DYNAMICS. 



mechanical arts have furnished us with 

 various instances of great approximation 

 thereto, fora time only. Yet all motions, 

 generally speaking, would be uniform, 

 were it not that obstacles perpetually 

 present themselves to retard their velo- 

 city, either perceptibly or imperceptibly. 

 We are, however, compelled to consider 

 uniform motion to exist ; else we could 

 form no just comparison on many oc- 

 casions ; and, as some standard is need- 

 ful, we estimate the velocity of bodies 

 by seconds of time ; taking a second as a 

 unit. The following will be sufficient to 

 give full insight into this part of our sub- 

 ject. 



When bodies have different uniform 

 motions, the spaces described are pro- 

 portional to tlie times and velocities, 

 jointly. Hence the velocity is as the space 

 divided by the time. For the velocities 

 of two bodies, moving uniformly, are di- 

 rectly as the spaces, and inversely as the 

 time ; for, in equal times, the velocities 

 are proportional to the spaces run over ; 

 and if the velocities are equal, the spaces 

 passed over are proportional to the 

 times ; again, if the spaces passed over 

 are equal, the velocities are reciprocally 

 as the times. 



We have an easy mode of exhibiting 

 the comparative velocities of bodies : let 

 the velocities be described by base lines, 

 and let the altitudes express the time ; 

 the area of each figure thus found will 

 display the space over which the body, of 

 which it is respectively the representa- 

 tive, has passed. This shows their pro- 

 gress, whatever may be their direction ; 

 but where they follow the same, or a pa- 

 rallel course, though their velocities 

 should be different, their several situa- 

 tions are easily ascertainable. In. such 

 case we may consider them as moving in 

 concentric orbits, and, after ascertaining 

 their several velocities, remove them, ac- 

 cording thereto, at suitable distances 

 from the centre, when all would be found 

 to persorm their revolutions within the 

 same period ; their velocities being equal 

 to the rectangle contained under the dia- 

 meters of the orbits in which they seve- 

 rally move. Or, we may consider them 

 all as moving in the same orbit, as the 

 hour, minute, and second hands of a 

 watch, all shew their progress upon the 

 same index, or dial plate. 



But we sometimes find two forces act- 

 ing upon the same body ; if they be si- 

 multaneous (or equal) the movement of 

 the body being equally acted upon by 

 either, it will assume a medium course, 



and divide the angle at which the two 

 forces stand apart. Thus, in fig. 1. Plate 

 Dynamics, if a body O be equally impelled 

 by two forces, the one in the direction of 

 S T, the other of N R, it will traverse the 

 diagonal line, O X, and arrive at the op- 

 posite corner of the square ; and that too 

 in the same time, say one second, as it 

 would have required, if acted upon by 

 only one of the forces, to have passed 

 from O either to T or to R. 



If the forces are unequal, the body will 

 be impelled in the same manner towards 

 the opposite point of a parallelogram, 

 and will thus gain more towards the 

 course of the stronger power, than in the 

 direction of the weaker; between which 

 it will exhibit a true proportion. Say 

 that A B, fig. 2. be the direction of a force 

 three times as powerful as the force AC. 

 The body will move along the diagonal 

 A D, in the same time that it would have 

 been urged by the greater power from A 

 to B ; or by the lesser power from A to 

 C. Perhaps no more obvious proof of 

 this could be deduced, than the course 

 of a ship, when laying, what is technically 

 called, " near the wind." The real track 

 of the ship is always seen by her wake, or 

 a peculiar mark left in the water ; though 

 the ship's head may lay quite in another 

 direction. Therefore, it is customary to 

 ascertain the angle made between the 

 wake and the ship's apparent course, by 

 means of a compass, and to set off that 

 angle under the head of lee-way ; the 

 wake always appearing rather towards 

 the weather (or wind-side) quarter of the 

 vessel. Thus, although it should seem 

 the vessel were proceeding in the direct 

 line E F, fig. 3, yet on account of the 

 wind acting as two different powers, that 

 is, partly causing her to proceed in the 

 direction of her keel, and partly in a line 

 with her beam, or diameter, she would 

 arrive at the opposite point G ; supposing 

 her progress forward to be twice the 

 amount of her lee-way, or lateral tenden- 

 cy, as above stated, the wake would de- 

 scribe her true course, while her apparent, 

 course would always appear to be parallel 

 with the line E F. 



Let us suppose that H and I, fig. 4. two 

 equal weights, were to be raised by 

 means of a chord from each meeting in 

 K : the line of force which should raise 

 them with equal velocity would be along 

 the diagonal K L. If the weights were 

 unequal, the line would not be the d'u 

 gonal of an equilateral quadrangle, as 

 the preceding case, but along the para! 

 Q V of the diagonal formed by a prop( 



