PRO 
Ac. = 1000 s, and by subtracting the for- 
mer equation from the Jatter, 123 = 999S} 
therefore s = 
999 333 
PROHIBITION, in law, is a writ pro- 
perly issuing only out of the Court of King’s 
Bench, being the King’s prerogative writ ; 
but, for the furtherance, pf justice, it may 
now also be had in some cases out of the 
Court of Chancery, Common Pleas, or Ex- 
chequer, directed to the judge and parties 
of a suit in an inferior court, commanding 
them to cease from the prosecution thereof, 
upon a suggestion, that either the cause 
originally, or some collateral matter arising 
therein, does not belong to that jurisdic- 
tion, but the cognizance of some other 
court. Upon the court being satisfied that 
the matter alleged by the suggestion is suf- 
ficient, the writ of prohibition immediately 
issues. 
PRO JECTILES,are such bodies as being 
put in a violent motion- by any great force, 
are then cast off or let go from the place 
where they received their quantity of mo- 
tion ; as a stone thrown from a sling, an ar- 
row from a bow, a bullet from a gun, &c. It 
is usually taken for granted, by those who 
treat of the motion of projectiles, that the 
force of gravity near the earth’s surface is 
every where the same, and acts in parallel 
directions ; and that the effect of the air’s 
resistance upon very heavy bodies, such as 
bombs and cailnon-balls, is too small to be 
taken into consideration. 
Sir Isaac Newton has shown, that the 
gravity of bodies which are above the su- 
perficies of the earth, is reciprocally as the 
squares of their distances from its centre ; 
but the theorems concerning the descent of 
heavy bodies, demonstrated by Gallileo, 
and Huygens, and others, are built upon this 
foundation, that the action of gravity is 
the same at all distances ; and the conse- 
quences of this hypothesis are found to 
be very nearly agreeable to experience. 
For it is obvious, that the error arising 
from the supposition of gravity’s acting uni- 
formly, and in parallel lines, must be ex- 
ceedingly small i because even the greatest 
distance of a projectile above the surface 
of the earlh, is inconsiderable, in compa- 
rison of its distance from the centre, to 
which the gravitation tends. But then, 
on the other hand, it is very certain, that 
the resistance of the air to very swift mo- 
tions, is much greater than it has been 
commonly represented. Nevertheless, (in 
the application of this doctiine to gunnery) 
PRO 
if the amplitude of the projection, answer- 
ing to one given elevation, be first found by 
experitnent (which we suppose) the am- 
plitudes in all oflier cases, where the eleva- 
tions and velocities do not very much differ 
from the first, may be determined, to a suf- 
ticient degree of exactness, from the fore- 
going hypoUiesis ; because, in all such cases, 
the effects of the resistance will be nearly as 
the amplitudes themselves ; and were they 
accurately so, the proportions of the ampli- 
tildes, at different elevations, would then be 
the very same as in vacuo. 
Now, in order to form a elear idea of 
the subject here proposed, the path of 
every projectile is to be considered as de- 
pending on two different forces ; that is to 
say, on the impellant force, whereby the 
motion is first bej^in, (and would be conti- 
nued in a right line) and on the force of 
gravity, by which the pinjectile, during the 
whole time of its flight, is continually urged 
downwards, and made to deviate more and 
more from its first direction. As whatever 
relates to the track and flight of a projectile, 
or ball, (neglecting the resistance of the air) 
is to be determined from the action of these 
two forces, it will be proper, before we 
proceed to consider their joint effects, to 
premise something concerning the nature 
of the motion produced by each, when 
supposed to act alone, independently of the 
other ; to which end we have premised the 
two following lemmata. 
Lemma I. Every body, after the im- 
pressed force whereby it is put in motion 
ceases to act, continues to move uniformly 
in a right line ; unless it be interrupted by 
some other force or impediment. 
This is a law of nature, and has its de- 
monstration from experience and matter of 
fact. 
Corollary. It follows from hence, that a 
ball, after leaving the mouth of the piece, 
would continue to move along the line of its 
first direction, and describe spaces therein 
proportional to the times of their descrip- 
tion, were it not for the action of gravity ; 
whereby the direction is changed, and the 
motion interrupted. 
Lemma II. The motion, or velocity, 
acquired by a ball, in freely descending 
from rest, by the force of an uniform 
gravity, is as the time of the descent ; and 
the space fallen through, as the square of 
that time. 
The first part of this lemma is extremely 
obvious ; for since every motion is pro- 
portional to the force whereby it is ge- 
