implements of war become, the more certain will be the extension and the
permanence of civilization. The great cost of such appliances as those
we are about to describe, the ingenuity needed for their contrivance,
the elaborate machinery required for their production, and the skill
implied in their use, are such that these weapons can never be the arms
of other than wealthy and intelligent nations. We know that in ancient
times opulent and civilized communities could hardly defend themselves
against poor and barbarous races. But the world cannot again witness
such a spectacle as Rome presented when the savage hordes of Alaric
swarmed through her gates, and the mighty civilization of centuries fell
under the assaults of the northern barbarians. In our day it is the poor
and barbarous tribes who are everywhere at the mercy of the wealthy and
cultivated nations. The present age has been so remarkably fertile in
warlike inventions, that it may truthfully be said that the progress
made in fire-arms and war-ships within the second half of the nineteenth
century surpasses everything that had been previously accomplished from
the time gunpowder came into use. Englishmen have good reason to be
proud of the position taken by their country, and may feel assured that
her armaments will enable her to hold her own among the most advanced
nations of the world.
The subject of fire-arms embraces a very wide ground, as will appear if
we consider the many different forms in which these weapons are
constructed in order best to serve particular purposes. Pertaining to
this subject, attention must also be directed to the modern projectiles
and to the newer explosives that have largely taken the place of
ordinary gunpowder. The shot gun, fowling-piece, and sporting rifle
properly come under the head of fire-arms, and in the march of
improvement these forms have most commonly been in advance of military
muskets and rifles, the ingenuity bestowed on all their details being
worthy of admiration. Nevertheless it is to the implements of war that
general interest attaches; for on them depends so much the fate of
battles and the destiny of nations, that whenever any country is engaged
in war the question of arms becomes one of surpassing importance,
enlisting the patriotic instincts of every citizen. Hence in the
following pages our space will be devoted mainly to weapons of war, and
more particularly to those that have been adopted by our own country.
Everyone of course is aware that guns, cannon, and gunpowder are by no
means inventions of the nineteenth century; but there are fewer
acquainted with the fact that rifling, breech-loading, machine guns, and
revolvers were all invented and tried hundreds of years before. The
devices by which some of these ideas were sought to be realised in past
ages appear to us in some instances very primitive, not to say childish,
when compared with modern work: but it must be remembered that nearly
all the appliances required for producing such weapons had themselves to
wait for their invention until the nineteenth century; such, for
instance, as the steam-hammer, powerful and accurate tools, refined
measuring implements, material entirely reliable such as the new steel,
and also scientific investigations of all the conditions involved. The
military fire-arms are of so many different forms and patterns that we
can deal here with but a selection from the various services. If a rough
classification had to be made, the most obvious distinction would be
between the weapons the soldier carries in his hands (small-arms) and
those which are mounted on some kind of carriage and discharge
projectiles of much greater weight (ordnance). Ordnance again includes
guns mounted on forts, carried in ships, or taken with an army into the
field, in each case coming into action under different conditions.
Partaking somewhat of the nature of both field-guns and of small-arms
are the machine guns, of which the French mitrailleur was the first
example, afterwards developing into much more effective weapons in the
hands of Gatling, Gardner, Nordenfelt, Maxim, and Hotchkiss.
As much will have to be said about _rifling_ the bores of muskets and
cannon, we may here explain the nature and object of this device. The
projectiles used in all guns down to comparatively recent times were
almost invariably of spherical form, and could indeed scarcely be
otherwise with smooth-bore weapons. As the diameter of the shot would
necessarily be something less than that of the bore of the barrel, a
considerable loss of power would result from the escape of the powder
gases between the shot and the barrel, which escape is known as
_windage_. Another disadvantage of the spherical projectile is that for
the same weight of metal the air offers a greater resistance to its
passage, and consequently checks its speed more quickly than that of any
other circular form; for the air resistance is proportional to the
square of the diameter, and therefore if we take a ball of 1 in.
diameter and a cylinder of 1 in. in length, each having the same weight
of metal, the diameter of the cylindrical shot will be a little more
than four-fifths of an inch, and the air resistance to the ball will be
exactly half as much again as to the cylinder, that is, in the
proportion of 3 to 2. Again, the passage of the spherical shot within
the barrel of the gun will not be in a straight line, but in a series of
rebounds from side to side, and its direction on leaving the muzzle will
depend upon which part of the bore it just before impinges on, as from
that it will also take a rotatory “twist” that will in part determine
its path through the air.
