ried at this low rate, instead of being detained weeks on the way by wind and tide, would travel with the regularity and speed of the mail coach. Edinburgh, February, 1825. C. M. NOTE EXPLANATORY OF THE LAWS OF FRICTION. I HAVE had a great number of communications addressed to me on various subjects connected with the laws of friction, which 1 have neither room nor leisure to answer in detail. A few observations, to render the views I have taken a little more intelligible, are all I can offer. 1. Vince's experiments, though made on a small scale, are very decisive, so far as they go, in proving a uniform acceleration in the case of bodies urged by a constant force, and retarded by friction. The body moved was dragged along a horizontal plane by a weight descending at the end of that plane, and attached to the body by a cord passing over a pulley. In one experiment the weight descended about five feet in four seconds, and, by a moveable stage employed to stop it at any point in its descent, it was ascertained that the spaces described were very accurately as the squares of the times. The experiments were varied and frequently repeated. It is not perfectly clear whether Vince's experiments were made exclusively with sliding bodies; but in the second part of his essay he distinctly applies his conclusions to rolling bodies also. 2. Coulomb's experiments were made on a large scale, and with greater precautions to insure accuracy than those of Vince, with which, however, they agree generally. But he showed that much depended on the matter of which the rubbing surfaces were composed. With oak on oak, and with iron on iron, there was a constant acceleration; but with iron rubbing on oak, the velocity, though it might accelerate for a little, always became very speedily uniform. His experiments on the iron axles of pullies working in copper, indicate that a constant acceleration exists in this case also, and we may draw the same conclusion by inference, with regard to rolling bodies in general, from these last experiments, in connexion with others made with pullies and wooden cylinders, to determine the obstruction arising from the stiffness of ropes. The acceleration of a rolling body, when it descends along an inclined plane by its own weight, is familiarly known; but this will scarcely be held quite conclusive as to what would take place on a horizontal surface. 3. I may state, then, to those who doubt this constant acceleration (of whom I find there are many), that, in the case of sliding bodies at least, the acceleration is the fact observed, and not an inference from the experiments. But it must be admitted, on the other hand, that we cannot speak with entire confidence with regard to rolling bodies; and that as to sliding bodies, since 1 Journal de Physique, September and October 1785. the velocities employed in the experiments scarcely exceeded one mile per hour, conclusions deduced from these cannot be very securely applied to velocities ten or fifteen times greater. 4. It happens fortunately, however, that within these two days, an account of some experiments has reached me, which supplies the void left by those of Vince and Coulomb, and affords results of the most conclusive and satisfactory kind, not as to friction in general, but as to that combination of rolling and sliding friction with which we have to do in Railroads. It occurred to Mr. Roberts, of Manchester, that he could conduct his experiments with peculiar advantage, if, instead of making the vehicle travel along the Railway, he made the Railway move under the vehicle. He accordingly obtained a cast iron cylinder or hoop six inches broad, and three feet in diameter, which was put into a frame and made to revolve vertically like the fly of a steam engine, by a pulley and strap. Exactly on the top or highest segment of this revolving cylinder, which answered the purpose of a Railroad, was placed a small waggon with four cast iron wheels, weighing with its load 50 pounds. Now, if the cylinder is made to revolve with any velocity, say four miles an hour, and the waggon is held steadily in its place, it is perfectly obvious that the wheels will turn on the curved surface of the cylinder precisely in the same manner as if the waggon had moved along a flat Railroad, and that the force required to hold the waggon in its place, will be exactly equal to what would have dragged it along the level Railroad with the same speed. In order to measure this force, which expresses the amount of the friction, the wire which holds the waggon in its