gunnery. 
projection given. From these two data 
find out the impetus at that point ; then 
2 X 16 feet 1 inch is the velocity acquired 
by the descent of a body in a second of 
time ; the square of which (4 X the square 
of 16 feet 1 inch) is to the square of the 
velocity required, as 16 feet 1 iiich is to the 
impetus at the point given ; wherefore mul- 
tiplying that impetus by four times the 
square of 16 feet 1 inch, and dividing the 
product by 16 feet 1 inch, the quotient 
will be the square of the required velocity ; 
whence this rule. Multiply the impetus by 
four times 16 feet 1 inch, or 64 feet^, and 
the square root of the product is the velo- 
city. 
Thus suppose the impetus at the point of 
projection to be 3,000. and the perpendicu- 
lar height of the other point 100 ; the im- 
petus at that point will be 2,900. Then 
2,900 feet multiplied by 64j feet gives 
186,566 feet, the square of 432 nearly, the 
space which a body would run through in 
one second, if it moved uniformly. 
And to determine the impetus or height, 
from which a body must descend, so as at 
the end of the descent it may acquire a 
given velocity, this is the rule : 
Divide the square of the given velocity 
(expressed in feet run through in a second) 
by 64j feet, and the quotient will be the 
impetus. 
The duration of a projection made per- 
pendicularly upwards, is to that of a pro- 
jection in any other direction whose im- 
petus is the same, as the sine complement 
of the inclination of the plane of projec- 
tion (which in horizontal projections is 
radius) is to the sine of the angle contained 
between the line of direction and that 
plane. , \ 
Draw out At (fig. 8,) till it meets »jB 
continued in E, the body will reach the 
mark B in the same time it would have 
moved uniformly through the line A E ; 
but the time of its fall through M A the 
impetus, is to the time of its uniform mo- 
tion through A E, as twice the impetus is 
to A E. And therefore the duration of the 
perpendicular projection being double the 
time of its fall, will be to the time of its 
uniform motion through A E ; as four times 
the impetus is to A E ; or as A E is to E B ; 
that is, as A t is to t D ; which is as the 
sine of the angle (DA (or M A B its com- 
plement to a semicircle) is the sine of the 
angle t A D. 
Hence the time a projection will take to 
arrive at any point in the curve, may be 
found from the following data, viz. the im- 
petus, the angle of direction, and the incli- 
nation of the plane of projection, which in 
this case is the angle the horizon makes 
with a line drawn from the point of projec- 
tion to that point. 
Hence also in horizontal cases, the dura- 
tions of projections in different directions 
with the same impetus, are as the sines of 
the angles of elevation. But in ascents or 
descents their durations are as the sines of 
the angles which the lines of direction make 
with the inclined plane. Thus, suppose 
the impetus of any projection were 4,500 
feet; then 16 feet 1 inch : l" : : 4,500 feet: 
275" the square of the time a body will take 
to fall perpendicularly through 4,500 feet, 
the square root of which is 16 ' nearly, and 
that doubled gives 32" the duration of the 
projection made perpendicularly upwards. 
Then to find the duration of a horizontal 
projection at any elevation, as 20°; say 
R : S. angle 20° : : 32" : duration of a pro- 
jection at that elevation with the impetus 
4,500. Or if with the same impetus a 
body at the direction of 35° was projected 
on a plane inclined to the horizon 17°, 
say as sine 73° : sine 18° : : 32" ; duration 
required. 
The tables in the next leaf, at one view, 
give all the necessary cases as well for 
shooting at objects on the plane of the ho- 
rizon, with proportions for their solutions, 
as for shooting on ascents and descents. AVe 
shall in this place mention some of the more 
important maxims laid down by Mr. Robins, 
as of use in practice. 1. In any piece of 
artillery, the greater quantity of powder 
with which it is charged, the greater will be 
the velocity of the bullet. 2. If two pieces 
of the same bore, but of different lengths, 
are fired with the same charge of powder, 
the longer will impel the bullet with a 
greater celerity than the shorter. 3. The 
ranges of pieces at a given elevation, are 
no just measures of the velocity of the 
shot : for the same piece fired successively 
at an invariable elevation, with the powder, 
bullet, and every other circumstance as 
nearly the same as possible, will yet range 
to very different distances. 5. The great- 
est part of the uncertainty in the ranges of 
pieces, arises from the resistance of the air. 
6. The resistance of the air acts upon pro- 
jectiles by opposing their motion, and di- 
minishing celerity ; and it also diverts them 
from the regular track which they would 
otherwise follow. 7. If the same piece of 
cannon be successively fired at an invariable 
