MOTION, 
hour, and B at the rate of three : here the 
difference of the velocity (m. two miles 
per hour) is that by which the ship, A, will 
appear to go from the ship, B, forwards, or 
the ship, B, will appear at A to go with tlie 
same velocity backwards, to a spectator in 
either respectively. 
If the two ships, A and B, move with the 
same degree of velocity, then will the dif- 
ference be notiiing, and so neither ship will 
appear to the other to move at all. Hence 
it is, that though the earth is continually re- 
volving about its axis, yet, as all objects on 
its surface partake of the same common mo- 
tion, they appear not to move at all, but 
are relatively at rest. 
If two ships, A and B, with the degrees 
of velocity as above, meet each other, the 
one will appear to the other to move with 
the sum of both velocities, viz. at tlie rate 
of eight miles per hour ; so that in this case 
the apparent motion exceeds the true, as in 
the other it fell short of it. Hence the rea- 
son why a person, riding against the wind, 
finds the force of it much greater than it 
really is, whereas, if he rides with it, he 
finds it less. 
The reason of all these phenomena of 
motion will be evident, if we consider we 
must be absolutely at rest, if we would dis- 
cern the true or real motions of bodies 
about us. Thus a person on the strand will 
observe the ships sailing with their real ve- 
locity; a person standing still will expe- 
rience the true strength and velocity of the 
wind ; and a person placed in the regions 
between the planets, will view all their true 
motions, which he cannot otherwise do, be- 
cause in all other cases the spectator’s own 
motion must be added to, or subtracted 
from, that of the moving body, and the sura 
or difference is therefore the apparent or 
relative motion, and not the true. 
Motion is also either equable or accele- 
rated. Equable motion is that by which a 
body passes over equal spaces in equal 
times. Accelerated motion is that which 
is continually augmented or increased, as 
retarded motion is that which continually 
decreases ; and, if the increase or decrease 
of motion be eqqal in equal lime, the mo- 
tion is then said to be equally accelerated 
or retarded. Equable motion is generated 
by a single impetus or stroke ; thus the mo- 
tion of a ball from a cannon is produced by 
the single action of the powder in the first 
moment, and, therefore, the velocity it first 
sets out with would always continue the 
same, wefe it void of gravity, and to move 
in an unresisting ifiedium; which, therefore, 
would be always equable, or such as would 
carry it through the same length of space 
in every equal part of time. Hence we 
may determine the theorems for the expres- 
sions of the time (T), the velocity (V), and 
the space (S), passed over in equable or 
uniform motion very easily thus : 
If the time be given, or remain the same, 
the space passed over will be as the velocity, 
viz. S : V ; that is, with twice the velocity, 
twice the space ; with three times the ve- 
locity, three times the space, will be passed 
over in the same time, and so on. 
If the velocity be given, or remain the 
same, then the space passed over will be as 
the time, viz. S : T ; that is, it will be greater 
or less, as the time is so. 
But if neither the time nor velocity be 
given or known, then will the space be in 
the compound ratio of both, viz. S : T V. 
Hence, in general, since S : T V, we have 
g 
V ; — ; that is, the velocity is always di- 
rectly as the space, and inversely as the 
time. And also T : ; that is, the time is 
as the space directly, and as the velocity 
inversely ; or, in other words, it increases 
with the space, and decreases with the ve- 
locity. 
If, therefore, in any rectangle, one side 
represent the time, and the other side the 
velocity, it is evident that the area of the 
said rectangle will represent the space 
passed over by an uniform motion in that 
time, and with that velocity. 
Accelerated motion is produced by a con- 
stant impulse of power, which keeps conti- 
nually acting upon the body, as that of gra- 
vity which produces the motion of falling 
bodies ; which sort of motion is constantly 
accelerated, because gravity every moment 
adds a new impulse, which generates a new 
degree of velocity; and, the velocity thus 
increasing, the motion must be quickened 
each moment, or fall faster and faster, the 
lower it falls. 
In like manner a body thrown perpendi- 
cularly upward, as a ball from a cannon, 
will have its motion continually retarded, 
because gravity acts constantly upon it in a 
direction contrary to that given it by the 
powder; so that its velocity upwards must 
be continually diminished, and its motion 
as continually retarded, till at last it be all 
destroyed. The body has then attained its 
utmost height, and is for a moment motion- 
less, after which it begins to descend with a 
