A
                                DISCOURSE
                                  ON THE
                           _Theory of Gunnery_.




                                    A
                                DISCOURSE
                                  ON THE
                           _Theory of Gunnery_.

                             DELIVERED AT THE
                Anniversary Meeting of the ROYAL SOCIETY,
                            November 30, 1778.

                       By Sir JOHN PRINGLE Baronet.

                        PUBLISHED BY THEIR ORDER.

                              [Illustration]

                                 LONDON:
                      PRINTED FOR THE ROYAL SOCIETY.
                               MDCCLXXVIII.




[Illustration]




    GENTLEMEN,

Among the several experiments communicated to the society, during the
course of the preceding year, none seeming so much to engage your
attention, as those contained in the Paper, intituled, _The force of
fired gun-powder, and the initial velocity of cannon-balls, determined
by experiments_: with much pleasure therefore I acquaint you, that, on
account of the pre-eminence of that communication, your Council have
judged the author, Mr. CHARLES HUTTON, worthy of the honour of the annual
medal, instituted on the bequest of Sir GODFREY COPLEY Baronet, for
raising a laudable emulation among men of genius, in making experimental
inquiries. But, as on former occasions, so now, your Council, waving
their privilege of determining the choice, have acted only as a select
number deputed by you, to prepare matters for your final decision. I
come then, on their part, briefly to lay before you the state of the
_Theory of Gunnery_, from its rise to the time when its true foundation
was laid, in order to evince how conducive those experiments may be
to the improvement of an art of public concern, as well as to the
advancement of _natural knowledge_, the great object of your institution.
And if, upon a review of the subject, you shall entertain no less
favourable an opinion of Mr. HUTTON’s performance, than what your Council
have done, it is their earnest request that you would enhance the value
of this prize, by authorizing your President to present it to our
ingenious brother in your name.

Artillery (in the large acceptation of the term) took place long before
the invention of gun-powder. We trace the art to the remotest antiquity,
since the Sacred Records acquaint us, that one of the kings of Judah,
eight hundred years before the Christian æra, erected on the towers and
bulwarks of Jerusalem engines of war, the contrivance of ingenious men,
for shooting arrows and great stones for the defence of that city[1].
Such machines were afterwards known to the Greeks and Romans by the
names of _balista_, _catapulta_ and others, which had amazing powers,
and were not less terrible in their effects than the cannon and mortars
of the moderns. It appears that the _balista_ was contrived to shower
volleys of darts and arrows of a very large size upon the enemy, whilst
the _catapulta_ or _onagra_ (as it was otherwise called) was fitted
not only for that purpose, but for discharging stones of an enormous
weight; I might say _rocks_, since some of them are reported to have
weighed several hundred pounds. Batteries composed of numerous pieces of
that kind of artillery, nothing could withstand. Yet, if we are rightly
informed, their sole principle of motion consisted in the spring of a
strongly-twisted cordage, made of animal substances singularly tough and
elastic. These warlike instruments continued, not only during the time
of the Roman empire, but to the 12th and 13th centuries, as we find from
history; nor indeed is it probable that they were totally laid aside,
till gun-powder and the modern ordnance, attaining a good degree of
perfection, superseded their use. The very intelligent commentator of
POLYBIUS[2] is of opinion, that the military art rather lost than gained
by the exchange of the _catapulta_ for the mortar: but however that
point may be determined in speculation, it is not likely that the ancient
_tormenta militaria_ will ever be revived; but that all nations will keep
to the art of gunnery and study how to improve it; that is, they will
adhere to a system of artillery, wherein the moving power depends on the
expansive force of gun-powder, or of some other substance of a similar
nature.

Upon the first application of this principle to the purposes of war,
nothing perhaps was less thought of than to assist so empirical a
practice by scientific rules; for, however aiding in these matters the
ancient mechanicians might have been, who, like ARCHIMEDES, had invented
or perfected some of the _balistic_ machines, no praise seemed now due
to the mathematicians for either the discovery or improvement of the new
artillery. In fact, we find the practice of the art had subsisted about
200 years, before any geometer considered it as one that admitted a
theory, or at least such a theory as was grounded on geometry.

