A Fragment of Hiftory relative to the Revolution. tation, accefs fhould be denied them, and therefore I thought it beft that we alone fhould meet the Bishop at the time appointed, and advife with him what was fit to be done; which was agreed to: and upon our meeting with the Bishop, Sir George made that overture to his Lordship, which he closing with very warmly, faid he would go into the King, and fee if he would appoint a time for the Scots epifcopal nobility and gentry to wait upon him in favour of the clergy of Scotland, fo fadly perfecuted. Whereupon the Bishop leaving us in a room of Whitehall, near adjoining to the place where the Prince was, ftayed above a full half-hour from us, and upon his return told us, the King's answer was, that he would not allow us to come to him in a body, left that might give jealoufy and umbrage to the Prefbyterians, neither would he permit them (for the same reason) to come to him in numbers; and that he would not allow above two of either party at a time to speak to him on church matters. Then the Bishop directing his difcourfe to me, faid, My Lord, you fee that the King, having thrown himfelf upon the water, muft keep himself a fwimming with one hand. The Presbyterians have joined him closely, and offer to fupport him, and therefore he cannot cait them off, unless he could fee how otherwile he can be ferved. And the King bids me tell you, that he now knows the state of Scotland much better than he did when he was in Holland; for while there, he was made believe that Scotland, generally all over, was Prefbyterians, but now he fees that the great body of the nobility and gentry are for Epifcopacy, and it is the trading and inferior fort are for Presbytery; wherefore he bids me tell you, that, if you will undertake to ferve him to the purpose that he is ferved here in England, he will take you by the hand, fupport the church and order, and throw off the Prefbyterians. My answer to this was, My Lord, I cannot but thank the Prince for his frankness and offer; but withall I must tell your Lordship, that, when I came from Scotland, neither my brethren nor I apprehended any fuch revolution as I have feen now in England, and therefore I neither was, nor could be, inftructed by them what answer to make to the Prince's offer, and therefore what I fay, is not in their name, but only my private opinion; which 155 is, that I truly think they will not serve Immediately upon this, the Prince going fomewhere abroad, comes thro our room, and Sir George Mackenzie takes leave of him, in very few words., I applied to the Bishop, and faid, My Lord, there is now no farther place for application, in our church-matters, and this opportunity for taking leave of the Prince is loft; wherefore I beg that your Lordship would introduce me for that effect, if you can, next day about. ten or eieven in the forenoon, which his Lordship promifed and performed; and upon my being admitted into the. Prince's prefence, he came three or four fteps forward fron his company, and prevented me, by faying, My Lord,, are you going for Scotland? My reply was, Yes, Sir, if you have any com-. mands for me. Then he faid, I hope. you will be kind to me, and follow the example of England; wherefore being fomewhat difficulted how to make a mannerly and difcreet anfwer, without entangling myself, I readily replied, Sir, I will ferve you fo far as law, reason, or confcience will allow me. How this answer pleafed I cannot well tell, but it seems the limitations and conditions of it were not acceptable, for inflantly the Prince, without faying any more, turned away from me and went back to his company. Confidering what had pafled the day before, I was much furprised to find the Prince accoft me in thefe terms; but I. prefume, that either the Bishop (not hav ing time) had not acquainted him with what had paffed, or that the Prince propofed to try what might be made of me by the honour he did me of that immediate demand. And as that was the firft, fo it was the laft time, I had the honour to speak with his High nefs. 156 Advantages of High and Low fures. And I am the more confirmed in this, for after my coming down here, my Lord St. Andrew and I taking occafion to wait on Duke Hamilton, his Grace told us, a day or two before the fitting down of the convention, that he had it in fpecial charge from King William, that nothing fhould be done to the prejudice of Epifcopacy in Scotland, in cafe the Bishops could by any means be brought to befriend his intereft, and prayed us most pathetically for our own fake to follow the example of the church of England; to which my Loid St. Andrew replied, that both by natural allegiance, the laws, and the most folemn oaths, we were engaged in the King's intereft, and that we were by God's grace to ftand by it in the face of all dangers, and to the greatest loffes; fubjoining that his Grace's quality and influence put it in his hands to do his Majesty the great honour; and if he acted otherwife, it might readily lie as a heavy tashe and curfe both upon himfelf and his family. I can fay no more for want of paper, fave that I am as before, ALEX. EDINB. Wheels mechanically confidered. Mr. URBAN, IN your laft Supplement I pointed out, in a manner which I think may not improperly be called demonstrative, that carriage-wheels, in their natural application to that purpofe, have nothing of the nature of a lever in them; that they give no other mechanical advantage than the quantity of friction they take off; and