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ject of the resistance of the air much farther, and If the terms of any arithmetical series be lays down rules for computing ranges made in squared, the second differences will be equal : the air. But these must be far from accurate, hence this table proves the truth of the former as they are founded on the two following princi- part of Dr. Hutton's assertion. The additional ples, which are known, from numerous experi- tracts of Mr. Robins, in the latter part of this voments, to be erroneous: viz. 1st, thal till the lume, which contain many useful and important velocity of the projectile surpasses that of 1100 matters, are numbered and titled as follows, viz. feet in a second, the resistance may be esteemed Number 1, Of the resistance of the air. Numto be in the duplicate proportion of the velocity.ber 2, Of the resistance of the air; together with 2d, That if the velocity be greater than that of 1100 the method of computing the motions of bodies or 1200 feet in a second, then the absolute quan- projected in that medium. Number 3, An Actity of that resistance in these greater velocities count of the experiments relating to the resistance will be near three times as great as it should be of the air ; exhibited at different times before the by a comparison with the smaller velocities.' Royal Society, in the year 1746. Number 4, For instead of leaping at once from the law of Of the force of fired gunpowder, together with the square of the velocities, and ever after being the computation of the velocities thereby comabout three times as much, experiments prove municated to military projectiles. Number 5, that the increase of the resistance above the law A comparison of the experimental ranges of canof the square of the velocity takes place at first in non and mortars, with the theory contained in the smallest motions, and increases gradually the preceding papers. Practical maxims relating more and more, to a certain point, but never to the effects and management of artillery, and rises so high as to be three times that quantity, the flight of shells and shot. A proposal for inafter which it decreases again. To render this creasing the strength of the British navy, by evident, Dr. Hutton has inserted the following changing all the guns, from the eighteen-pounders table of the actual quantities of resistances, downwards, into others of equal weight, but of which are deduced from accurate experiments, a greater bore.' With several letters, and other and which show also the nature of the law of the papers, 'On pointing, or the directing of the canvariations by means of the columns of differences non to strike distant objects; Of the nature and annexed, reserving the detail of the experiments advantage of rifled barrel pieces,' &c. themselves to another occasion. These resistances I have,' continues Dr. Hutton, 'dwelt thus are, upon a ball of 19-65 inches in diameter, in long on Mr. Robins's New Principles of Gunavoirdupois ounces, and are for all velocities nery, because it is the first work that can be confrom O up to that of 2000 feet per second of time. sidered as attempting to establish a practical

system of gunnery, and projectiles, on good exThe quantity of the resistance of the air to a ball periments, on the force of gunpowder, on the of 1.965 inches in diameter.

resistance of the air, and on the effects of differ

ent pieces of artillery. Those experiments are Veloc. in Resist. in 1st. Dif. | 2d. Dif. not however sufficiently perfect, both on account feet. ferences. ferences. of the smallness of the bullets, and for want of

good ranges to form a proper theory upon. I 0 0.000

have supplied some of the necessary desiderata 5 0-006

for this purpose, viz. the resistance of the air to 10 0-025

cannon balls moving with all degrees of velocity, 15 0.054

and the velocities communicated by given charges 20 0-100

of powder, to different balls, and from different 25 0.155

pieces of artillery. But there are still wanting 30 0-23

good experiments with different pieces of ord40 0.42

nauce, giving the ranges and times of flight, with 50 0-67

all varieties of charges, and at all different an100 21 81 54 gles of elevation. A few, however, of those I 200 11


have obtained, as in the following small table, 300 25


which are derived from experiments made with

a medium one-pounder gun, the iron ball being 500 72 35 9

nearly two inches in diameter:-
600 107 44 10
700 151
54 12

Elevation Velocity of

Time of
66 13


flight. 900 271

79 13
1000 350
92 12

feet. feet.
1100 442 104 11

860 4100

9 1200 546 115


1230 5100 12
1300 661 124

1640 6600

144 1400 785 131



15 1680 6700 153 1500 916 135



45 860 5100 21 1600 1051 135


133 5
1800 1319 128


Dr. Hutton's second set of experiments were 1900 1447 122

made with four brass guns very nicely bored and 2000 1569

cast on purpose, of different lengths, but regular in all other respects, viz. of weight and bore.


of gun.


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1 ; 15

The lengths of the bores of the guns were, increase with the charges of powder for each gun, No. 1, 15 calibres, length of bore 28.5 inches.

and also how they increase as the guns are longer, 2, 20 calibres


with the same charge, in every instance. 3, 30 calibres


By increasing the quantity of the charges con4, 40 calibres


tinually, for each gun, it was found that the ve

locities continued to increase till they arrived at the calibre of each being 256 inches, and the me a certain degree, different in each gun; after dium weight of the balls 16 oz. 13 dr.

which they constantly decreased again, till the The mediums of all the experimental velocities bore was quite filled with the charge. The of the balls, with which they struck the pendul- charges of powder when the velocities arrived at ous block of wood, placed at the distance of their maximum or greatest state were various, thirty-two feet from the muzzle of the gun, for as might be expected, according to the lengths of several charges of powder, were as in the follow- the guns; and the weight of powder, with the ing table,

length it extended in the bore, and the fractional part of the bore it occupied, are shown in the

following table, of the charges for the greatest TABLE OF INITIAL VELOCITIES.


