DYNAMICS. 
not exist naturally. It is, perhaps, not to 
be found any tvhere ; though our mechani- 
cal 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 velocity, either perceptibly or 
imperceptibly. AVe are, however, compelled 
to consider uniform motion to exist; else we 
could form no just comparison on many 
occasions ; and, as some standard is needful, 
we estimate the velocity of bodies by 
seconds of time ; taking a second as a unit. 
The following will be sufficient to give a 
full insight into this part of our subject. 
AA^hen bodies have different uniform mo- 
tions, the spaces described are proportional 
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 directly as the 
spaces, and inversely as the time; for, in 
equal times, the velocities are proportional 
to the spaces run over ; and, if the veloci- 
ties 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. 
AFe have an easy mode of exhibiting the 
comparative velocities of bodies: let the 
velocities be described by base lines, and 
let tlie 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 representative, has passed. 
This shews their progress, whatever may be 
their direction ; but where they follow the 
same, or a parallel course, though their 
velocities should be different, their several 
situations are easily ascertainable. In such 
case we may consider them as moving in 
concentric orbits, and after ascertaining 
their several velocities, remove them, ac- 
I 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 diameters of 
the orbits in which they severally move. 
Or, we may consider them all as moving in 
the same orbit, as tlie hour, minute, and 
second hands of a watch, all shew their pro- 
gress upon the same index, or dial plate. 
But we sometimes find two forces acting 
upon the same body ; if they be simultane- 
ous (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 ar- 
rive at the opposite corner of the square ; 
and that too in the same time, say one se- 
cond, 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 parallelo- 
gram, 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 de- 
duced, 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 fire ship’s head may lay 
quite in another direction. Therefore, it is 
customary to ascertain the angle made be- 
tween the vyake and the ship’s apparent 
course, by means of a compass ; and to set 
off tliat 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 tendency, as above stated, 
the wake would describe her true course, 
while her apparent course would always ap- 
pear 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 cord 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 diagonal of an equilateral 
quadrangle, as in the preceding case, but 
along the parallel QV of the diagonal 
formed by a proportionate parallelogram, 
