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ject of the resistance of the air much farther, and lays down rules for computing ranges made in the air. But these must be far from accurate, as they are founded on the two following principles, which are known, from numerous experiments, to be erroneous: viz. 1st, “that till the velocity of the projectile surpasses that of 1100 feet in a second, the resistance may be esteemed to be in the duplicate proportion of the velocity. 2d, That if the velocity be greater than that of 1100 or 1200 feet in a second, then the absolute quantity of that resistance in these greater velocities will be near three times as great as it should be by a comparison with the smaller velocities.’ For instead of leaping at once from the law of the square of the velocities, and ever after being about three times as much, experiments prove that the increase of the resistance above the law of the square of the velocity takes place at first in the smallest motions, and increases gradually more and more, to a certain point, but never rises so high as to be three times that quantity, after which it decreases again. To render this evident, Dr. Hutton has inserted the following table of the actual quantities of resistances, which are deduced from accurate experiments, and which show also the nature of the law of the variations by means of the columns of differences annexed, reserving the detail of the experiments themselves to another occasion. These resistances are, upon a ball of 19.65 inches in diameter, in avoirdupois ounces, and are for all velocities from 0 up to that of 2000 feet per second of time.

The quantity of the resistance of the air to a ball of 1.965 inches in diameter.

Veloc. in Resist. in 1st. Dif- || 2d. Diffeet. ounces. | ferences. | ferences. 0 0-000 5 0-006 10 0-025 15 0-054 20 0-100 25 O-155 30 0-23 40 O'42 50 O-67 100 2? 84 5? 200 11 14 6 300 25 20 7 400 45 27 8 500 72 35 9 600 107 44 10 700 151 54 12 800 205 66 13 900 271 79 13 1000 350 92 12 1100 442 104 11 1200 546 115 9 1300 661 124 7 1400 785 131 4 1500 916 135 0. 1600 1051 135 2 ! 1700 1186 133 5 1800 1319 128 6 1900 1447 122 2000 1569

If the terms of any arithmetical series be squared, the second differences will be equal: hence this table proves the truth of the former part of Dr. Hutton's assertion. The additional tracts of Mr. Robins, in the latter part of this volume, which contain many useful and important matters, are numbered and titled as follows, viz. Number 1, ‘Of the resistance of the air. Number 2, Of the resistance of the air; together with the method of computing the motions of bodies projected in that medium. Number 3, An Account of the experiments relating to the resistance of the air; exhibited at different times before the Royal Society, in the year 1746. Number 4, Of the force of fired gunpowder, together with the computation of the velocities thereby communicated to military projectiles. Number 5, A comparison of the experimental ranges of cannon and mortars, with the theory contained in the preceding papers. Practical maxims relatin to the effects and management of artillery, .# the flight of shells and shot. A proposal for increasing the strength of the British navy, by changing all the guns, from the eighteen-pounders downwards, into others of equal weight, but of a greater bore.' With several letters, and other papers, “On pointing, or the directing of the canmon to strike distant objects; Of the nature and advantage of rifled barrel pieces,’ &c.

“I have,' continues Dr. Hutton, dwelt thus long on Mr. Robins's New Principles of Gunnery, because it is the first work that can be considered as attempting to establish a practical system of gunnery, and projectiles, on good experiments, on the force of gunpowder, on the resistance of the air, and on the effects of different pieces of artillery. Those experiments are not however sufficiently perfect, both on account of the smallness of the bullets, and for want of good ranges to form a proper theory upon. I have supplied some of the necessary desiderata for this purpose, viz. the resistance of the air to cannon balls moving with all degrees of velocity, and the velocities communicated by given charges of powder, to different balls, and from different pieces of artillery. But there are still wanting good experiments with different pieces of ordnance, giving the ranges and times of flight, with all varieties of charges, and at all different angles of elevation. A few, however, of those I have obtained, as in the following small table, which are derived from experiments made with a medium one-pounder gun, the iron ball being nearly two inches in diameter:—

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increase with the charges of powder for each gun, and also how they increase as the guns are longer, with the same charge, in every instance.

By increasing the quantity of the charges continually, for each gun, it was found that the velocities continued to increase till they arrived at a certain degree, different in each gun; after which they constantly decreased again, till the bore was quite filled with the charge. The charges of powder when the velocities arrived at their maximum or greatest state were various, as might be expected, according to the lengths of the guns; .." the weight of powder, with the 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 effect:

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In this table are contained the following concomitant data, determined with a tolerable degree of precision; viz. the weight of the powder, the weight and diameter of the ball, the initial or projectile velocity, the angle of elevation of the gun, the time in seconds of the ball's flight through the air, and its range, or the distance where it fell on the horizontal plane. From which it is hoped that some aid may be derived towards ascertaining the resistance of the medium, and its effects on other elevations, &c., and so afford some means of obtaining easy rules for the cases of practical gunnery; though the completion of this enquiry, for want of time at present, must be referred to another work.

