DYNAMICS. 
fig. 5. The angle being more acute with 
the line of the greater weight B, and more 
obtuse with that of the lesser w'eight C : the 
parallelogram would be formed of sides 
corresponding with the proportions of the 
two w'eigfats ; which are in this instance 
considered at 4 to 1. 
When various bodies, moving in the same 
course, are acted upon equally by a second 
power, not in a line with that of the pri- 
mary momentum, they will each preserve 
tiieir relative situations in regard to each 
other. We have a familiar proof of this in 
the descent of rain, &c. which will be found 
to preserve a parallel course among the 
drops respectively, though they may each 
be driven from the line of gravity, and be 
impelled into an oblique direction, by the 
force of wind. The case is similar among 
the vessels of a fleet, supposing all to sail 
alike, when they get into a ciuTcnt ; they 
will preserve their relative situations, and 
perform all their evolutions, precisely as 
though they were in stagnant water. 
Uniformly varied motion relates to bodies 
which at regular periods, or at regular dis- 
tances, receive new impulses, either in the 
same direction, or in opposition thereto : in 
the first case the new momentum is to be 
added to the former velocity : in the latter 
case it is to be deducted from it. In va- 
riable motions we compute the velocity ac- 
cording, either to a medium taken at the 
average of the accession of forces, or we 
consider the velocity at the instant chosen 
for calculation to be equal to an unit ; i. e. 
a second of time ; we may thus calculate 
each unit separately. A force causing a 
body to move quicker, is termed an acce- 
lerating force ; though the term is also ap- 
plied to forces which cause the motion to 
vary : when it occasions a regular encrease 
of velocity, by an equable addition of im- 
pulse, it is termed an uniformly accelerating 
force ; but if it occasions a body to move 
regularly slower, as an additional weight in 
mechanics, or a lengthened pendulum in 
clock-work, it is called an unifonnly re- 
tarding force. 
A single body would, by a constant 
force, give four objects of consideration, 
viz. the space, the time, the velocity, and 
the force : any three of these being given, 
the fourth may be found. For, the veloci- 
ties generated in equal bodies, by the action 
of constant forces, are in the compound 
ratio of the forces and the times of acting. 
The momenta generated in unequal bodies 
are also conjointly as the forces, and their 
times of action ; and the momenta lost or 
destroyed in any times, are likewise con- 
jointly as the retarding forces, and their 
times of action : for an equal opposing 
force would, in equal time, destroy the im- 
pelling force. The velocities generated or 
destroyed in any limes, are directly as the 
forces, and times ; and reciprocally <is the 
bodies, or masses. In all motions unifonnly 
accelerated, when tlie force and body are 
given, the space described during a certain 
time, is the half of that which the body, 
moving uniformly with the last acquired 
velocity, wmuld describe in an equal time ; 
and the spaces described by a body uni- 
formly accelerated, are as the squares of 
the times ; hence the velocities acquired 
being as the times, we shall find the spaces 
described to be the squares of the veloci- 
ties. Therefore cither the velocities, or the 
times, are as the square roots of the whole 
of the described spaces. And this applies 
equally to motions uniformly retarded. 
Of variable motions in general. By this 
we immediately refer to those forces which 
act incessantly, but always in different de- 
grees of strength : of this we have an in- 
stance in the release of springs from heavy 
pressure ; whence they gradually recover 
the form in which they were made. A 
carriage set in motion, though the horses 
may appear to act uniformly, nevertlieless 
occasions less exertion to them, when it 
has acquired its due degree of velocity. For 
bodies in a state of rest, are, in a manner, 
disposed to remain so ; and bodies in mo- 
tion, ai-e disposed, in a certain degree, to 
continue so, as will be subsequently sliewn : 
therefore, we find the first effort to be 
considerable ; while, on tlie other hand, it 
often requires much resistance on the part 
of the horses, even on level ground, to dis- 
continue that motion of which their forces 
were the cause. Besides this illustration, 
we find that bodies are vei-y sensibly af- 
fected by the fonns of those spaces over 
which they have to pass: admitting the 
ascents to be equal, and the whole to be 
perfectly level, and free from impediments ; 
which, indeed, must ever be understood, 
while treating of the motion of bodies, 
especially by comparison. If a body X 
should have to pass over the point A, fig. 6, 
along the plane A B, its motion would 
be uniformly continued by the power C ; 
but if the surface were concave as A D B, 
then the first part of the motion would be 
more rapid than the latter ; because the 
commencement of the concave space being 
