great advantages to society; yet, these arts, in the hands of the rash and unskilful, too often occasion the most fatal mischiefs; as errors of this kind are errors of the most dangerous consequence. II. AN INVESTIGATION of the Principles of STEAM CARRIAGES. Communicated to the Editors by the late JAMES SHARPLES, Esq. of this city. THERE is no mechanical project, except the perpetual motion, that has been so often and so unsuccessfully attempted, as the self-moving carriage, or carriage to go by means of some internal power borne along with it; and I believe there is no engine of this kind in use, except the Bath chair, by which gouty persons can move themselves about from place to place, upon level ground, with a slow motion. Some attempts have been made to give motion to carriages by means of steam; but none ever promised more than the one made by Mr. Trivithick, who invented an engine to act with steam of so high a temperature, as to preclude the necessity of using the condensing apparatus and air-pump. Having got rid of these incumbrances, he was confident of success. A carriage was constructed for the purpose, every thing was well contrived, and as the inventor was a man of acknowledged abilities and ingenuity, it was generally believed he would succeed; but as I had been led into much reflection on this subject by some projects of my own, I made no hesitation to predict its failure to some mechani cal philosophers of high repute in England, who strenųously combated the reasonings and theorems which oc casioned me to pronounce so decidedly; hence I am inclined to believe, that a strict investigation of this subject has not appeared in any book of natural philosophy, and if I should be fortunate enough to throw any new light upon it, I shall please myself with the reflection that I may be the means of preventing ingenious men of ardent minds from squandering their property, or ruining themselves by so wild a project. I have here given an outline of Mr. Trivithick's carriage and engine. A and B are the fore and hind wheels; on the axle B a ratchet wheel is fixed for the piston rod of the cylinder E to act against, and if roads were perfectly hard, smooth, and level, such an engine would probably have the advantage over common carriages, because a small power continually exerted would give a degree of velocity that could not be supported by horses; but in estimating the powers necessary to impel carriages on roads in general, we must take into consideration the impediments that are usually met with, all of which may be considered as so many short inclined planes. Thus a force to drive the wheels A B over the obstacles D C, would, the first moment of exertion, be the same as a continued force to carry them up D L, provided the inclined plane was perfectly hard and smooth; now g D M may be considered as a bended lever, g D being the long arm, and M D the short one, and the power drawing out of the carriage in the direction o v would be to the whole weight of the carriage and load, pressing perpendicularly in the points I and M, as M D is to g D, the points of the obstacles being the fulcrum or centre of motion. These proportions being as four to seven, and as four horses can, by a sudden exertion, raise 2000 lbs. perpendicularly by a rope over a pulley, (Desagueliers, vol. 1. p. 260.) four horses would raise a weight in the carriage and load over the obstacles C D equal to 3500 lbs. but no force in the engine acting against the ratchet wheel at H would effect the same. We must keep in view, that whilst the action within a carriage is exerted in any line of direction against the ratchet wheel, its reaction is against some part of the carriage in a contra-direction, and that the intensity of its action is the same, whether its direction be horizontal, oblique, or perpendicular. Now let the direction of the force be changed from the direction E H to e g, and nothing, in my opinion, can be more self-evident, than the impossibility of forcing the wheels over the obstacles by a power exerted perpendicularly upon the centre of motion; for it would be absurd to attempt to raise a weight suspended on either of the ends of a scale-beam, by the application of a perpendicular force upon the fulcrum. A scientific friend of mine near Brunswick, who at first opposed the foregoing proposition, afterwards not only convinced himself, but had formed a demonstration of the truth of it. As I am not acquainted with the mode of his solution, I shall endeavour to supply it. Let it be required to draw the carriage wheel up the inclined plane P L, by means of any power or weight W suspended by a chain coiled round the ratchet wheel. If the power W will descend by rolling the carriage wheel up the ascent, the descending line of its power must hang beyond the centre of motion on that side which would have a tendency to raise the carriage wheel, and it would consequently have some mechanical force. But to demonstrate that the wheel will not descend, let PL be drawn perpendicular to the radius B D, and let the length BD be set off from D to L, it is evident that the wheel, in rolling from D to L, will apply as much of its circumference on the inclined plane as is equal to D L or DB; and it is also evident that the weight W will draw as much in length of chain from the ratchet wheel, as is equal to the line Bg, which is the radius of the lesser circle; for the greater circumference is to the lesser one, as the greater radius is to the lesser radius; then set off L. K-B g, in the angle D L K, equal to the angle D Bg ; draw K D and g D; then the triangles D L K D and DB g D will be every way equal and similar; consequently, the line L K will be equal in length to the line Bg, which has been shown to be the length of chain drawn off from the ratchet wheel; but as the line L K hes all above the horizontal line D K, the length D W will have received no addition, and the weight W must have been carried along in a line parallel to D K, and consequently cannot have descended or ascended, which proves that the power is exerted perpendicularly over the centre of motion. Let us now consider such impediments and inclined planes as present themselves in almost every road. If there were obstacles T under each wheel, any power out of the carriage, drawing in the direction o v, would be to the weight of the carriage and load, as AS to the line extending from S to the point of the obstacle, which being nearly as 1 is to 4, four horses would draw 4x2000=8000 pounds in the carriage and load over such |