DYNAMICS. 



mechanical arts have furnished us with 

 various instances of great approximation 

 thereto, for a 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 the 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 perform 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 equalj 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 A C. 

 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 dia- 

 gonal of an equilateral quadrangle, as in 

 the preceding case, but along the parallt 1 ' 

 Q V of the diagonal formed by a proper- 