place was attached to a delicate weighing machine, the index of A tempering screw which pointed out the smallest variation of pressure. was employed to keep the centre of the waggon at all times exactly over the axis of the cylinder, that no part of the weight of the waggon might be blended with the pressure produced by the friction. The waggon was protected by a board placed on one side, from the current of air generated by the motion of the cylinder. And it ought to be mentioned as one material advantage attending this experiment, that the disturbing effect produced by the resistance of the atmosphere is completely excluded. With these precautions to insure accuracy, a number of experiments were made. The periphery of the cylinder was made to revolve at different velocities, varyThat this uniformity ing from 2 to 24 miles an hour; but in every case the friction, as indicated by the weighing machine, was precisely the same. of result did not arise from any thing fallacious in the nature of the machinery, was evident; for although the index of the weighing machine was not affected in any degree by an addition to the velocity, it immediately showed an increase of friction when any addition was made to the weight. This experiment is quite decisive with regard to the grand principle upon which the advantage of the railroad depends, that the friction is the same at all velocities. Had the waggon been placed on a flat horizontal railroad, and urged forward by a weight exceeding in any degree the pressure indicated by the weighing machine, there is no doubt that it would have experienced a continual acceleration, till the extra force was balanced by the growing resistance of the atmosphere. It is material to observe, that there is one species of friction of consider The friction may be a very little greater than on a plane of the same materials, but this will not affect the relative friction at different velocities. 2 An interesting account of these experiments, illustrated by an engraving, is given in the Manchester Guardian of Feb. 12.-of which the above statement is an abridgment. able importance, still to investigate that occasioned by the rubbing of the flaunch or guiding edge of the waggon wheel upon the side of the rail. This will probably be found much greater in practice than what arises from the mere vertical pressure of a cylindrical wheel upon a horizontal surface, and we cannot even be sure that it follows the same law as regards velocity. Mr. Roberts should employ his apparatus to ascertain what the amount of this lateral friction is with wheels of different forms, and also what is the effect of using wheels of various breadths. DE L'EUROPE RELATIVEMENT À L'AMÉRIQUE ET À LA GRÈCE. PAR M. DE PRADT, ANCIEN ARCHEVÊQUE DE MALINES. Le genre humain est en marche, et rien ne le fera rétrograder. VRAI SYSTÈME DE L'EUROPE, &c. &c. CHAP. X.-Que perdent l'Espagne et la Turquie? Ici reviennent les considérations relatives aux spécialités de chaque colonie: celles-ci doivent être appréciées d'après leur éloignement de la métropole, leurs richesses, leur étendue, leur population, leur voisinage, et la facilité de les garder. Autre chose est une colonie qui forme un monde entier, telle que l'Amérique, autre chose sont des points isolés, tels que la Jamaïque et la Guadeloupe, ou des arsenaux tels que la Martinique et Antigoa; autres sont des colonies très peuplées, ainsi que l'est le Mexique, ou des colonies désertes, comme celle de la pointe d'Afrique, le Cap et la Nouvelle-Hollande; il faut tenir un compte exact de ces différences, pour évaluer une colonie et fixer ce qu'il y a à perdre ou bien à gagner dans sa séparation ou dans sa conservation. Quand une colonie est vaste, riche, peuplée, les accroissemens du commerce provenant infailliblement de l'introduction de la liberté, peuvent servir d'indemnité pour la perte de la propriété territoriale et souveraine. Il y a plus, quand la métropole peut prendre part à ces profits, dans quelques cas, elle peut avoir à gagner en perdant sa colonie, c'est-à-dire en la laissant s'affranchir. Cette théorie n'est pas vaine; il en existe sous le soleil un exemple visible pour tout l'univers, et bien fait pour dissiper tous les préjugés, même chez les esprits les plus revêches; c'est celui de l'Angleterre vis-à-vis des Etats-Unis! Que n'aurait-elle pas gagné à ne pas leur contester leur indépendance! Quels regrets ne doit-elle pas avoir aux dix-huit cents millions qu'elle a dépensés pour l'empêcher? Que faisait-elle en s'opposant à l'émancipation de son Amérique? Le |