ory. ~and Aer Hinge He has published the actual 
’ ranges of di t pieces of artillery, at small elevations, 
not exceeding ten and among these are some 
trials made with the cannon the basilisk, a 
epee _and well known to those who visit 
' Dover castle. He found that this gun, which carries a 
10 Ib. shot, noes 3600 feet with 18 Ib. of powder, at 
an inclination of 2°,and 6000 feet at an elevation of 43° 
The subject of gunnery was now destined to receive 
the most im t improvements from the genius of 
Galileo. By the application of mathematics to the doc- 
trines of motion, he has given the form of a science to 
this branch of natural philosophy, and has enabled us 
to ascertain every ching that ee tr amt of mi- 
 litary p es, on the supposition are dis- 
rg apap bet sedi: His Dioareid et 
© Demonstrationes Mathematica, &c. which contains these 
~~ fine investigations, were published in 1638. They are 
~ given in the fourth dialogue, entitled De Motu Projec- 
torum, and occupy fourteen propositions, in which he 
has proved that a projectile must describe a parabolic 
_curve by the combination of the force of gravity with 
the force of projection, and has shewn how to compute 
the distance to which the body will be thrown, the 
time of its flight, and the momentum with which it 
falls, when projected in a given direction, and with a 
given velocity. Galileo was perfectly sensible that the 
resistance of the air would produce a considerable 
change in these results, and he has describeda method of 
discovering the magnitude of the effects which this re- 
sistance would produce on the motion of a bullet ‘at 
some given distance from the gun. 
The opinions which prevailed at this time respecting 
the extreme rarity and tenuity of the air, prevented phi- 
losophers and military engineers from availing-them- 
selves of this important part of Galileo’s work. They 
anticipated no great variation from the theory, and ac- 
cordingly we find it to have been, for a long time, the 
received opinion, that all projectiles moved in a parabo- 
lic curve. 
. . This erroneous opinion was stoutly maintained by 
‘of our countryman Anderson, in his treatise Of the Ge- 
erson, meine use and effects of the Gun, published in 1674. 
This work is founded on the Galilean theory ; and its 
author boldly undertakes to overturn all objections that 
can be -arged against the parabolic motion of projectiles. 
A similar notion is maintained by M. Blondel, in 
his L’ Art de jetter les bombes, which a ed at Paris 
in 1683. He applies the doctrines of Galileo to the 
flight of shells and bullets of every ’kind ; and after a 
discussion relative to the air’s resistance, he con- 
cludes that it is too minute to affect the accuracy of his 
deductions. 
_. The celebrated Dr Halley held the same false 
opinion. He was, however, not merely. misled by a be- 
lief in the extreme tenuity of the air; but he was con- 
firmed in his errors by some very imperfect experi- 
ments. After treating of the motion of projectiles, 
o_ Phil. Trans, 1685, No. 179. p. 3.) he observes, 
“ these rules would be rigidly true, were it not for 
» the resistance of the medium, by which not only the 
an |) direct pam cnr motion is continually retarded, but 
___ likewise the increase of the velocity of the fall, so that 
the spaces described thence are not~exactly as the 
of the times ; but what this resistance of the 
airis, against several. velocities, bulks, and weights, is 
Not so easy to determine. It is certain that the weight 
of — ~ oe bie 2 is nearly as 1 to 800; whence its 
me it to that of any project is given. It is very 
likely, that to the same velocity and magnitude, but of 
rents of 
GUNNERY. 
563 
different matter, the resistance will be reciprocally as _ History. 
the weights of the shot; as also, that to shot of the same “~~” 
velocity and matter, but of different sizes, it should be sy 
as the diameters reciprocally ; whence, generally, the Halley. 
resistance to shot with the same velocity, but of differ. 
ent diameters and materials, should be as their vifie 
vities into their diameters he ahem ; but whether 
the opposition to different velocities of the same shot be 
as the squares of those velocities, or as the velocities 
themselves, or otherwise, is yet a more difficult ques- 
tion. However it be, it is certain that in large shot of 
metal, whose weight many thousand times surpasses 
that of the air, and whose force is very great in pros 
portion to the surface, this resistance is scarcely dis- 
cernible ; for by several experiments made with all care 
and circumspection, with a mortar-piece, extraordinarily 
well fixed to the earth on , which carried a so-« 
Lo Sythe aed of 43 aoe diameter, and of about 14 
. weight, the above and below 45 degrees were 
pacha pact eaiaal 3 if there were any difference, the 
under ranges went rather the farthest ; but those dif. 
ferences were usually less than the errors committed in 
ordinary practice, by the unequal goodness and dryness 
of the same sort of powder, by the unfitness of the shot 
to the bore, and by the looseness of the carriage. 
In a smaller brass shot, of about 14 inch diameter, 
cast by a cross-bow, which ranged it at most about 400 
feet, the force being much more equal than in the mor- 
tar-piece, this difference was found more curiously and 
constantly, and most evidently the under ranges ex~ 
ceeded the upper. From which trials I conclude, that 
although, in small and light shot, the opposition of the 
air ought and must be accounted for ; yet in shooting 
of great and weighty bombs, there need be very little 
or no allowance made ; so that these rules A put 
in practice, to all intents and purposes, as if this impe~ 
diment were absolutely removed.” 
Although the opinion which we have been consid 
ering was entertained chiefly by speculative writers, 
yet those who made extensive experiments on the 
motion of projected bodies, began to suspect some lurk- 
ing error. Anderson, whom we have already men- Subsequent 
tioned, as a keen abettor of the parabolic theory, had experi- 
occasion to make a number of new experiments on the i's by 
of shells discharged with small velocities, which “"“*°™ 
he published in 1690, in his treatise entitled, To hit a 
mark. He found that the track of shells and bullets was 
much less incurvated in the first part of their path than 
they ought to be, on the Galilean theory ; but instead 
of supposing the theory practically incorrect, or con- 
jecturing that the deviations were produced by the re- 
sistance of the air, he imagined that the shell or bul- 
let was discharged from the gun to a certain distance 
in a right line, and that gravity only began to deflect 
it into a parabolic curve at the end of this line, which 
he calls the line of the impulse of the fire, and which he 
supposes to be the same at all elevations. By giving 
a proper magnitude to this imaginary line, he was al- 
ways able to reconcile the ranges of any two shells _ 
jected at different elevations; though, as Mr Robins 
remarks, he would have found it impossible to recon- 
cile the irregularities of three or more ranges, 
So deeply rooted was the erroneous notion that the air Newton on 
offered only an unappreciable resistance to moving balls, ‘he — 
that the publication of Sir Isaac Newton's Principia, in “°° * 
which the resistance of the air in slow motions is as- * 
certained and confirmed by experiment, was not able 
to correct it. By extending the law for slow motions 
to those in which the velocity was very great, it was 
obvious that the resistance opposed to cannon balls 