Now if an elongated projectile were fired from a smooth-bore gun, its
course through the air would be erratic to a degree impossible to the
spherical shot, for it would turn end over end with deviations that
would make aiming impracticable. But if the elongated projectile is made
to spin rapidly enough about its longitudinal axis, it flies through the
air quite steadily, the axis of rotation remaining parallel to that of
the gun throughout the whole flight. The steadiness due to rapid
rotation has familiar examples in spinning tops, in gyroscopic tops, in
the way arrows are feathered so that the air may cause them to revolve
axially, and so on. The axial rotation of the projectile is effected by
ploughing out in the cylindrical barrel of the gun a number of spiral or
twisting grooves, which the projectile is compelled to follow as it
travels along the barrel, either by means of corresponding protuberances
formed upon its surface in the first instance, as in Jacob’s bullets, or
by studs let into it, as in the studded shots and shells for ordnance
which constituted at one time the regulation plan adopted by the British
Government; or otherwise by making the force of the explosion expand
some portion of the projectile in such a manner that this portion shall
completely fill up the grooves, thus preventing windage, and causing the
projectile to follow the twist of the grooves. This is the more general
method, especially since the adoption of breech-loading. The Lancaster
rifling, and that advocated by Whitworth, are the same in principle, but
differ in appearance, from the section of the barrel being made in the
one case oval, in the other hexagonal or polygonal, but with the twist
necessary to produce rotation.
Incident to the discharge of all fire-arms, great and small, is a
phenomenon of which we have to speak, because it is one which in the
mounting of heavy ordnance especially has to be taken into account. And
as it also illustrates in a very direct way one of the most general laws
of nature, while people often have very vague and erroneous ideas of its
cause and operation, it deserves the reader’s attention. In gunnery it
is called the _recoil_, and is familiar to anyone who has ever fired a
pistol, fowling-piece, or rifle, in the kick backwards felt at the
moment of the discharge. This law is in operation whenever the condition
of a body in respect to its rest or motion is changing. That is,
whenever a body at rest has motion given to, or if when already moving
it is made to go faster or slower, or to stop, or when the direction of
the motion is changed from that in a straight line. Now although these
changes or actions are frequently occurring before our eyes, the
operation in them of Newton’s third law of motion does not generally
present itself to common observation. This third law was stated by Sir
Isaac Newton thus:—“To every action there is always an opposite and
equal reaction.” Now the expanding gases due to the gunpowder explosion
press the bullet forwards and the barrel (with its attachments)
backwards, with the same pressure in both cases, but at the end of the
bullet’s passage along the bore the same velocity is not imparted to the
two bodies, because the same pressure acting for the same time on bodies
of unequal _mass_ always produces velocities that are inversely
proportional to the _masses_. The reader should try to acquire this
conception of _mass_, remarking that it is a something quite distinct
from that of _weight_. A given lump of metal, for instance, would have
exactly the same _mass_ in any part of the universe, whereas its weight
would depend upon its position; as, for instance, at the distance from
the earth of the moon’s orbit, it would _weigh_ only as 1/3600th part of
its weight at the earth’s surface, and if it could be carried to the
very centre of the earth it would there have no weight at all. Though
the lump of metal will have different weights at different parts of the
earth’s surface, it has been found (by experiment) that the weights of
bodies at any one place are proportional to their masses. Therefore the
same numbers that express the weights of bodies might also express their
masses; but for certain good reasons these quantities are referred to
different units. In England a piece of metal weighing 32 lbs. under
standard conditions is said to have mass = 1; and so on. As with the
_same pressure acting for the same time_, the velocities imparted are