that this effect is in the proportion of the diameter of the wheels and axis one to another; whence it follows, that wheels may be high or low, broad or narrow, without any alteration in their friction: and Mr. Sharpe's affertion, "that low wheels, on a fmooth and hard surface, are drawn as easy as high ones," may be true under particular circumstances, notwithstanding it contradicts another of his own advancing," that car, riages are moved eafier in proportion to the height of their wheels;" for it is only to reduce the axles in the tame proportion that the wheels are reduced, and the friction must remain the fame. But herein lies his mistake, he fuppofes the axle must be enlarged in proportion as the wheels diameter is increased: but this, evidently, is not the cafe; for the axles have nothing to do but fupport the waggon and contents, which, remaining the fame, can require no more ftrength for their fupport on a high than on a low wheel; confe quently, friction may be leffened by enlarging the wheels. It is taken for granted by both of us, that the breadth of a wheel makes no difference in the friction: but this is only the cafe fo long as the motion is continued in a direct line straight for wards; for whenever the carriage moves circularly, as in turning, &c. friction of a very different kind is introduced. Under this circumstance the circumference of the wheel, and its whole incumbent weight, grates more or lefs upon the ground; and this effe is greater in proportion to the breadth of the wheel: to evince which, let any one take a pair of compaffes, and with a given radius ftrike a circle, then draw a line from the center to the circumference; let this line reprefent the breadth of a wheel, which is required to move round the center it touches; it is plain, as the wheel has no progreflive motion forwards, it cannot move on its own axis, conlequently its external edge will rub against the ground with a force equal to the weight it fupports, without any thing to cafe its friction; and the space paffed ་་་ Advantages of High and Low Wheels mechanically confidered. 157 in this manner, fuppofing the wheel to be 16 inches broad, and half a turn made, will be 4 feet; but if the wheel be only 3 inches broad, and the fame motion performed, the fpace will be but 9 inches; therefore narrow wheels are to be wished for where much turning and winding is required. This, too, points out of how much confequence it is to make our roads as traight as poffible; and that drivers fhould be careful to keep one straight track on the road, and not make crooked S's, as the watermen call it, as that must increase friction in all, but more particularly in broad wheels. It was likewife proved, in the fame magazine, that the only most advantageous place of applying power is at the center of the wheel, in a line with the plane on which the carriage moves; to which let me add, what few or none will difpute, that, whenever this line, from an elevated plane of progreffion, is obliged to be above the plane of the horizon, the horfes have a greater load to draw, in exact proportion with the angle of the elevation. Surely, then, no one would ever purposely contrive to have an elevated angle of draught, for that is nearly, if not quite, the fame as going up a hill of the like elevation. But all this was advanced upon the fuppofition of a true plane, altogether impenetrable, and perfectly horizontal; but as thefe, though neceffary to be conceived for establishing the true theory of a wheel or roller, feldom, if ever, all concur in our roads, we will now drop that idea, and examine feparately how far each real occurrence will affect or alter the feveral properties here recapitulated. First, let us ftill confider the roads as true planes, but various-inclined, longitudinally, tranfverfely, &c. or, in other words, let us conceive our carriages when going up hill, down-hill, and along the fide of a hill, where the roads are firm and smooth; and, that our idea may be determinate, let the elevation of each hill be an angle of 25 degrees. In going up or down a hill, the line of draught, be it what it will on level ground, is varied according to the line of afcent or deicent: as, for instance,"a waggon, whofe line of draught is horizontal on a horizontal plane, in going an afcent of 25 degrees, will have the line of draught ftill parallel to the line of progreffion, and only 25 degrees above the horizon; but Mr. Sharpe's, being elevated 25 degrees on the level, will, on the afcent, be fifty degrees above the horizon. If he apprehends this to be no difadvantage, I would advife him to try the experiments on his models; for I am confident he will find fuch a thought moft egregioufly wrong. In going down hill, likewife, difadvantage will arife from this boasted elevation of draft. In this cafe, horfes, instead of drawing, have frequent occafion to stop the carriage; but his line of draught being above the plane of progreffion, the power applied to stop must be the fame, and confequently more power must be applied to produce the fame effect: whence it follows, there will be more frequent occafion to lock a low than a high wheel carriage; which, though not a matter of very great moment, ought not to be left out of confideration, where it can be avoided without greater inconvenience. In backing a carriage, likewife, on level ground, which is fimilar to stopping on a defcent, the difadvantage is fo great againft low wheels, that I much question if Sharpe's