It seems but just to trace and commemorate the inventors of the ingenious
arts which furnish matter for discourses on these occasions; and not
only the main inventors, but even those who first turned their thoughts
upon the subject: for, though such men may not have produced any thing
perfect, yet they may have suggested ideas to others of a less inventive,
but of a more executive genius, and who, unprovided with those hints,
would never have made any notable discovery. I must therefore observe,
that the _Italians_ were the first who emerged out of those thick clouds
of ignorance and barbarism which had so long overspread this quarter of
the world. They profited by the unhappy fate of Constantinople; for by
liberally receiving the learned emigrants on that distressful occasion,
they were largely repaid by their arts and sciences, and still more
abundantly by their language, whereby they were enabled to read and to
translate those ancient manuscripts, which the Greeks had saved out of
the wreck of their country. The art of printing, which was established
soon after, was the means of quickly disseminating those treasures of
knowledge, and concurred with the fall of the eastern empire to form an
epoch for the advancement of learning, unparalleled in the annals of
letters.

The end of the 15th century, and the whole of the 16th, were chiefly
employed by the Italians in the study and in the translation of the
old Greek authors. The geometry of the ancient Greeks, as well as the
arithmetic in numbers and species of the Arabians, were cultivated;
but both remained, as it were, sciences by themselves, unassisting to,
or at best but weak and reluctant auxiliaries to the philosophy of the
schools: and indeed how could the abstracted doctrines of numbers and
quantities be strained to co-operate with a system, in which neither
the laws of motion, nor any but the superficial, and often delusive
properties of matter, were to be met with? The genius of the Greeks, all
acute and brilliant as it was, had never been properly directed to the
interpretation of nature, and was indeed unfit (as Lord Bacon pronounced)
for a study that made so slow and painful a progress, by re-iterated and
varied experiments and observations. It was no wonder then, if the _mixed
mathematics_, as they are called, descended to the moderns in a state
no-wise corresponding to the elegance and certainty of those parts of the
science which were elementary and pure; and that those mixed parts should
have been found defective and erroneous, in proportion (if I may so
express myself) to the physical considerations that were to be taken into
the inquiry. The imperfection of the ancients, with regard to natural
philosophy, was not perceived at that time; nay, at the period we are
treating of, the learned were firmly persuaded of the contrary, and that
all that was wanting to be known concerning the laws of nature, and the
properties of matter, was to be taken either directly, or by deduction,
from the physics of ARISTOTLE. It was not till the 17th century was
somewhat advanced, that men of science began to listen to Lord BACON and
GALILEO, the great founders of the experimental and the true philosophy.

Mean while, in the beginning of the 16th century, unqualified as the
Italians then were for entering upon physico-mathematical inquiries[3],
they nevertheless made the attempt, and in particular took the theory
of projectiles into consideration. Some imagined that a body impelled
with violence, such as a ball discharged from a cannon, moved in a right
line till the force was spent, and that then it fell in another right
line perpendicularly to the earth. Upon this principle, absurd as it
was, we find one of the earliest authors grounding his whole theory
of gunnery[4]; whilst others, dissenting from his hypothesis, admitted
only the straight line, in which the ball moved for some time after
coming out of the piece, and that other straight line in which it fell
to the ground; but asserted that these two were connected by a curve
line, and that this curve was the segment of a circle. NICOLAS TARTAGLIA
of Brescia, a mathematician of the first rank in those days, and still
celebrated for his improvements in algebra, hath been supposed to be the
author of this doctrine, no less erroneous than the former, and for which
two of his books have been quoted[5]. Those I have never seen; but from
another of his works, professedly written on this subject, and translated
into English under the title of _Colloquies concerning the art of
shooting in great and small pieces of artillery_[6], him I find, contrary
to the opinion of his contemporaries, maintaining that no part of the
track of a cannon-ball is in a right line, though the curvature in the
first part of its flight be so small, that it needeth not to be attended
to. But TARTAGLIA is far from supposing, that the line in question hath
any relation to a _parabola_, or to any regular curve. It would seem
then, that if this mathematician had at first been so far mistaken, as
to fancy that some part of the course of a projectile was in a straight
line, he had afterwards changed his opinion, and was perhaps singular in
what he finally embraced.