The charge
No. 1. No. 2. No.3 No. 4

Gun, Length Weight.

835 920 970

of the
4 1100 1180 1300 1370

No. bore. 6 1340 1445 1590 1680


Part of 8 1430 1790 1940

12 1436 1640

1 28.5 12

2 38.4 14 9:5


3 57.7 16 10.7
4 80-2 18 12:1

The guns.





placed in the first column, for all the four guns, Of the few experiments in this course made to the numbers denoting so many feet per second. obtain the ranges and times of flight, the meWhence in general it appears how the velocities diums are exhibited in the following table:

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In this table are contained the following con- charges of two, four, and eight ounces of powder ; comitant data, determined with a tolerable de- and the mediums of the penetrations, as placed gree of precision; viz. the weight of the powder, in the last line, are found to be seven, fifteen, the weight and diameter of the ball, the initial or and twenty inches, with those charges. These projectile velocity, the angle of elevation of the penetrations are nearly as the numbers 2, 4, 6, gun, the time in seconds of the ball's fight or 1, 2, 3; but the charges of powder are as 2, through the air, and its range, or the distance 4, 8, or 1, 2, 4; so that ihe penetrations are prowhere it fell on the horizontal plane. From portional to the charges as far as to four ounces, which it is hoped that some aid may be derived but in a less ratio at three ounces; whereas, by towards ascertaining the resistance of the me the theory of penetrations, the depths ought to be dium, and its effects on other elevations, &c., proportional to the charges, or, which is the same and so afford some means of obtaining easy rules thing, as the squares of the velocities. So that for the cases of practical gunnery; though the it seems the resisting force of the wood is not completion of this enquiry, for want of time at uniformly or constantly the same, but that it inpresent, must be referred to another work. creases a little with the increased velocity of the

Another subject of enquiry, in the foregoing ball. This may probably be occasioned by the experiments, was, how far the balls would pene- greater quantity of fibres driven before the ball; trate into solid blocks of elm wood, fired in the which may thus increase the spring and resistdirection of the fibres. The following tablet ance of the wood, and prevent the ball from peshows the results of a few of the trials that were ne ting deep as it otherwise might do. made with the gun No. 2, with the most frequent

ragraph, it is evident that we gain extremely little Penetrations of balls into solid

in the range by a great increase in the length of elm wood.

the gun, with the same charge of powder. In Powder 2

fact, the range is nearly as the fifth root of the 4. | 8 oz.

length of the bore; which is so small an increase,

as lo amount only to about a seventh part more 7 16.6 18.9

range for a double length of gun. From the same 13:5 21.2

table it also appears that the time of the ball's 18:1

flight is nearly as the range; the gun and ele20.3

vation being the same. 20:5

It has been found, by these experiments, that

no difference is caused in the velocity, or range, Means 7 15 20

by varying the weight of the gun, nor by the use

of wads, nor by different degrees of ramming, The deductions and observations made on the nor by firing the charge of powder in different former course are here corroborated respecting the parts of it. But that a very great difference in the velocities and weights of the balls, &c. The velocity arises from a small degree in the windvelocity of the ball, however, increases with the age; indeed with the usual established windage increase of the charge only to a certain point only, viz. about one-twentieth of the calibre, no peculiar to each gun, beyond which increase of less than between one-third and one-fourth of the the charge, the velocity of the ball diminishes till powder escapes and is lost: and, as the balls are the bore is full of powder. That is to say, the often smaller than the regulated size, it frequentvelocity increases with the length of the gun, but ly happens that half the powder is lost by unnot in equal proportion. The part filled with necessary windage. powder bears å less proportion to the whole bore It appears too that the resisting force of wood, in the long guns than in the shorter ones; it is to balls fired into it, is not constant: and that Dearly in the inverse ratio of the square root of the depths penetrated by balls, with different vethe empty part.

locities or charges, are nearly as the logarithms It appears that the velocity, with equal charges, of the charges, instead of being as the charges always increases as the gun is longer; though themselves, or, which is the same thing, as the the increase in velocity is but very small in com- square of the velocity. Lastly, these and most parison to the increase in length; the velocities other experiments show, that balls are greatly being in a ratio somewhat less than that of the deflected from the direction in which they are square roots of the length of the bore, but greater projected; and that as much as 300 or 400 yards than that of the cube roots of the same, and is in a range of a mile, or almost one-fourth of the indeed nearly in the middle ratio between the two. range.