Another subject of enquiry, in the foregoing experiments, was, how far the balls would penetrate into solid blocks of elm wood, fired in the direction of the fibres. The following tablet shows the results of a few of the trials that were made with the gun No. 2, with the most frequent

charges of two, four, and eight ounces of powder; and the mediums of the penetrations, as placed in the last line, are found to be seven, fifteen, and twenty inches, with those charges. These penetrations are nearly as the numbers 2, 4, 6, or 1, 2, 3; but the charges of powder are as 2, 4, 8, or 1, 2, 4; so that the penetrations are proo to the charges as far as to four ounces, ut in a less ratio at three ounces; whereas, by the theory of penetrations, the depths ought to be proportional to the charges, or, which is the same thing, as the squares of the velocities. So that it seems the resisting force of the wood is not uniformly or constantly the same, but that it increases a little with the increased velocity of the ball. This may probably be occasioned by the greater quantity of fibres driven before the ball; which may thus increase the spring and resistange of the wood, and prevent o ball from penetrating so deep as it otherwise might do.

Penetrations of balls into solid
elm wood.

Powder 2 4. 8 oz.
7 16-6 | 18-9
13-5 21-2




Means 7 || 15 20

The deductions and observations made on the former course are here corroborated respecting the velocities and weights of the balls, &c. The velocity of the ball, however, increases with the increase of the charge only to a certain point peculiar to each gun, beyond which increase of the charge, the velocity of the ball diminishes till the bore is full of powder. That is to say, the velocity increases with the length of the gun, but not in equal proportion. The part filled with powder bears a less proportion to the whole bore in the long guns than in the shorter ones; it is nearly in the inverse ratio of the square root of the empty part. It appears that the velocity, with equal charges, always increases as the gun is longer; though the increase in velocity is but very small in comE. to the increase in length; the velocities eing in a ratio somewhat less than that of the square roots of the length of the bore, but greater than that of the cube roots of the same, and is indeed nearly in the middle ratio between the two. It appears, from the table of ranges, that the range increases in a much lower ratio than the velocity, the gun and elevation being the same. And, when this is compared with the o

ragraph, it is evident that we gain extremely little
in the range by a great increase in the length of
the gun, with the same charge of powder. In
fact, the range is nearly as the fifth root of the
length of the bore; which is so small an increase,
as to amount only to about a seventh part more
range for a double length of gun. From the same
table it also appears that the time of the ball's
flight is nearly as the range; the gun and ele-
vation being the same.
It has been found, by these experiments, that
no difference is caused in the velocity, or range,
by varying the weight of the gun, nor by the use
of wads, nor by different degrees of ramming,
nor by firing the charge of powder in different
parts of it. But that a very great difference in the
velocity arises from a small degree in the wind-
age; indeed with the usual established windage
only, viz. about one-twentieth of the calibre, no
less than between one-third and one-fourth of the
powder escapes and is lost; and, as the balls are
often smaller than the regulated size, it frequent-
ly happens that half the powder is lost by un-
necessary windage.
It appears too that the resisting force of wood,
to balls fired into it, is not constant: and that
the depths penetrated by balls, with different ve-
locities or charges, are nearly as the logarithms
of the charges, instead of being as the charges
themselves, or, which is the same thing, as the
square of the velocity. Lastly, these and most
other experiments show, that balls are greatly
deflected from the direction in which they are
rojected; and that as much as 300 or 400 yards
in a range of a mile, or almost one-fourth of the
A third series of experiments enabled this ex-
cellent mathematician to furnish. the three fol-
lowing tables of resistances, for three different
sizes of balls, and for velocities between 100 feet

of the velocity and length of gun in the last pa- and 2000 feet per second of time. TABLE I. TABLE II. TABLE III. - - Resistances to a ball 2:781Resistances to a ball 3-55 Resistances to a ball of 1965 inches inches diameter, and 31b, inches diameter, and 6 lb. diameter, and 16 oz. 13 dr. weight. weight. 1 oz. 8 dr. weight. Veloc. Resistances. 1st. Dif.2d. Dif|Veloc. | Res. | Difs. Veloc. Res. | Difs. feet. lbs. ozs. feet. lbs. feet. lbs. 100 0-17 2: 8. 900 35 6 1200 || 115 9 200 969] 11 | 1." 5% 950 || 41 ... I 1250 | 124 9 300 1.56 25 20 6 1000 47 6 1300 133 9 400 2-81 45 27 7 1050 53 7 1350 | 1.42 10 500 4.50 72 35 8 100 60 7 1400 | 152 10 600 6-69 107 44 9 1150 67 7 1450 | 162 104 700 9°44 151 54 10 1200 74 8 1500 172} 11 800 | 12-81 205 66 12 1250 82 9 1550 184 13 900 16'94 || 271 79 13 1300 91 10 1600 197 14 1000 || 21-88 350 92 13 1350 | 101 11 1650 211 15 1100 27-63 442 104 12 1400 || 112 10} 1700 226 ić 1200 || 34°13 || 546 115 11 1450 | 122} 10 1750 242 17 1300 || 41' 31 661 124 9 1500 || 132} 9 1800 || 259 1400 || 49-06 785 131 7. 1550 | 1.41% 8} 1500 57-25 || 916 135 4 1600 150 8 1600 || 65-69 || 1051 135 0 1650 | 158 7 1700 || 74.13 1186 13. —2 1700 | 165 6 1800 82.44 1319 128 —5 1750 | 171 5 1900 90-44 1447 122 –6 1800 176 2000 || 98-06 || 1569