From numerous instances one would imagine, that in those days, so far
were men of science from making experiments themselves, that they even
shut their eyes against what chance would have presented to their sight.
For, whoever had minded the roving shot of an arrow, the flight of a
stone from a sling, or had attended to a stream of water issuing from the
spout of a cistern, might have been convinced, that the path of every
projectile was in a continued curve, whatever little he otherwise knew
concerning the properties of that one.

But had the observation of the philosophers gone so far, they had
still been at a distance from the truth. They might have perceived a
likeness between the track of those bodies in motion and a parabola,
and concluded, from analogy, that all projectiles delineated that curve
in the air; but they could never have realized their conjectures by
mathematical demonstration, without previously knowing the law of
_acceleration_ in falling bodies: a discovery reserved for the next
century, and for GALILEO[7], one of the greatest ornaments of it.

It was he who first investigated the effects of _gravity_ on falling
bodies, and upon that foundation demonstrated, that all projectiles
would move in a parabola in a non-resisting medium. And as he made
little account of the resistance of the air, whose properties were then
imperfectly known, he proved that a ball shot horizontally would, in its
flight, describe half a parabola; and when the piece had an elevation
above the horizon, the ball would describe a whole parabola, supposing it
to fall on the plane of the battery. By the same method of reasoning he
shewed, that whatever the ranges of the projected body, or the elevations
of the piece were, the ball would still trace that curve line, of a
greater or lesser amplitude, by the time it descended to the level of the
place from whence it came.

Thus far went GALILEO, confining his projections to the horizontal plane
of the battery; but TORRICELLI his disciple soon after carried the
theory farther, by tracing the shot to its fall, whether that place was
above or below the plane; and still found, by geometrical deductions,
that it flew in a parabola of a larger or a smaller amplitude, according
to the angle of elevation of the piece, and the strength of the powder.

Various and numerous had been the disputes in Italy about the laws of
motion in general, and especially about those of projectiles, from the
time the mathematicians had begun the inquiry, till the publication of
the dialogues of GALILEO on that subject (a space of upwards of a hundred
years) but from that period, so evident did his demonstrations appear,
that all contest ceased, and every man of science was convinced, that
all projectiles moved in the track which he had discovered. For, as to
the resistance of the air, which he had not passed unnoticed (as GALILEO
himself had been the first, at least of the moderns, who started the
notion of the weight of the air and the pressure of the atmosphere) yet
so thin and so yielding did they esteem that fluid to be, that they were
assured it could occasion no sensible, at least no material, deviation
from that curve. As they had the principle from GALILEO, so they believed
themselves warranted by that respectable author, not to fear from that
cause any objection, which he himself had suggested, but had removed.
_Among these projectiles_ (says he) _which we make use of, if they are of
a heavy matter and a round form; nay if they are of a lighter matter, and
have a cylindrical form, such as arrows shot from bows, their track or
path will not sensibly decline from the curve of a parabola_[8].

