summit, where it is nothing, it increases in the descending branch from
the summit to its termination, and if the ground did not interpose an
obstacle, it would become vertical at an infinite distance. An element
of the trajectory in the descending branch has a greater inclination
than the corresponding element of the ascending branch. Strictly
speaking, therefore, the trajectory of a projectile in air is not a
parabola, but is an exponential curve with two asymptotes, the first the
axis of the piece, which is tangent to the trajectory when the initial
velocity is infinite, the second a vertical line toward which the
trajectory approaches, as the horizontal component of the velocity
diminishes and the effect of the force of gravity increases. The
curvature of the trajectory increases in the ascending branch to a point
a little beyond the summit. The point of greatest curvature is situated
nearer the summit than the point of minimum velocity. In the fire of
mortar-shells, under great angles of projection, the trajectory may be
considered as an arc, in which the angle of fall is slightly greater
than the angle of projection. In the formulæ deduced by Didion, in
consequence of considering the inclination of the trajectory as
constant, the resistance of the air is slightly underestimated in the
more inclined portions of the trajectory or at the beginning and end,
and slightly overestimated in the less inclined portions or about the
summit. It follows that the calculated trajectory will at first rise
above the true one, then pass below it and again pass above it; the
calculated ranges are therefore slightly in excess of the true ones.
_Trajectory of Oblong Projectiles._--From the law of inertia, a rifle
projectile moves through the air with its axis of rotation parallel to
the axis of the bore. Hence it follows that an oblong projectile, fired
under a low angle of projection, presents a greater surface toward the
earth, and less parallel to it, than a round projectile of the same
weight, consequently the vertical component of the resistance of the air
is greater, and the horizontal component less, in the first case than in
the second. The effect of this will be to give an oblong projectile a
flatter trajectory and longer range than a round one.
_Deviation of Projectiles._--The path described by the centre of inertia
of a projectile, moving under the influences of gravity and the
tangential resistance of the air, is called the _normal trajectory_. In
practice, various causes are constantly at work to deflect a projectile
from its normal path. All deviating causes may be divided into two
classes,--those which act while the projectile is in the bore of the
piece, and those which act after the projectile has left it. The first
class includes all the causes which affect the initial velocity, and
give rotation to the projectile; the second includes the action of the
air.
_Causes which affect Initial Velocity._--The principal causes which
affect initial velocity are variations in the weights of the powder and
projectile, the manner of loading, the temperature of the piece, and the
balloting of the projectile along the bore. _Rotation._ The principal
cause of the deviation of a projectile is its rotation combined with the
resistance of the air. _By balloting._ If the projectile be spherical
and homogeneous, rotation is produced by the bounding or balloting of
the ball in the bore, arising from the windage. In this case the axis of
rotation is horizontal, and passes through the centre of the ball; the
direction of rotation depends on the side of the projectile which
strikes the surface of the bore last. The velocity of rotation from this
cause depends on the windage, or depth of the indentations in the bore,
the charge being the same. _By eccentricity._ If, from the structure of
the ball, or from some defect of manufacture, the centre of gravity does
not coincide with the centre of figure, rotation generally takes place
around the centre of gravity. This arises from the fact that the
resultant of the charge acts at the centre of figure, while inertia, or
resistance to motion, acts at the centre of gravity. For the same charge
the velocity of rotation passes through the centre of gravity, and is
perpendicular to a plane containing the resultant of the charge and the
centres of figure and gravity. For the same charge, the velocity of
rotation is proportional to the lever arm, or the perpendicular, let
fall from the centre of gravity to the resultant of the charge. Knowing
the position of the centre of gravity of the ball in the bore, it is
easy to foretell the direction and velocity of rotation. In general
terms the front surface of the projectile moves toward the side of the
bore on which the centre of gravity is situated, and the velocity of
rotation is greatest when the line joining the centres of gravity and
figure is perpendicular to the axis of the bore.