inversely proportional to the masses, it follows that the number
expressing the velocity multiplied by that representing the mass in each
such case of action and reaction will give the same product, or in other
words the _amount of motion_ (momentum) will be the same. This is what
Newton meant by saying the reaction is _equal_ to the action. We may now
by way of illustration calculate the velocity of recoil of a rifle under
conditions similar to those that might occur in practice. Let us suppose
that the rifle, including the stock and all attachments, weighs 10 lbs.,
and that from it is fired a bullet weighing one-sixteenth of a pound,
with a velocity at the muzzle of 1,200 ft. per second. To obtain the
amount of motion or the momentum, we should here multiply the number
expressing the _mass_ of the bullet by 1,200, but for our present
purpose the weight numbers may be used for the sake of simplicity;
therefore 1/16 x 1,200 = 75 will represent (proportionately) the forward
momentum of the bullet, and according to Newton’s law the backward
momentum of the rifle will be, on the same scale, 75 also. We must
therefore find the number which multiplied by 10 will give 75, and this
obviously is 7·5. That is as much as to say that at the instant the
bullet is leaving the muzzle, the rifle itself, _if free to move_, would
be moving backward at the speed of 7½ ft. per second. Observe that this
result would be the same if the rifle were fired where weight is
non-existent; nor is the recoil due, as sometimes is erroneously
supposed, to the resistance of the air to the passage of the bullet
along the barrel, for even if the air were abolished, the recoil, so far
as due to the masses and velocities, would remain the same, as indeed
may be seen from the fact of our calculation taking no account of the
bore of the rifle or of the shape of the bullet, circumstances of the
utmost importance where atmospheric resistance is concerned.
The foregoing calculation however involves an assumption not in exact
conformity with actual conditions, by taking for granted that the
_centre of gravity_ of the rifle is in the line of the axis of the
barrel, while in fact this centre is almost always lower, and therefore
the kick of the recoil acts in part as a turning-over push, tending to
tilt up the muzzle of the gun, and for that reason the firer must hold
the weapon very firmly or he will miss his aim. When such a rifle as we
have supposed is fired, say from the shoulder, it would follow from the
above calculation that the backward kick of the recoil is equivalent to
a blow from a 10–lb. weight moving at the speed of 7½ ft. per second.
This would certainly be a very uncomfortable experience, but the
backward momentum must be met somehow. We have supposed that the gun is
free to move, but we know the firer presses it firmly against the
muscles of his shoulder, and the stock of the gun is spread out and
provided with a smooth hollow heel plate, so that any pressure from it
is felt as little as possible, especially as the muscle against which it
is applied acts as an elastic pad. With the rifle thus firmly held we
may regard the marksman and his rifle as forming only _one mass_, and
the centre of gravity of this being now much below the axis of the
barrel, the effect of the recoil tends to overthrow the man backwards;
but he learns to resist this by standing firmly, so that the elasticity
of his whole frame comes into play; and besides this, the mass factor of
the momentum being now so large, the velocity factor becomes
comparatively insignificant.
Although the momenta of gun and projectile are, according to Newton’s
law, _equal_ and opposite, the case is very different with regard to
their _energies_, or powers of doing work, for the measure of these is
jointly mass and _the square of the velocity_. The _energy_ (_vis viva_)
of a body of weight in pounds = W, moving with the velocity of v feet
per second is always Wv^2/64·4, that is, it will do this number of
foot-lbs. units of work before it comes to rest. It would require too
much space to demonstrate and fully explain here what this means, but
the reader may refer to our index under the entries “Energy” and “Work,”
or to any modern elementary treatise on dynamics. If the calculation be
made of the energies of the ball and of the rifle due to our calculated
velocities of recoil, it will be found that that of the ball is 160
times greater than that of the other, and the ball possesses this energy
in a much smaller compass.