Here then was the theory of gunnery laid, in appearance, on the most
solid foundation. And thus far the Italians having proceeded, they seemed
to have taken leave, and to commit the subject to other nations, whose
greater power, or greater ambition, was more likely to make them avail
themselves of the perfection of a military art, than their instructors.
We had reason therefore to expect, that a neighbouring state, intent upon
the advancement of the arts and sciences in general, would not fail to
give particular attention to those that should appear most subservient
to its grandeur. Accordingly we find, that our sister-society of that
kingdom had not been many years established, when an ingenious member of
that illustrious Body, not questioning the soundness of the Galilean
principle in regard to projectiles, in the year 1677, proposed to the
academy, as a problem for the improvement of artillery, how to direct
a piece (suppose a mortar) so as to make the shot fall where one had a
mind; or in the common expression, _to hit a mark_, the strength of the
powder being given[9]. This thought met with general approbation, and so
far were the academy from raising any difficulty about the obstruction
which the air might occasion to a body moving with so much velocity
in it, that we do not find the making experiments on that head was
considered by them as an essential step to the solution; but that their
principal geometers straightway set about solving the problem as it had
been announced to them, some following one method, some another, and all
upon the supposition of a projectile moving in the line of a parabola.
But M. BLONDEL, who had been the proposer, and who more particularly had
studied the question, composed a large volume on the subject, which he
published a few years after[10], under the title of _L’Art de jetter les
Bombes_; a performance much celebrated at the time, and that continued in
no small request long after, as containing, besides his own, the labours
of several other members of that society of the most distinguished
merit. So many, and such hands concurring in framing this work, it was
no wonder that the learned throughout Europe were confirmed by it in
the Galilean theory; and the more as M. BLONDEL had obviated the only
objection they supposed could be made to it, the _resistance of the air_,
which he had taken care expressly to mention, and so to combat as to
persuade the reader, that the retardation arising from that cause was so
inconsiderable as to be of no account in the practice.

This illusion about the small or non-resistance of the air to bodies
rapidly moving in it, was so prevalent at the end of the last century,
and in the beginning of the present, that in the history of the Royal
Academy for the year 1707, we find their worthy and most accomplished
secretary, after taking notice of the joint labours of so many able
mathematicians concerned in BLONDEL’s publication, venturing to say, _it
did not appear that any thing was then wanting for the practice of the
art_ [of Gunnery] _except perhaps perfecting the instruments for pointing
a cannon or mortar ... but that geometry had done its part, so to speak,
with regard to practice_. &c.[11]

But far be it from our intention to relate the imperfections of others,
in order to raise ourselves by the comparison. Candour requires of us not
only to acknowledge, that in this country, as to the point in question,
we did not surpass our neighbours; but ingenuously to own that, on the
contrary, we were perhaps more liable to exception. For, some years
before BLONDEL’s work appeared[12], a treatise was published by one of
our own artillerists, ANDERSON (a person of eminence in his profession)
intituled _The genuine use and effects of the gun_, in which the author
strenuously supports the Galilean theory; nor do we learn he was ever
contradicted among us, although he undertook to answer all those who
should make objections to it. Nay, when he had an opportunity afterwards
of making experiments on the ranges of bombs, and by those trials was
assured that their flight was not in a parabola; yet so far was he from
ascribing the deviation from that figure to the resistance of the air,
that he had recourse to an hypothesis, repugnant to all the laws of
motion, to salve appearances, and to reconcile those experiments with his
former doctrine[13].

And did not Dr. HALLEY, so long the ornament of this society, communicate
in the year 1686 a Paper, which he calls _A discourse concerning
gravity_, in which, treating of the motion of projectiles, he says, that
being aware of the deflexion from the parabolic curve that might be
occasioned by the resistance of the air, he had made some experiments,
even with cannon-balls, to estimate the force of that resistance; yet
conclude, _That in large shot of metal, whose weight many thousand times
surpassed that of air, and whose force is very great, in proportion to
the surface wherewith they press thereupon, this opposition was not
discernible_. And again, _Though in small and light shot, the opposition
of the air ought and must be accounted for; yet in shooting great and
weighty bombs, there need be very tittle allowance made; and so these
rules_ [those, to wit, grounded on the principle of GALILEO] _may be put
in practice to all intents and purposes, as if this impediment_ [the
resistance of the air] _were absolutely removed_[14]. Such conclusions,
which we now find to be erroneous, were the less to be expected from so
eminent a person, as they argued too much haste to finish a theory, that
was to be made subservient to present use.