It appears, from the table of ranges, that the A third series of experiments enabled this exrange increases in a much lower ratio than the cellent mathematician to furnish the three folvelocity, the gun and elevation being the same. lowing tables of resistances, for three different And, when this is compared with the proportion sizes of balls, and for velocities between 100 feet of the velocity arid length of gun in the last pa- and 2000 feet per second of time.

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It is remarkable that, notwithstanding the of their accuracy, In consequence of these decisive manner in which Dr. Hution recom trials the committee fixed the quantity of windmended the diminution of windage, it should age for field-guns at oue-tenth of an inch; the not have been adopted in practice till very lately; same which I had suggested. and that in consequence principally of the re Now it is clear that this improvement may presentations of Sir Howard Douglas. This either be applied to save one-sixth part of the able officer, in part second of his Naval Gun- quantity of powder provided for field-service, nery, points out the extraordinary anomalies in without diminishing the power of range, and the previously received system of windage, and consequently to economise, without detriment, ex patiates with great good sense upon their pre- the means of transport for ammunition : or the judicial effects. He satisfactorily refutes the alteration may be applied to produce longer popular objections to any change, and then ranges, if this be preferred to the economical proceeds thus :

—The preceding remarks on consideration. This preference has very properly windage having been brought under the consi- been given, and the established charges adhered deration of the master general of the ordnance to accordingly. A great collateral advantage in 1817, his lordship referred the paper to the has followed from this correction of windage. consideration of a select committee of artillery It was at first apprehended that the increased officers, who stated in their report that they effects arising from the additional weight of shot were very desirous that experiments should be and diminished windage would injure brass made with a view to ascertain to what extent the guns; but it is quite the reverse. With the benefits which I had anticipated could be reali- reduced quantum of windage guns are much less sed.' The committee, therefore, proposed to the injured, and will last much longer than formerly; master general to be permitted to make a course and this has been so well ascertained, that in of experiments on this subject, commencing consequence of this correction, it is now prowith field-artillery, and for that purpose recom- posed to abandon the wooden bottoms to which mended that a proportion of shot of various in- shot were fixed for the purpose of saving the creased magnitudes should be provided. These cylinder, substituting for them the paper cap measures having been approved, a course of taken off the end of the cartridge.

This being experiments was instituted accordingly,' found. put over the ball is quite sufficient to keep it ed upon the suggestions communicated by' me. from rolling or shifting, whilst, by supporting or

• Ilaving first adopted an opinion (asserted in fixing it thus, the centre of the ball coincides my Observations, articles 49, 53), that the pre- with the axis of the cylinder, and the space for sent mode of apportioning a part of the calibre windage is reduced to a complete annulus, which is not so distinct and advantageous as a fixed admits of the percussion from the charge being quantum expressed in parts of inches for all equally received, and which prevents, or very natures (of ordnance), the committee proceeded much reduces, that injury or indentation which to determine what that quantum should be the cylinder receives when the ball touches it on After repeated trials with a six-pounder, a nine- the lower part only.'— Naval Gunnery, p. 82. pounder, and a twelve-pounder, at 300, 600, and An abridged account of the experiments with 1200 yards, it was proved, that with charges of the ballistic pendulum, to which Sir Howard powder one-sixth less than usual, the larger shot Douglas refers, is given in Annales de Chimie and smaller windage produced rather the longest et de Physique, tome ix. p. 289, &c. We shall range.' * Recourse was also had to the ballistic transcribe the results of one day, May 19th, 1818. pendulum, to discover the proportional excess of The day was dry, but cloudy; the thermomeinomentum of the larger balls over the smaller; ter stood at 13.30 centigrade (56° Fahrenheit), and the result

, after a very satisfactory course of the barometer at 29.99 inches. The pendulum experiments, assisted by the scientific research weighed 7008 pounds avoirdupois. "The gun and well known mathematical abilities of Dr. was a twelve-pounder; its weight 2025 pounds; Gregory of the Royal Military Academy, cor- its length 74.25 English inches; its calibre 4.62 roborated the trials by ranges, leaving no doubt inches.