_The Effect of Rotation._--The effect of rotation in producing deviation
may be discussed under three heads: 1st. When the projectile is
spherical and concentric; 2d. When it is spherical and eccentric; and,
3d. When it is oblong. If a projectile be spherical and concentric,
rotation takes place from contact with the surface of the bore around a
horizontal axis, and the effect will be to shorten or lengthen the
range, as the motion of the front surface is downward or upward. If the
projectile be eccentric, the motion of the front surface is generally
toward the side on which the centre of gravity is situated, and the
deviation takes place in this direction. The extent of the deviation for
the same charge depends on the position of the centre of gravity; the
horizontal deviation being the greatest when the centres of gravity and
figure are in a horizontal plane, and the line which joins them is at
right angles to the axis of the piece; the vertical deviation will be
the greatest when these centres are in a vertical plane, and the line
which joins them is at right angles to the axis of the piece. If the
axis of rotation coincide with the tangent to the trajectory throughout
the flight, all points of the surface have the same velocity in the
direction of the motion of translation, and there will be no deviation.
This explains why it is that a rifle projectile moves through the air
more accurately than a projectile from a smooth-bored gun. In accurate
firing, therefore, it is important to know the true position of the
centre of gravity. In ricochet firing over smooth water, the number of
grazes may be increased or diminished by placing, in loading, the centre
of gravity above or below the centre of figure.
_Deviation of Oblong Projectiles._--The cause of the deviation of an
oblong rifle projectile is quite different from one of spherical form.
An oblong projectile moving in the air is acted upon by two rotary
forces, viz.: one which gives it its normal rotary motion around its
axis of progression, and another the resistance of the air, which, in
consequence of the deflection of the axis of progression from the
tangent to the trajectory by the action of gravity, does not pass
through the centre of inertia, but above or below it; depending on the
shape of the projectile. From a law of mechanics, a body thus
circumstanced will not yield fully to either of the forces that thus act
upon it, but its apex will move off with a slow uniform motion to the
right or left of the vertical plane, depending on the relative direction
of the two rotary forces. If the action of these forces be continued
sufficiently long, it will be seen that the axis of the projectile
before referred to describes a cone around a line passing through the
centre of inertia and parallel to the direction of the resistance of the
air. Owing to the short duration of the flight of an ordinary
projectile, it is only necessary to consider the first part of this
conical motion. If the projectile rotates in the direction of the hands
of a watch to the eye of the marksman, and the resultant of the
resistance of the air pass above the centre of inertia, as it does in
the service bullet with a conoidal point, then the point of the
projectile will move to the right, which brings the left side of the
projectile obliquely in contact with the current of the air. The effect
of this position with reference to the air will be to generate a
component force that will urge the projectile to the right of the plane
of fire. This peculiar deviation was called by the French officers that
first observed it, “_derivation_,” or “_drift_.”
_Summary of Deviating Causes._--The following summary may be considered
as embracing nearly all the causes of deviation of cannon and small-arm
projectiles: 1st. _From the construction of the piece._ These causes
are, wrong position of the sight; bore not of the true size; windage,
etc. 2d. _From the charge of powder._ Improper weight; form of grain and
variable quality of the powder, etc. 3d. _From the projectile._ Not of
the exact size, shape, or weight; disfiguration in loading, or on
leaving the bore; eccentricity. 4th. _From the atmosphere_, _etc._ The
effect of wind; variations in the temperature, moisture, and density of
the air; position of the sun as regards the effect on the aim;
difference of level between the object and the piece; and rotation of
the earth. It is found that a projectile will deviate to the right of
the object in the northern hemisphere whatever may be the direction of
the line of fire, and at a distance from it, depending on the latitude
of the place, and on the time of flight and the range of the projectile.
=Projectiles, Effects of.= The effects of projectiles, and particularly
that of penetration, depend on the nature of the projectile, its initial
velocity, and the distance of the object. The effects of the various
kinds of projectiles upon iron and steel plates are not yet thoroughly
understood, and experiments are still being made, particularly in
England, to determine the best combinations of wrought and cast iron,
and steel, to resist the penetration of the enormous projectiles of the
present day. Their effects upon wood, earth, etc., are, however, better
understood.