It might indeed have been expected, that men of science applying
themselves to this study, would have been sooner awakened to the
consideration of the great opposition of the air, by the _Principia_ of
NEWTON, published a little after this Paper of HALLEY’s[15]. For in that
excellent work the illustrious author had demonstrated, that the curve
described by a projectile, in a strongly resisting medium, differed much
from a parabola, and that the resistance of the air was great enough to
make the difference between the curve of projection of heavy bodies and a
parabola far from being insensible, and therefore too considerable to be
neglected.

Have we not then less to plead for not attending to the _Principia_ of
NEWTON in this article[16], than the mathematicians of other nations,
who, as M. de FONTENELLE observes[17], partly from the difficulty
of understanding that concise and profound work, and partly from a
misapprehension of its tendency (which they fancied was to revive the
exploded doctrine of _occult qualities_) were late in becoming acquainted
with it? But it is not so easy to account for their inattention to
HUYGENS, a known and even then a much esteemed author, and who indeed
was second to NEWTON alone in science and in genius. For he in the year
1690 had published a treatise on _Gravity_, written in a popular manner,
wherein he gave an account of some experiments he had made at Paris, and
in the academy, by which, as well as by mathematical investigations,
he was convinced of the truth of NEWTON’s conclusions, in regard to
the great opposition of the air to bodies moving swiftly in it; and,
by consequence, believed that the track of all projectiles was very
different from the line of a parabola[18].

But excepting NEWTON and HUYGENS, the learned seemed universally to
acquiesce in the justness and sufficiency of the principles of gunnery
invented by GALILEO, enlarged by TORRICELLI, confirmed and reduced to
system by ANDERSON, BLONDEL, HALLEY and others; and so far were the
theorists, in that branch of science, from suspecting any defect or
fallacy in these principles, that they seemed rather to reproach the
practical artillerists, for not profiting more by the instructions which
they had so liberally imparted to them. Nor do we find that an apology
was made for the empirical exercise of the art, by any author of note
in that line, earlier than the sixteenth year of this century, when M.
de RESSONS, a French officer of artillery, distinguished by the number
of sieges at which he had served, by his high military rank, and by his
abilities in his profession; when he, I say, thus qualified to bear
testimony, presented a _memoire_ to the Royal Academy (of which he was
a member) importing, that _although it was agreed that theory joined to
practice did constitute the perfection of every art, yet experience had
taught him, that theory was of very little service in the use of mortars.
That the work of M. BLONDEL had justly enough described the several
parabolic lines, according to the different degrees of the elevation of
the piece; but that practice had convinced him there was no theory in the
effects of gun-powder: for that having endeavoured, with the greatest
precision, to point a mortar agreeably to those calculations, he had
never been able to establish any solid foundation upon them[19]._

Thus, after the theory of gunnery had exercised the genius of the
learned for nearly two hundred years, and for almost fourscore of that
time had rested on fundamentals which had never been contested, it was
pronounced at once to be almost intirely useless, and that by one of
the most competent judges. Now, whether it were owing to the deference
due to the authority of that experienced artillerist, or to some other
cause, I shall not determine, but observe, that it appears not from the
history of the academy, that the sentiments of M. de RESSONS were at this
time controverted, or any reason offered afterwards for the failure of
the theory of projectiles when applied to use. Nor can I pass unnoticed
the pause that ensued before any further attempts were made to improve
the theory of the art, either upon the old principles or upon new ones,
except by such authors as seemed ignorant of this transaction, and who of
course were not sufficiently apprized of the inefficacy of the properties
of the parabola for directing practice. Or by those who were employed in
speculatively investigating the nature of the curve traced by a ball in
the air; a curve which began at last to be considered as one deviating
much from the line of a parabola. Or, finally, by such as, having taken
notice that NEWTON’s ideas had not been duly attended to, endeavoured
to avail themselves of them, and of some experiments that had been made
by others, for proving the great opposition of the air to bodies of
swift motion; but without ascertaining the degree of that resistance, or
enriching the art by any practical rules[20].