[Illustration:
FIG. 80.—_Trajectory of a Projectile._
]
The course or track of a projectile through the air after it leaves the
gun is called the _trajectory_, and this has been studied both
experimentally and theoretically, with interesting results. Assuming
that the shot passed through empty space, or that the air offered no
resistance to its passage, it would be very easy to trace the path of a
projectile. Let us suppose that Fig. 80 represents a gun elevated at a
high angle. The moment the projectile leaves the muzzle, gravity begins
to act upon it, causing it to move vertically downwards with
ever-increasing velocity until it finally reaches the ground; the onward
uniform movement parallel to the axis of the piece being continued all
the time. We could find the position of the projectile at the end of
successive equal periods of time by drawing a straight line AC, a
prolongation of the axis of the piece, or a line of the same
inclination; on this we mark off equal distances representing by scale
the velocity of the projectile per second, the points B, C, D, E being
the positions the projectile would be in at the end of each successive
second if gravity did not act. In order to bring the diagram within
moderate compass, we suppose the projectile to have only the small
velocity of 115 ft. per second. At the end of the first second it would
be at B, but now suppose that gravity is allowed to act for one second,
it would at the end of that time have fallen 16 ft. vertically below B
and have arrived at _b_. Similarly we may set off by scale on verticals
through C, D, and E distances representing 64 ft., 144 ft., and 256 ft.
respectively. Because, for instance, the ball, without gravity acting,
would at the end of 3 seconds be at D, where we may suppose its course
arrested and gravity then allowed to act for 3 seconds to pull the ball
down from its position of rest at D; at the end of this period, gravity
alone acting, its position would be 144 ft. vertically below D, because
gravity pulls a body that distance in 3 seconds, and the actual position
3 seconds after the ball had left the muzzle would be at _d_, after it
had described the curved path A, _b_, _c_, _d_. Supposing _d_ to be the
highest point of the trajectory, another 3 seconds would bring the ball
along a downward curve, and at the end of 6 seconds from the discharge
it would be at a point on the same level as A. Now the complete curve
would be symmetrical on each side of a vertical line through its highest
point, and it would be in fact a regular _parabola_ with its vertex at
_d_.
The foregoing presupposes that the air offers no resistance to the
passage of the projectile through it. The fact however is quite
otherwise, for no sooner does the projectile begin its flight than its
velocity is constantly diminished by the air’s resistance. Now this
resistance is complex, depending upon a number of different conditions,
the effect of which can be taken into account only by extremely complex
calculations. Obviously it will vary according to the area of the
section presented by the projectile to the line of its flight, and again
by the shape of its front, for a pointed shot will cleave the air with
less resistance than one with a flat front. Then the density of the air
at the time will also enter into the calculation. The mass of the
projectile and also its velocity, upon which depend its _vis viva_,
energy, or power of overcoming resistance in doing work, will also have
to be considered. Most complex of all is the law, or rather laws (_i.e._
relations), which connect the air resistance with the velocity; for this
relation no definite expression has been found. It is a function of the
velocity (known only by experiment under defined conditions), and
varying with the velocity itself. Thus for velocities up to 790 ft. per
second, it is a function (determined experimentally) of the second power
or square of the velocity; between 790 ft. per second and 990 ft. per
second the law of resistance is changed and becomes a function of the
third power of the velocity; between 990 ft. and 1,120 ft. velocity the
law again changes and is related to the sixth power of the velocity;
between 1,120 ft. and 1,330 ft. the resistance is again related to the
third power of the velocity; and with higher speeds than that last named
it is again more nearly related to the square of the velocity. It will
be seen that to calculate the path of a projectile is really a very
difficult mathematical problem, and indeed one which can be solved only
approximately when all the known data are supplied.
The air resistance to the motion of a projectile is much greater than
before trial would be supposed. Let us take an experiment that has
actually been recorded, in which a bullet three-quarters of an inch in
diameter, weighing one-twelfth of a pound, was found to have a velocity
of 1,670 ft. per second at a distance of 25 ft. from the gun, and this
50 ft. farther was reduced to 1,550 ft. per second. Now if the reader
will calculate, according to the formula we have given above, the
_energy_ due to the bullet’s velocity at these points, he will find it
must have done 500 foot-lbs. units of work in traversing the 50 ft., and
as this could have been expended only in overcoming the resistance of
the air, we learn that this last must have been equivalent to a mean or
average pressure of 10 lbs. thrusting the bullet backwards.