It is remarkable that, notwithstanding the decisive manner in which Dr. Hutton recommended the diminution of windage, it should not have been adopted in practice till very lately; and that in consequence principally of the representations of Sir Howard Douglas. This able officer, in part second of his Naval Gunnery, points out the extraordinary anomalies in the previously received system of windage, and expatiates with great good sense upon their prejudicial effects. He satisfactorily refutes the popular objections to any change, and then proceeds thus:—‘The preceding remarks on windage having been brought under the consideration of the master general of the ordnance in 1817, his lordship referred the paper to the consideration of a select committee of artillery officers, who stated in their report ‘that they were very desirous that experiments should be made with a view to ascertain to what extent the benefits which I had anticipated could be realised.’ The committee, therefore, proposed to the master general to be permitted to make a course of experiments on this subject, commencing with field-artillery, and for that purpose recommended that a proportion of shot of various increased magnitudes should be provided. These measures having been approved, a course of experiments was instituted accordingly, ‘founded upon the suggestions communicated by’ me.

“Having first adopted an opinion (asserted in my Observations, articles 49, 53), that the present mode of apportioning a part of the calibre is not so distinct and advantageous as a fixed quantum expressed in parts of inches for all natures (of ordnance), the committee proceeded to determine what that quantum should be. After repeated trials with a six-pounder, a ninepounder, and a twelve-pounder, at 300, 600, and 1200 yards, it was proved, “that with charges of powder one-sixth less than usual, the larger shot

and smaller windage produced rather the longest

range.’ ‘Recourse was also had to the ballistic pendulum, to discover the proportional excess of momentum of the larger balls over the smaller; and the result, after a very satisfactory course of experiments, assisted by the scientific research and well known mathematical abilities of Dr. Gregory of the Royal Military Academy, corroborated the trials by ranges, leaving no doubt

of their accuracy. In consequence of these trials the committee fixed the quantity of windage for field-guns at one-tenth of an inch; the same which I had suggested. ‘Now it is clear that this improvement may either be applied to save one-sixth part of the quantity of powder provided for field-service, without diminishing the power of range, and consequently to economise, without detriment, the means of transport for ammunition: or the alteration may be applied to produce longer ranges, if this be preferred to the economical consideration. This preference has very properly been given, and the established charges adhered to accordingly. A great collateral advantage has followed from this correction of windage. It was at first apprehended that the increased effects arising from the additional weight of shot and diminished windage would injure brass guns; but it is quite the reverse. With the reduced quantum of windage guns are much less injured, and will last much longer than formerly; and this has been so well ascertained, that in consequence of this correction, it is now proposed to abandon the wooden bottoms to which shot were fixed for the purpose of saving the cylinder, substituting for them the paper cap taken off the end of the cartridge. This being }. over the ball is quite sufficient to keep it om rolling or shifting, whilst, by supporting or fixing it thus, the centre of the ball coincides with the axis of the cylinder, and the space for windage is reduced to a complete annulus, which admits of the percussion from the charge being equally received, and which prevents, or very much reduces, that injury or indentation which the cylinder receives when the ball touches it on the lower part only.’—Naval Gunnery, p. 82. An abridged account of the experiments with the ballistic pendulum, to which Sir Howard Douglas refers, is given in Annales de Chimie et de Physique, tome ix. p. 289, &c. We shall transcribe the results of one day, May 19th, 1818. The day was dry, but cloudy; the thermometer stood at 13.3° centigrade (56°Fahrenheit), the barometer at 29.9° inches. The pendulum weighed 7008 pounds avoirdupois. The gun was a twelve-pounder; its weight 2025 pounds; its length 74.25 English inches; its calibre 4.62 inches.