Such was the unhinged state of this part of the mixed mathematics,
when within our memory Mr. BENJAMIN ROBINS took cognizance of it: nor
could the subject have fallen into abler hands, endowed as he was by
nature with a superior genius and unwearied application. Mr. ROBINS was
deeply versed in geometry and the doctrine of numbers; but he knew the
limits as well as the powers of both, and how insufficient they were for
establishing any theory where matter was concerned, without preparing
the way, by finding out the physical properties of that _matter_, by
many and varied experiments and attentive observation. Those who had
hitherto treated of the foundation of gunnery, by being too forward in
the application of their mathematics, had in a manner hurt the credit
of that admirable science. They ought to have seen the necessity of
minutely examining every circumstance which could affect the course of
a projectile, besides that of gravity. Mr. ROBINS perceived the error
of his predecessors in that inquiry, and corrected it. Persuaded as he
was from sir ISAAC NEWTON’s _Principia_ of the great resistance of the
air to bodies moving in it, and also of the uncertainty of the force
of gun-powder, and of the variations in the flight of shot, occasioned
by the unavoidable varieties in the make of it, and in the make of the
pieces of artillery which discharged it; apprized, I say, of so many
causes of aberration, he justly concluded, that the foundation here was
at least as much an affair of physics as of geometry, and that if the art
of throwing bombs had not been advanced by theory, it was not because
the art admitted of none, but because the theory which had hitherto been
devised had been both defective and erroneous. He suspected that most of
the writers on gunnery had been deceived, in supposing the resistance
of the air to be inconsiderable, and thence asserting the track of all
shot to be nearly in the curve of a parabola, by which means it came to
pass that all their determinations, about the flight of projectiles of
violent motion, had declined considerably from the truth. But in order
to clear this point from every doubt, he found it necessary to ascertain
the force of gun-powder, and by that step to estimate the velocity of
the shot impelled by its explosion. That being done, he proceeded to
measure the quickness of a musket-bullet, shot out of a given barrel,
with a given quantity of powder; and to confirm the truth of his
conclusions, he contrived a machine, by which the velocity of a bullet
might be diminished in any given _ratio_, by being made to strike on a
large body of a weight justly proportioned to it; whereby the swiftest
motions, which otherwise would escape our examination, were to be exactly
determined by these slower motions that had a given relation to them. The
machine was a large wooden pendulum, which swung freely, but in so slow
a manner, that its vibrations could easily be counted, whatever was the
celerity of the bullet discharged against it. The thought was simple,
ingenious, and incontestably his own.

He next inquired into the resistance made by the air to projectiles of
rapid motion, and which he discovered to be much greater than had been
supposed by any writer on the subject; and indeed so great, that it
was manifest the curve described by any shot was very different from a
parabola, and consequently that all the applications of the properties
of that conic section to gunnery were so erroneous as to be totally
useless. For by means of this pendulum, placed at different distances
from the mouth of the piece, he clearly demonstrated how much a bullet,
flying with a given velocity, would gradually lose of that motion by the
opposition of the air: therein furnishing to the learned a signal and
instructive instance of the fallacy of the most specious theories, that
do not proceed hand in hand with experiments.

I should too much exceed the just bounds of a discourse of this kind,
were I to enter more minutely into the system founded by Mr. ROBINS,
confirmed and improved, as I find, by the labours of several of the
learned in foreign parts of great celebrity[21]. I shall only add,
that his performance well deserves the title he gives it of _The new
principles of gunnery_, since the author may more properly be said to
have invented a new science than to have added to an old one. And I
believe I may venture to say, that no physico-mathematical disquisition
hath done more honour to this country, or to the age, than the writings
of Mr. ROBINS on this subject, which have been published, partly by this
Society, partly by himself, and partly since his death (in the collection
of his whole mathematical tracts) by his learned friend.

