570 GUNNERY. 
Parabolic for or explained. Aristotle, or his immediate pupils, time can be measured with as much accuracy as a line Par 0 
Theory of had said that the velocities of falling bodies increased , can be divided. _ : : ‘— 
Gunnery. with their weights ; Galileo’s doctrine was incompatible Aided by these inventions, we have now obtained the 
with this, and he thought himself obliged to use argu- 
ments in his support. He said that if Aristotle’s doc- 
trine be true, two crown pieces must fall faster when 
sticking together than when unconnected, which, said 
he, is contrary to common experience. Not doubting 
that he had convinced his audience, he described. the 
experiments which he was to exhibit next day, shewing 
that in a double time a body would fall four times as far, 
&c. The experiments were performed in the dome of 
the great church, before a vast concourse of people, and 
succeeded most perfectly. Yet so little were the, phi- 
losophers moved by this kind of argument, that they 
represented Galileo as a dangerous person, unfriendly 
to the state ; and he was obliged to leave his native city 
in a few days, and take shelter in Padua. It is very 
remarkable, that Baliani, one of the first geometers and 
mathematicians of that age, and who perfectly under- 
stood Galileo’s speculations on this subject, should teach 
another doctrine, reviving or supporting an old seho- 
lastic assertion, that the velocity of a falling body might 
be as the space fallen through, calling this motion also 
a uniformly accelerated motion. 
Galileo found more difficulty than one should expect 
in his endeavours to obtain an exact measure of the 
power of gravity; and indeed could not obtain one that 
was satisfactory. But the difficulty of the task, and his 
struggle to accomplish it, were big with advantages to 
science. A body falls so fast, that a considerable error 
in the conclusion arises from a very small error in esti- 
mating the time; and the great difficulty was how to 
estimate the time. It was in this casting about for a 
measure of a small portion of time that Galileo first 
thought of the pendulum. His penetrating and saga~< 
cious mind enabled him to see that there must be a fix- 
ed proportion between the time of a vibration and that 
of falling through its length, although his mathematical 
knowledge did not yet enable him to find it out; he saw 
an immediate consequence of this if true, namely, that 
the vibrations of two pendulums should be in the sub- 
duplicate ratio of the lengths, because this must be the 
peppers of the times of falling through those lengths. 
$s he would try ; and he found that it was so. De- 
lighted with this success, he immediately compared 
the time of falling from the top of the great dome with 
that of a pendulous vibration, by making a pendulum 
of such a length that it performed precisely one vibra- 
tion in the time of the fall. In this time, the body, mo- 
ving with the final velocity, would describe a space 
double of that fallen through. He then counted: with 
patience the number of vibrations made by his pendu- 
um in an interval of time, measured by the transit. of 
two stars. Thus he obtained the time, and the velocity 
generated in that time by the uniform action of gravity. 
Galileo made this to be about $1 feet of our measure in 
a second, and said that it was certainly somewhat more; 
because his experiments on falling bodies convinced 
him that their motion is retarded by the air. 
These efforts and resources of an ingenious mind are 
worthy of record, and are instructive. to others, . But 
Galileo did not attain the accuracy in this measure that 
we now possess. The honour of the accurate state- 
ment of the time of a pendulous oscillation, and that of 
the fall through its length, was reserved for Mr Huy- 
gens. This proportion was determined by him bya 
most ingenious and elegant physico-mathematical pro- 
cess, Me also gave us the pendulum clock, by which 
most precise measure of the accelerating powers of (ee 
vity ; and we can now say that its intensity is such in 
the latitude of London, that by acting uniformly on a 
body for one second of time, it generates in it the velo- 
city of 32 feet two inches per second, and a heavy body 
falls 16 feet one inch in that time. ~  -~ ae 
These are standard numbers, of continual use in all 
mechanical discussions, and should be carefully kept in 
remembrance. Not only so, but we should acquire dis- 
tinct notions of them in this respect, viz. as standard 
numbers. Gravity is known to us in two ways; our 
most familiar acquaintance with it is as a pressure, which 
we feel when we carry a heavy body. With this we 
can compare the pressure of a spring, the exertion of 
an animal, the pressure of a stream of water or wind, 
the intensity of an attraction, &c. by setting them in 
opposition and equilibrium. The philosopher, and-es- 
poues the physical astronomer, and cultivator of the 
ewtonian philosophy, is well acquainted with gravity 
as an accelerating a moving force, capable of acce« 
lerating, retarding, or deflecting the body in which it 
inheres, or on whose intimate particles it acts without 
intermedium. He can compare the gravity of a stone 
with that of the moon, or of Jupiter, or with the force. 
that produces the precession of the equinoxes. The 
general mechanician, observing that all other pressures, 
such as that of a spring, of an animal, &c. are also mo« 
ving forces, by combining those two aspects of gravity, 
makes a most important use of it by comparing other 
forces with weights, and thence inferring the motions 
which those forces will produce. Thus, knowing that 
an arrow 7 oz. weight, by falling 18 inches acquires the 
velocity of 104 feet per second, he infers, that when 
drawn to the head by a bow of 62 pounds, it will be 
discharged with the velocity of 233 feet per second. 
We shall therefore, in future, com every force 
with gravity, and express the accelerative power of this 
standard by 32, meaning that by acting on every par« 
ticle of a body for a second, it will generate the velo« 
city of 32 feet per second, and cause the bouy to de« 
scribe 16 feet with a motion uniformly accelerated. 
We may find it convenient, on some occasions, to use 
the numbers 386, and 193, which are the inches in 32,3, 
and 16, feet. , 
The questions that interest us at present are those 
concerning the relations between the time tof ane 
the beige h. of that fall, and the velocity v is 
uniformly acquired in falling ; so that when any one of 
those thingsis given, the may be found out.. 
I. Since the variations of velocity are proportional to 
the times in which they are produced, we have 
V2 == 82 182e" 
and v= 32 t” 
N.B. The time ¢ is always supposed to be a number, 
of seconds, and. the height 4 a number of feet, and the. 
velocity v a, number of feet uniformly moved over in 
one second... , yeaa 
A falling body, therefore, acquires an increment of 
$2 feet per second in every second of its fall, and an as- 
cending bay has its velocity lessened as much during 
every second of its rise. A /body falling during four 
seconds, acquires the velocity of 128 feet per second. 
But if the body hae been projected downward, with. 