rollers, with any thing of a load upon them, could be moved to any purpose by the thill horfes alone. In order to afcertain the effect of going along the fide of a hill, I must beg leave to make a fmall digreffion on gravitation. All bodies, without exception, have a natural propensity to defcend, or fall downwards, which is called gravitation. All bodies have, likewife, a certain point or place in them, under which if a fingle prop or fupport be put, they will be kept from falling; but, if the fame fingle prop or fupport be placed in any other part, they will fall notwithstanding. This point or place in any particular body, is called its center of gravity; and the natural tendency in all bodies to defcend, is in a perpendicular let fall from this center of gravity to the hori zon. As for inftance; fuppofe it was required to fupport a carriage-wheel, by one prop, in a horizontal pofition, any given distance from the ground, the place of application will be in the center of the wheel; but, if the prop be placed ever fo little on either fide the center, that edge towards which the center of gravity is will fall to the ground, and the wheel must have two props, or continue to reft in that pofition: or, if it be required to fet a wheel on its edge on level ground, the center must be fo placed, that a perpendicular let 158 Advantages of High and Low let fall from thence will pafs through the middle of that part of the rim on which it ftands; for, if the perpendicular falls without the rim, the top of the wheel will defcend towards the fide on which the perpendicular falls. From these data may be deduced the two following corollaries, viz. that, when a body is to be fupported by two props, of equal frength, they should he placed equidiftant from the center of gravity; and, where the props are of unequal ftrength, their distances from the center of gravity fhould be proportioned to their different ftrengths, because the weight they bear will be proportioned to their nearness to the center of gravity. We may from hence conclude, that a waggon judiciously loaded, when on level ground, has its common center of gravity fomewhere in a line drawn thro' the middle of it from end to end; and, if the wheels are alike, it should be equidiftant from them all. It is eafy to conceive, that this carriage, going along the fide of a hill whofe elevation is twenty five degrees, will have its load thrown fo much towards the lower Tide; and a perpendicular let fall from the center of gravity, will approach much nearer the lower than the upper wheels, and, of confequence, they, at fuch times, bear the greatest part of the load. Add to this, the wheels themFelvés, being feparate from the carriage, require a feparate confideration under this circumftance; they, by this inclination, being thrown off their own peculiar center of gravity, have a tendency to fall flat, and, of confequence, increase friction in proportion to their height and weight. There is also another increase of friction from this position, which is alike in high and low wheels; the carriage lides down the fmooth inclined furface of the box, and bears hard against the fides of the naves of the lower wheels. But the most material difadvantage is, when this fide-eleva tion becomes any thing confiderable, the wheels take upon themselves a property quite foreign to their intended purpose: the inner and lower edge of the box becomes the fulcrum or center of a lever, the upper and outer edge of the box is the fhort arm, and the spoke next the ground is the long arm, which is acted upon by the defcending propenfity of the whole load; for the wheels on the upper fide bear but very little. The effect of fuch preffure must, indeed, be great; and it must be aç Wheels mechanically confidered. knowledged, that wheels, when put in this fituation, are acted upon more powerfully in proportion to the length of their spokes: but it is quite a mistake in Mr. Sharpe to fuppofe, that, because the axles of his rollers are longer than the radii or fpokes, they cannot act at all in this manner; this can do no more than leffen the effect. It is plain, the bed of his waggon must have the fame tranfverfe propensity as another; and this can have no other counter action than the wheels acting thus as levers. The effect, then, mult be the fame in both, only in different degrees. However, it must be granted, if our carriages were always to move along the fides of hills, and there were no better method to be contrived, low wheels, whether broad or narrow, would have greatly the preference. This, perhaps, is the only unexceptionable advantage they have; and I trust it will be allowed, I have fairly and candidly given the utmost weight to the arguments. Let us now fee how far we ought to be influenced thereby. In the first place, comparatively, it is granted, that high wheels give a much greater force to this compreffure; but then, as a counterbalance, it must be admitted, that low wheels have theirs more frequently repeated, because they make more revolutions in any given space; which in a great measure removes the objection. Next, let it be confidered, that the number and length of thefe fideling declivities bear but very little proportion to the space patled in a horizontal pofition; conlequently, we fhould be lofers, if we adopted low wheels on this account only: and, if any roads are fo circumftanced as to confift entirely, or moftly, of tranfverfe or fideling inclinations, I think it would not be difficult to construct fuitable carriages, without losing the benefit derived from high wheels. Indeed, I should fuppofe it was an idea of this kind, together with that of turning, that gave the hint for making the fellies of our nine-inch wheels rounding, or higher on one fide than the other; for this contrivance, alone, will greatly remove the difadvantage of a small declivity; whereas Mr. Sharpe's rollers, from their cylindric shape, must feel every the least inclination: but then it mult be confeffed, that this curved shape takes off fomewhat of the benefit propofed from broadwheels when on level ground. This fideling fituation, likewife, militates against high wheels in another respect : Advantages of High and Low Wheels mechanically confidered. 