But though our worthy brother will ever be celebrated for being the
inventor of the true principles of gunnery, yet it would be too
flattering to his memory, to say he had carried the theory of this art
to perfection. He himself was far from entertaining so high an opinion
of his labours; nay he expressly declared, that he left some material
points to be inquired into at more leisure (which other occupations
and his immature death deprived him of) and he much regretted that he
wanted conveniency and opportunities for making experiments on balls of
a greater weight, than what he had used for ascertaining the initial
velocity of them.

Much therefore are we indebted to Mr. HUTTON, who, treading in the
footsteps of the deceased, hath resumed and prosecuted this last
_desideratum_, and hath shewn himself not unequal to so difficult an
enterprize.

Mr. ROBINS, for determining the initial velocity of shot, arising from
different quantities of powder, made use of balls of about an ounce
weight; whereas Mr. HUTTON, for the same purpose, hath employed those of
different weights, from one pound to nearly three; or, in other words,
Mr. ROBINS made trial with musket-shot only, Mr. HUTTON with cannon-balls
from 20 to about 50 times heavier. This was a considerable step gained
in a disquisition of that part of the science, in which the resistance
of the air and other circumstances were not concerned; and where neither
analogy alone, nor mathematical deductions alone, nor the two combined,
were sufficient for establishing principles applicable to the motion of
cannon-balls, without making a new series of experiments: and with what
labour and judgment these have been performed, you understood by the
account which Mr. HUTTON gave of them in his Paper.

But should it now be inquired, what advantages may be derived from Mr.
HUTTON’s experiments, for the advancement of the art of gunnery, and of
philosophy in general? I would reply, that as to the former it may be
sufficient to observe, that though the improvements be only such as can
be deduced from the force of fired gun-powder; yet they are in a higher,
more certain, and in a more general manner, than what resulted from the
labours of Mr. ROBINS; who indeed led the way, but who made, as it were
in miniature, those experiments which Mr. HUTTON hath executed at large,
and which ROBINS himself wished to have made, as well as others who have
considered the subject since his time. Now these experiments, though made
by Mr. HUTTON with cannon-balls of a small size, may nevertheless form
just conclusions when applied to cannon-shot of the largest size. And
such conclusions inform us of the real force of powder when fired, either
in a cannon or a mortar, impelling a ball or bomb of a given weight;
that is, they discover with what velocity a given quantity of powder
drives those projectiles in a second, or in any other assigned portion
of time. They also shew the law of variation in the velocity arising
from different quantities of powder, with the same weight of metal,
and likewise that law which takes place upon using balls of different
weights. Further, they point out the advantage obtained by diminishing
the windage in cannon, and teach us how we may increase the weight of
the shot in the same piece, by making it of a cylindrical form, instead
of a spherical: by this device, a smaller ship may be enabled to do the
execution of a larger one. And experiments of the same kind will also
determine the just length of cannon for shooting farthest with the same
charge of powder.

Lastly, it is from these experiments, or from others that may be made
after the like manner, we are instructed how to answer every question
relative to military projectiles, except such as depend on the resistance
of the air to bodies moving swiftly in it. This indeed is a consideration
which leaves room for greater improvement in the art, and for conferring
fresh honours on those, who, like Mr. HUTTON, shall have opportunities
and abilities for continuing and perfecting this very curious and useful
inquiry.

As to the advantages accruing to philosophy from the labours both of
Mr. ROBINS and Mr. HUTTON, speak they not for themselves? The sciences
of motion and pneumatics are promoted by them; and of what avail their
perfection would be for the farther interpretation of nature, you need
not be informed. In fine, we have here before us, in these experiments,
the surest test of our advancement in true knowledge, which is, the
improvement of a liberal art, and the enlargement of the powers of man
over the works of creation.