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Here it is evident that the velocity corre- though in the former case the charge was less sponding to a windage of 0.75, or fiths of an inch, by fth part than the latter. is at a mean 1568 feet, rather ing 1550 Assuming the correctness of the results, as feet, obtained when the windage was -20, or oths; tabulated above, we are by no means inclined to

agree with Sir Howard, however, in recommend. Woolwich experiments of 1817, and the result ing an adherence to the established charges, viz. of was uniformly and decidedly against the short a third of the weight of the ball, after the new rate guns. That additions to the length of the piece of windage is completely adopted. Supposing should occasion increased velocity of projection that, cæteris paribus, the initial velocity varies as is obviously the joint effect of two causes. 1st, the square root of the charge, a four-pound The expansive force of the inflamed gunpowder charge with the new windage would propel a acts longer upon the ball in a long than in a twelve-pound ball wit an initial velocity of short gun, and therefore communicates a greater about 1720 feet, a velocity which would be very velocity. 2dly, In short guns no small portion effective indeed if the ball were moving through of the gun-powder is carried out of the muzzle a non-resisting medium, but which experiences a without being at all inflamed. The lengths, most rapid retardation as the projectile passes however, must be limited by practical considerathrough the air. The experiments of Dr. Hut- tions, as well as by the theoretical ones deduciton prove, not only that the resistance of the air ble from our quotation a few pages back from becomes very enormous when the velocities ex. Dr. Hutton. ceed 1300 feet, but that the law of the resistance Sir Howard Douglas, who has the happy no longer accords nearly with the square of the faculty of confirming his theoretical positions by velocity, but, to be correctly exhibited, requires reference to historical facts, adduces some with a higher exponent. The reason is very evident. a view to this question, which we make no apoAtmospheric air rushes into a vacuum with a logy for citing.–Viewing the matter purely velocity of about 1346 feet per second, and it as an artillery question, there is no doubt that inanifestly cannot make way for a ball moving preference should be given to long guns. As to with a greater velocity than this without being its application to naval matters, I do not hesitate condensed before it. "In such cases, the air thus to recommend that a frigate which cannot carry condensed in front of the ball, opposes its eight feet twenty-four pounders, had better be motion not only by a simple resistance, but by a fitted with long eighteen pounders, than with six force of elasticity proportional to the compres- feet or six feet and a half twenty-four pounders, sion, and therefore rapidly increasing as the or with any nature of carronade, exclusively. The velocity of the projectile exceeds 1346 feet. very mortifying situation in which the gallant This repulsion soon reduces the higher velocities Sir James Yeo found himself in September, of 1600 or 1700 feet to the limit of from 1350 1813, on Lake Ontario, shows the danger of the to 1400, and consequently renders them of carronade system of armament. Sir James scarcely any use in either increasing the hori- states, in his letter of the 12th of September, zontal range, or the effective impetus of the ball

, the enemy's fleet of eleven sail, having a partial except at comparatively small distances from the wind, succeeded in getting within range of their mouth of the piece. This accords with the ex- long twenty-four and thirty-two pounders; and, perience of our artillery officers when employed having obtained the wind of us, I found it imin Spain; they found that balls fired with velo- possible to bring them to close action. We cities of 1600 feet had scarcely any advantage remained in this mortifying situation five hours, over those propelled with velocities of 1400 in having only six guns in the feet that would the destruction of distant objects.

reach the enemy. Not a carronade was fired. Theorists have long known that the elastic At sun-set a breeze sprang up from the westward, force exerted by the air against small bodies, when I manæuvred to oblige the enemy to meet moving with considerable velocities, may become us on equal terms. This, however, he carefully so great in proportion to the weight as not avoided.'' merely to destroy the motion communicated, but • Captain Barclay states, in his letter of the even to repel the bodies ; and this, indeed, is 12th of September, 1813: The other brig of frequently experienced when · small shot are the enemy, apparently destined to engage the thrown from a musket by large charges of pow- Queen Charlotte, supported in like manner by der, the shot being driven back in the contrary two schooners, kept so far to windward as to direction to that in which they were propelled. render the Queen Charlotte's twenty-four poundThe same thing of course does not precisely er corronades useless, whilst she and the Lady happen in the practice of artillery ; but it is a Prevost were exposed to a heavy and destructfact strictly coincident with theory, that a smaller ive fire from the Caledonian and four other charge of powder, by giving the shot less initial schooners, armed with long and heavy guns."'. velocity, will cause it to fly further than a greater Sir Howard next describes the action of the charge, which would propel the ball with a Phæbe with the American frigate Essex, as convelocity that exceeds a certain limit.

firming the theoretical view of the business; A military officer of some eminence, but de and adds :- This brilliant affair, together with fective, as we should conjecture, in mathemati- the preceding facts, cannot fail to dictate the cal knowledge, has recently proposed the use of necessity of abandoning a principle of armashort guns, especially in the service of the navy, ment exposed to such perils, and to teach the strangely fancying that the loss of velocity and importance of adapting the tactics of an operarange, that would attend the shortening of the tion to the comparative natures and powers of gun, would be more than compensated by some arms.'-Naval Gunnery, p. 116. suggested peculiarities in the external configura On the whole, we trust we shall not be action of the piece. This is utterly repugnant to cused of any unworthy feeling, if we remark that correct theory, and we believe to correct practice all, or nearly all, which is truly valuable in this also. The question was put to the test in the department of research has been the produce of

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