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agree with Sir Howard, however, in recommending an adherence to the established charges, viz. of a third of the weight of the ball, after the new rate of windage is completely or. Supposing that, caeteris paribus, the initial velocity varies as the square root of the charge, a four-pound charge with the new windage would propel a twelve-pound ball with an initial velocity of about 1720 feet, a velocity which would be very effective indeed if the ball were moving through a non-resisting medium, but which experiences a most rapid retardation as the projectile passes through the air. The experiments of Dr. Hutton prove, not only that the resistance of the air becomes very enormous when the velocities exceed 1300 feet, but that the law of the resistance no longer accords nearly with the square of the velocity, but, to be correctly exhibited, requires a higher exponent. The reason is very evident. Atmospheric air rushes into a vacuum with a velocity of about 1346 feet per second, and it manifestly cannot make way for a ball moving with a greater velocity than this without being condensed before it. In such cases, the air thus condensed in front of the ball, opposes its motion not only by a simple resistance, but by a force of elasticity proportional to the compression, and therefore rapidly increasing as the velocity of the projectile exceeds 1346 feet. This repulsion soon reduces the higher velocities of 1600 or 1700 feet to the limit of from 1350 to 1400, and consequently renders them of scarcely any use in either increasing the horizontal range, or the effective impetus of the ball, except at comparatively small distances from the mouth of the piece. This accords with the experience of our artillery officers when employed in Spain; they found that balls fired with velocities of 1600 feet had scarcely any advantage over those propelled with velocities of 1400 in the destruction of distant objects. Theorists have long known that the elastic force exerted by the air against small bodies, moving with considerable velocities, may become so great in proportion to the weight as not merely to destroy the motion communicated, but even to repel the bodies; and this, indeed, is frequently experienced when small shot are thrown from a musket by large charges of powder, the shot being driven back in the contrary direction to that in which they were propelled. The same thing of course does not precisely happen in the practice of artillery; but it is a fact strictly coincident with theory, that a smaller charge of powder, by giving the shot less initial velocity, will cause it to fly further than a greater charge, which would propel the ball with a velocity that exceeds a certain limit. A militarv officer of some eminence, but desective, as we should conjecture, in mathematical knowledge, has recently proposed the use of short guns, especially in the service of the navy, strangely fancying that the loss of velocity and range, that would attend the shortening of the gun, would be more than compensated by some suggested peculiarities in the external configuration of the piece. This is utterly repugnant to correct theory, and we believe to correct practice also. The question was put to the test in the

Woolwich experiments of 1817, and the result was uniformly and decidedly against the short guns. That additions to the length of the piece should occasion increased velocity of projection is obviously the joint effect of two causes. 1st, The expansive force of the inflamed gunpowder acts longer upon the ball in a long than in a short gun, and therefore communicates a greater velocity. 2dly, In short guns no small portion of the gun-powder is carried out of the muzzle without being at all inflamed. The lengths, however, must be limited by practical considerations, as well as by the theoretical ones deducible from our quotation a few pages back from Dr. Hutton. Sir Howard Douglas, who has the happy faculty of confirming his theoretical positions b reference to historical facts, adduces some wi a view to this question, which we make no apology for citing.—“Viewing the matter purely as an artillery question, there is no doubt that preference should be given to long guns. As to its application to naval matters, I do not hesitate to recommend that a frigate which cannot carry eight feet twenty-four pounders, had better be fitted with long eighteen pounders, than with six feet or six feet and a half twenty-four pounders, or with any nature of carronade, exclusively. The very mortifying situation in which the gallant Sir James Yeo found himself in September, 1813, on Lake Ontario, shows the danger of the carronade system of armament. Sir James states, in his letter of the 12th of September, ‘the enemy's fleet of eleven sail, having a partial wind, succeeded in getting within range of their long twenty-four ...i thirty-two pounders; and, having obtained the wind of us, I found it impossible to bring them to close action. We remained in this mortifying situation five hours, having only six guns in the fleet that would reach the enemy. Not a carronade was fired. At sun-set a breeze sprang up from the westward, when I manoeuvred to oblige the enemy to meet us on equal terms. This, however, he carefully avoided.'' ‘Captain Barclay states, in his letter of the 12th of September, 1813:—“The other brig of the enemy, apparently destined to engage the Queen Charlotte, supported in like manner by two schooners, kept so far to windward as to render the Queen Simio, twenty-four pounder corronades useless, whilst she and the Lady Prevost were exposed to a heavy and destructive fire from the Caledonian and four other schooners, armed with long and heavy guns.” Sir Howard next describes the action of the Phoebe with the American frigate Essex, as confirming the theoretical view of the business; and adds:– This brilliant affair, together with the preceding facts, cannot fail to dictate the necessity of abandoning a principle of armament exposed to such perils, and to teach the importance of adapting the tactics of an operation to the comparative natures and powers of arms.'—Naval Gunnery, p. 116. On the whole, we trust we shall not be accused of any unworthy feeling, if we remark that all, or nearly all, which is truly valuable in this department of research has been the produce of

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