Some however may think, that the objects of this society are the arts of
peace alone, not those of war, and that considering how numerous and how
keen the instruments of death already are, it would better become us to
discourage than to countenance their farther improvement. These naturally
will be the first thoughts of the best disposed minds. But when upon
a closer examination we find, that since the invention of arms of the
quickest execution, neither battles nor sieges have been more frequent
nor more destructive, indeed apparently otherwise; may we not thence
infer, that such means as have been employed to sharpen the sword, have
tended more to diminish than to increase the number of its victims, by
shortening contests and making them more decisive. I shall not however
insist on maintaining so great a paradox; but only surmise, that
whatever State would adopt the Utopian maxims, and proscribe the study of
arms, would soon, I fear, become a prey to those who best knew how to use
them. For yet, alas! far seem we to be removed from those promised times,
_when nation shall not lift up sword against nation, neither shall they
learn war any more_!

       *       *       *       *       *

_Here ended the President’s Discourse: after which he turned to Mr.
HUTTON, and said_,

You have heard, Sir, the account I have given of the rise and progress
of the _theory of gunnery_, and of your improvement of it; a recital,
which by no means would have done either you or the subject justice, had
it been addressed to any other audience than to the present. But as my
intention was only briefly to recall to the memory of these gentlemen
what they knew of this subject, antecedently to your Paper, and to remind
them of the result of your experiments, I flatter myself I have said
what was sufficient on the occasion; being now authorized by them to
deliver into your hand this medal, as the perpetual memorial of their
approbation. And let me add, Sir, that they make you this present with
the more cordial affection, as by your other ingenious and valuable
communications they are assured, not only of your talents, but of your
zeal, for promoting the interests and honour of their Institution.

[Illustration]




FOOTNOTES


[1] 2 Chron. xxvi. 15.

[2] M. FOLARD.

[3] The chief exception that occurs to this general remark, is the rapid
progress which in that age COPERNICUS made in astronomy; who was not
indeed an Italian, but was supposed to have profited by his early travels
into Italy, which he enlightened afterwards by his admirable discoveries.

[4] See MONTUCLA, Hist. des Mathem. vol. I. p. 623.

[5] Those were _La Nuova Scientia_, and _Quesiti ed Inventioni diverse_.

[6] Published at London, A. 1588.

[7] He was born in the year 1564; but few if any of his works were
published till after the year 1600, and his dialogues on motion not
before 1638.

[8] See his 4th Dialogue on Motion.

[9] See Hist. de l’Academ. Roy. des Sciences, A. 1707.

[10] In the year 1683, see Hist. de l’Acad. R. des Sci. A. 1707.

[11] Hist. de l’Acad. R. des Sc. A. 1707, under the article _Mechanique_.

[12] Viz. in 1674.

[13] See his treatise _To hit a Mark_, published in 1690.

[14] Philos. Trans. No. 179, p. 20.

[15] In the year 1687.

[16] NEWTON, Princip. Mathem. lib. ii. sect. 7.

[17] Eloge de NEWTON.

[18] Discours de la Cause de la Pesanteur. Leide, 1690.

[19] Mem. de l’Acad. R. des Sc. A. 1716.

[20] DAN. BERNOULLI, Comment. Acad. Petropol. T. 2. & 3.

[21] It is also much to the honour of Mr. ROBINS, that his writings on
this subject have been translated into foreign languages by men that were
the best judges of their merit. I need only name MM. EULER, and LE ROY.




ERRATA.


    Page 4. l. 5. _for_ this _read_ the
        16.    9. _for_ combate _read_ combat
        20.   17. _for_ tract _read_ track
        26.   last line of the note, _for_ M. M. _read_ MM.

Transcriber’s Note: The errata have been corrected.