112 GUNNER Y. 
Deg. of Elevatlo 
or o 
7l - 
*5 
”4 - 
30 
371 - 
45 
5 2 4 
- 60 
67.^ 
75 
82i 
n. Range in Paces. 
268 
594 
7.94 
- - 954 
- - 1010 
1040 
1053 
between the 3d and 4th. 
between the 2d and 3d. 
between the ill and 2d. 
between the o and 1 ft. 
fell very near the piece. 
The next ferles of experiments were given by William 
Bourne, in 1643, in his Art of Shooting in Great Ord¬ 
nance. His elevations were not regulated by the points 
of the gunner’s quadrant, but by degrees ; and he gives 
the proportions between the ranges at different eleva¬ 
tions, and the extent of the point-blank fhot, thus : if 
the extent of the point-blank fhot be reprefented by 1, 
then the proportions of the ranges at feveral elevations 
will be as follow : 
Elevation. Range. 
10 - 3? 
15 - 4^ 
zo - 4-f- 
and the greateft random 5^ 
which greateft random, he fays, in a calm day, is at 42 0 
elevation ; but according to the flrength of the wind, 
and as it favours or oppofes the flight of the fhot, the 
the elevation may be from 45 0 to 36°. He does not fay 
with what piece he made his trials; though from his 
proportion it feems to have been a fmall one. This, 
however, ought to have been mentioned, as the relation 
between the extent of different ranges varies extremely 
according to the velocity and denfity of the bullet. 
, After him, Eldred and Anderfon, both Englifhmen, 
publifhed treatifes on this fubjedt. The former of thefe 
was many years gunner of Dover-caftle, where mod of 
his experiments were made, the earlieft of which are 
dated in 1611, though his book was not publifhed till 
1646, and was intitled The Gunner’s Glafs. His prin¬ 
ciples were fufficiently Ample, and within certain limits 
very near the truth, though they were not rigoroufly 
fo. He has giveq the adtual ranges of different pieces 
of artillery at fmall elevations, all under ten degrees. 
His experiments are numerous, and appear to be made 
with great care and caution ; and he has honeftly fet 
down Tome, which were not reconcileable to his method : 
upon the whole he feems to have taken more pains, and 
to have had a jufter .knowledge of the fubjedt, than is 
to be found among his praifical brethren. 
Galileo printed his Dialogues on Motion in 1,646. In 
thefe he pointed out the general laws obferved by na¬ 
ture in the production and compofition of motion, and 
was the fir ft who defcribed the aCtion and effects of 
gravity op falling bodies: on thefe principles he deter¬ 
mined, that the flight of a cannon-ball, or of any other 
projeClile, would be in the curve of a parabola, unlefs 
fo far as it fltould be diverted from that track by the 
refiftance of the air. He alfo propofed the means of exa¬ 
mining the inequalities which arife from thence, and of 
tlifcovering wlwt fenfible effeCts that refiftance would 
produce in the motion of a bullet at fome given diftance 
from the piece. Yet notwithftanding thefe valuable hints 
of Galileo, it feems that thofe who came after him never 
imagined that ft was neceffary to confider how far the, 
operations of gunnery were affedle.d by this refiftance. 
Inftead of this, they boldly afferted, without making the 
experiment, that no great variation could arife from the 
refiftance of the air in the flight of fhells or cannon-ftiot. 
In this>perfuafion they fupported themfelves chiefly by 
confidering^he extreme rarity of the air, compared with 
thofe denfe and ponderous bodies; and at laft It became 
an almoft generally eftablifhed maxim, that the flight of 
thefe bodies was nearly in the curve of a parabola. 
Thus Robert Anderfon, in his Genuine Ufe and Ef¬ 
fects of the Gunne, publifhed in 1674, and again in his 
book To hit a Mark, in 1690, relates a great many ex¬ 
periments ; but, proceeding on the principles of Galileo, 
he ftrenuoufly afferts that the flight of all bullets is in 
the curve of a parabola; undertaking to anfwerall ob¬ 
jections that could be brought to the contrary. The 
fame thing was alfo undertaken by Blondel, in his Art 
dejetter les Bombes, publifhed in 1683 ; where, after long 
difcuflion, he concludes, that the variations from the 
air’s refiftance are fo flight as not to deferve any notice. 
The fame fubjeCt is treated of in the-Philof. Tranf. 
No. 216, p. 68, by Dr. Halley ; who alfo, fwayed by the 
great difproportion between the denfity of the air and 
that of iron or lead, thought it reafonable to believe that 
the oppofition of the air to large metal fhot is fcarcely 
difcernible; although in fmall and light fhot he owns 
that it requires to be accounted for. 
But though this hypothefis went on fmoothly in fpe- 
culation, yet Anderfon, who made a great number of 
trials, found it impollible to fupport it without fome 
new modification. For though it does not appear that 
he ever examined the comparative ranges of either can¬ 
non or mufket fhot when fired with their ufual velocities, 
yet his experiments on the ranges of fhells thrown with 
velocities that were but fmall in comparifon of thofe 
above-mentioned, convinced him that their whole track 
was not parabolical. But inftead of making the proper 
inferences from hence, and concluding that the refiftance 
of the air was of confiderable efficacy, he framed a new 
hypothefis ; which was, that the fhell or ball at its firft: 
difcharge flew to a certain diftance in a right line, from 
the end of which line only it began to deferibe a para¬ 
bola : and this right line, which he calls the line of the 
impulfe of the fire, he fuppofes is the fame for all ele¬ 
vations. So that, by affigning a proper length to this 
line of impulfe, it was always in his power to reconcile 
any two fliots made at any two different angles ; though' 
the fame method could not fucceed with three fhots 3 
nor indeed does he ever inform us of the event of his 
experiments when three ranges were tried at one time. 
But after the publication of Newton’s Principia, it 
might have been expedited, that the defedts of the theory 
would be afcribed to their true caufe, which is the great 
refiftance of the air to fuch fwift motions; as in that 
work he particularly confidered the fubjedt of fuch mo¬ 
tions, and related the refult of experiments, made on 
flow motions at leaft ; by whidi it appeared, that in fuch 
motions the refiftance increafes as the fquare of the ve¬ 
locities, and he even hints a fufpicion that it will in- 
create above that law in fwifter motions, as is now known 
to be the cafe. So far, however, were thefe who treated 
this fubjedt fcientifically from making a proper allow¬ 
ance for the refiftance of the atmofphere, that they fti 11 
negledted it, or rather oppofed it; and their theories 
ftill differed moll egregioully from the truth. Huygens 
alone feems to have attended to this principle : for in 
1690 he publifhed a treatife on gravity, in which he gave 
an account of fome experiments tending to. prove that 
the track of all projectiles, moving with very fwift 
motions, was widely different from-that of a parabola. 
The other mathematicians generally acquiefced in the 
fufficiency of Galileo’s dodtrine, and accordingly very 
erroneous calculations concerning the ranges of cannon 
were given. . Nor was any farther notice taken of thefe 
errors till the year 1716, at which time M. Iteffons, a 
French officer of artillery, of great merit and experience,. 
gave in a memoir to the royal academy, importing that, 
“ although it was agreed That theory joined with prac¬ 
tice did conflitute the perfection of every art; yet expe¬ 
rience had taught him that theory was of very little lei* 
vice in the ufe of mortars ; that the works of M. Blondel 
