ine, through the same medium, to apprise your numerous readers, that these Studs are not sold; but if you wish to avail yourself of the benefit of the invention, you must send your boots. and shoes to the patentee to have the Studs put in. The cost, I understand, is 1s. 6d. (by no means an exorbitant charge): but would not the patentee reap more benefit from his invention by selling the Studs alone to such as are or may be inclined to purchase them? I live at some distance from the metropolis, and would avail myself of the proprietor's ingenuity, but for the expense of carriage to and from London, together with the expense of studding, which would, at the lowest calculation, be 4s. 6d. per pair. Since I first entertained the idea of writing to you, I have learnt that no patent has been taken out for the invention, and that a Tradesman in our neigh. bourhood will make some slight improvement in them, and establish an agent in Loudon, as also all the large towns in England, for the sale of the Studs." [Our Correspondent has been misinformed; there is an existing patent for the Studs in queston, which it will be dangerous, we apprehend, to infringe.-EDIT.] MISCELLANEOUS. Men-of-War's Boats.-A new inode of constructing boats for ships of war has been invented by Mr. Johns, of Plymouth dock-yard. There are no timbers used, all the planks coining up from the keel to the gunwale, diagonally, not very stout, but rendered strong by being again crossed by others, diagonally placed, but in the opposite direction. The boat so constructed is stronger than the ordinary one now in use; the seams never open in straining, which prevents leakage; and another great advantage is that she is only half the weight of one on the old construction of the same size. The planks are all fastened together by copper nails, thickly set. There has been a boat of this construction on trial attached to the Britannia, 120, and although in constant use for eighteen months, it has not required any other repair than the gunwale streak."-United Service Journal. Sparkles in the Sea,-The phosphorescent-like lights observed in the Mexican Sea, shine with greater brilliancy (in April) than any other part of the ocean; and this, I can assert without mistake, as I bestowed great attention on the subject, and had the acquiescence of others. Some of these lights were very large, and flashed like the priming of a cannon, sometimes at a long distance from the vessel. I observed that the little shining sparkles were here confined to the sides of the vessel and her wake, and that the waves when they broke into foam did not sparkle, which is quite different from what we had noticed before in the passage out, and in the Carribean Sea. Contrary to Dr. Franklin's assertion, the sparkles are seen in the water of the Florida stream as in other parts of the ocean.-Correspondent of the United Service Journal. The statement of Dr. Franklin, to which this contradiction is offered, was in these words :-" Having crossed this stream (Florida) several times; in passing between America and Europe, I have been attentive to sundry circumstances relating to it, by which to know when one is in it; and besides the gulf-weed with which it is interspersed, I find that it is always warmer than the sea on each side of it, and that it does not sparkle in the night." The Pantouranion.-A valuable astronomical instrument, invented by Mr. W. Shires, the mathematical tutor, in January, 1829, has been since improved by the same author, and rendered capable of finding its own meridian, the right ascension, declinations, longitudes, and latitudes of any celestial object; the day of the month and hour; the hourly, daily, and annual variations; the state of refraction, moon's parallax, and precession of the equinoxes. It will also direct the observer in finding any planet, &c. mentioned in the "Nautical Ephemeris," will point out the fixed stars, foretell eclipses, and, in a word, will form of itself a complete abservatory. The instrument is an improvement on the equatorial of Mr. Shires; the principle of which, as first conceived, was explained to the Western Literary Institution, and in the chanics' Magazine," No. 297, for April, 1829. Me Communications received from J. G.-S. Y. -Mr. Baddeley-T.-Mr. Jopling-A. B.Mr. Gray-Mr. Thorold-R. L. D. 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), ale requested to be addressed. M. SALMON, Printer, Fleet-street. |