It will be interesting to compare the difference in the trajectory of a
projectile under defined conditions, worked out with the air resistance
taken into account, compared with the trajectory when the air is
supposed to be non-existent. We find an example of the former problem
fully worked out by many elaborate mathematical formulæ in Messrs. Lloyd
and Hadcock’s treatise on Artillery. The problem is thus stated:—“An
11–in. breech-loading howitzer” (a howitzer is a piece of ordnance used
for firing at high angles) “fires a 600–lb. projectile with an initial
velocity of 1,120 foot-sec. at an elevation of 20°. Find the range, time
of flight, and angle of descent.” We shall calculate these points on the
suppositions adopted with regard to Fig. 80, and with no higher
mathematics than common multiplication and division.
It will have been observed that we supposed two motions that really take
place simultaneously to take place successively and independently: one
in the direction of the line of fire, due to the initial velocity; the
other vertically downwards, due to the action of gravity, the final
result being the same. This affords an excellent illustration of another
of Newton’s laws of motion, and should be considered by the reader in
this connection. The law itself admits of being stated in various ways,
as thus:—“Whenever a force acts on a body, it produces upon it exactly
the same change of motion in its own direction, whether the body be
originally at rest or in motion in any direction with any velocity
whatever—whether it be at the same time acted on by other forces or
not.” Or again: “When two forces act in any direction whatever on a body
free to move, they impress upon it a motion which is the _superposition_
(or compounding) of those that it would receive if each force acted
separately.” The law is given also in the following form (Thomson and
Tait):—“When any forces act on a body, then, whether the body be
originally at rest or moving with any velocity and in any direction,
each force produces in the body the exact change of motion which it
would have had had it acted singly on the body originally at rest.” In
all of these expressions the word “forces” is used, and a very
convenient word it is, but it may be noted in passing, nothing but a
word; for it stands for no real self-existing things, since, apart from
observed changes of motion in bodies, forces for us have no existence.
Nevertheless, it is useful for the sake of abbreviating statements about
changes of motion, to regard these actions as produced by imaginary
agents—imagined for the time and for this purpose, and therefore vainly
to be sought for in the realm of reality.
[Illustration:
FIG. 81.—_Diagram._
]
In dealing with the trajectory of the howitzer’s projectile through
airless space we have no concern with its diameter nor with its weight.
We use the little diagram, Fig. 81, to represent the motions,—_c_ being
a horizontal line, _a_, a vertical one, the angle at B is therefore a
right angle, and we assume that at A to be 20°. Now, the most elementary
geometry teaches us that every triangle having these angles will have
the lengths of its sides in the same invariable proportions one to
another whatever may be the size of the triangle itself, and it has been
found convenient to calculate these proportions once for all, not merely
for angle 20°, but for every angle up to 90°. Besides this, distinct
names have been given to the proportions of every side of the triangle
to each of the other two sides. Thus in the triangle before us, if we
take _a_, _b_, and _c_ to represent the numbers expressing the lengths
of the sides against which they are placed, _a_ divided by _b_, that is
_a_ ÷ _b_, or _a_/_b_, is called the _sine_ of angle 20°, while _c_/_b_
is named the _cosine_ of that angle, etc. These therefore are _numbers_
which are given in mathematical tables, and we find by these that _sine_
20° = 0·3420201, and _cosine_ 20° = 0·9396926, and these with the
initial velocity give us all the data we require. We may first find the
_time_ the projectile would take to reach the ground level, or strictly
that of the muzzle of the gun at B. Taking _t_ to stand for this time,
we know that AC = 1,120 × _t_, but CB will be the distance that a body
would fall from rest at C by the influence of gravity in that same time,
_t_, and it is known by experiment that this distance is 16·1 feet
multiplied by the _square_ of the time from rest in seconds. We have now
therefore the length of the line CB, and put _a_/_b_ = CB/AC = (16·1 ×
_t_^2)/(1,120 × _t_) = _sine_ 20° = ·3420201, and dividing numerator and
denominator by _t_ and multiplying the above 3rd and 5th expressions by
1,120, we have
16·1 × _t_ = 1,120 × ·3420201
1,120 × ·3420201
and therefore _t_ = ———————————————— = 23·7927 secs.
16·1