159 refpect the extraordinary degree of preffure they are fubject to,requires their axles to be fomewhat larger than the weight they carry would otherwise require, by which means we lofe a part of the benefit arifing from thein with refpect to perpendicular friction; yet not fo much as to make low ones preferable on the generality of roads. I would next confider the roads ftill as planes firmly refitting the preffure upon them, but varioully interfperfed with little prominences, fome loofe, fome fixed; which definition compre. hends the stoney roads to be met with in many counties. In this, as in every other cafe, where the action of any two objects is to be compared, it is neceffary to have certain dimenfions given, otherwife no precifion can be come at; and it is pretty much a matter of indifference what we affume, fo that it is within the limits of the question fought. Let, then, one fet of wheels, now to be confidered, be two feet high, and fixteen inches broad, with the angle of draugh, elevated about twenty five degrees: let the other be fix feet high, and nine inches broad, with a horizontal line of draught. Let the obstacles, whether loofe or fixed, be fix inches high. When the low wheels come abreaft of one of these fixed obftacles, fo as to touch, a line drawn from the top of the obitacle to that part of the wheel that touches the ground, will form an angle of about thirty-two degrees, that is, even degrees above the line of draught. The fix-feet wheels, when they come abrealt the fame obfacle in like manner, will have the line of progreffion only varied about 17 degrees, but, as the line of draught was hoizontal before, it will now, as the carriage afcenes, become juit as much depreffed. Now, if we fuppofe elevation and depreffion to be equally difadvantageous, the high wheels will then meet with an obftruction equal to 34 ; but the low wheels will have 32 by elevation and 7 by depreffion, that is, 39 upon the whole. But admit the carriages were upon a par in paffing the obftacles, if we fuppofe them to be fix feet alunder, and two feet taken up in paffing each, the low wheels will have two thirds of the space to pafs with a difadvantageous line of draught; whereas the high ones will have the fame proportion in the best fituation poffible, with the advantage of lefs friction fuperadded; which is quite fufficient objection to the rollers on this kind of roads: but, if we fuppofe the obftacles only two feet afunder, the advantage is ftill more in favour of highs wheels; for the rollers (as Mr. Sharpe affects to call them) will always go to the bottom between each, whereas the high wheels will pals from obftacle to obitacle and not go more than onethird down. Again, if we fuppofe the obftacles loofe, ftill further impediment rifes to the roller; for there will frequently happen a double friction, of the roller against the obftacle, and the obftacle against the ground, by its being driven before the wheel, which can never happen to a high wheel from an obftacle of equal height. Indeed, Mr. Sharpe feems thoroughly fenfible of the force of this objection; for he fays, "Every time a road is new covered, it is an impediment to borfes and carriages of every kind, but to rollers in particular it is doubly fo:" which makes me doubly wonder that he fhould venture to affert " they pass over obAtacles better;" for it seems a plain and natural inference, that all other obftacles must have an effect upon them fomewhat fimilar. He cannot, furely, fuppofe the obstacles now described do not afually occur upon roads. If we reverse the idea laft mentioned, and fuppofe our roads ftill firm planes, but interfperfed with holes of different dimenfions, yet greater inconvenience must be derived from two-feet wheels; for, as they are always drawn at a difadvantage by the elevated draught, that difadvantage will be increafed by their falling deeper in thefe holes than fixfeet wheels can do. Let us now imagine the roads to be foft, and liable to give way under the preffure sustained; which definition, I apprehend, will take in every species of road not hitherto taken notice of the fandy when dry, the loamy when wet, the gravelly when either very wet or very dry, come more or lefs under this defcription; and, as the two firft, and most troublefome, feldom occur but upon tolerably level ground, there will be no occafion to confider them in any other point of view. As geometricians, in their elementary treatifes, always lay down certain felf-evident data, on which they purpole to found their future demonitiations, fo I would here premise, that, in all fubftances where folution of continuity is the confequence of force applied, this effect is produced in a ratio or proportion compounded of the nuru ber |