_Effect on Wood._--The effect of a projectile fired against wood varies
with the nature of the wood and the direction of the penetration. If the
projectile strikes perpendicular to the fibres, and the fibres be tough
and elastic, as in the case of oak, a portion of them are crushed, and
others are bent under the pressure of the projectile, but regain their
form as soon as it has passed by them. In consequence of the softness of
white pine, nearly all the fibres struck are broken, and the orifice is
nearly the size of the projectile; for the same reason the effects of
the projectile do not extend much beyond the orifice; pine is therefore
to be preferred to oak for structures that are not intended to resist
cannon projectiles, as block-houses, etc.
_Effect on Earth._--Earth possesses advantages over all other materials
as a covering against projectiles; it is cheap and easily obtained, it
offers considerable resistance to penetration, and to a certain extent
regains its position after displacement. It is found by experience that
a projectile has very little effect on an earthen parapet unless it
passes completely through it. Wherever masonry is liable to be breached,
it should be masked by earthworks with natural slopes. Gen. Gillmore
states that the powers of resistance of pure, compact, quartz sand to
the penetration of projectiles very much exceed that of ordinary earth,
or mixture of several earths. The size of the openings formed by the
passage of a projectile into the earth is about one-third larger than
the projectile, increasing, however, towards the outer orifice. Rifle
projectiles especially are easily deflected from their course in earth,
hence their penetration is variable. Unless a shell be very large in
proportion to the mass of earth penetrated, its explosion will produce
but little displacement,--generally, a small opening is formed around an
exploded shell by the action of the gas in pressing back the earth.
Time-fuzes, being liable to be extinguished by the pressure of the
earth, are inferior to percussion-fuzes, which produce explosion when
the projectile has made about three-fourths of its proper penetration.
The penetration in earth of oblong, compared to round projectiles, when
fired with service charges, and at a distance of about 400 yards, is at
least _one-fourth greater_. This difference, however, is less at short
and greater at long distances. The penetrations of similar projectiles
into a given substance, are proportional to the squares of the
velocities of impact and to the diameters and densities of the
projectiles.
_Penetration in Water._--The penetration of a rifle projectile in water
depends much on the direction of its axis with respect to penetration;
for instance, penetration rapidly diminishes at long distances, as the
axis of the projectile strikes the surface of the water under a
diminished angle.
_Effect on Masonry._--The effect of a projectile against masonry is to
form a truncated conical hole, terminated by another of a cylindrical
form. The material in front of and around the projectile is broken and
shattered, and the end of the cylindrical hole even reduced to powder.
The exterior opening varies from four to five times the diameter of the
projectile, and the depth varies with the size and density of the
projectile, and its velocity. When a projectile strikes against a
surface of oak, as the side of a ship, it will not stick if the angle of
incidence be less than 15°, and if it do not penetrate to a depth nearly
equal to its diameter. Solid cast-iron shot break against granite, but
not against freestone or brick. Shells are broken into small fragments
against each of these materials.
_Breaching._--Formerly stone projectiles were much used for breaching,
but from the want of sufficient hardness in these projectiles, the
besiegers were forced to commence battering at the top of the wall where
the least resistance was offered, and gradually to lower the shot until
the breach reached the wrecks already formed at the base of the wall.
Iron projectiles superseded stone, and then more rapid modes of
effecting a practicable breach were suggested. The easiest manner of
making the cut is to direct the shots upon the same line, and form a
series of holes a little greater than a diameter apart, and then to fire
a second series of shots, directed at the intervals between the first,
and so on, until an opening is made completely through the wall. If the
portion of the wall between the vertical cuts should not be overthrown
by the pressure of the earth behind, it must be detached by a few
volleys of solid shot, fired at its centre.
_Breaching with Rifle-cannon._--The foregoing has reference particularly
to breaching masonry with smooth-bored guns. The same principle is
applicable to rifled guns, the only difference being that, from their
superior penetration and accuracy, the latter are effective at much
longer distances. The most destructive projectile against masonry is the
elongated percussion shell.
_Effect of Bullets._--From experiments made in Denmark, the following
relations were found between the penetration of a bullet in pine and its
effects on the body of a living horse, viz.: 1st. When the force of the
bullet is sufficient to penetrate 0.31 inch into pine, it is only
sufficient to produce a slight contusion of the skin. 2d. When the force
of penetration is equal to 0.63 inch, the wound begins to be dangerous,
but does not disable. 3d. When the force of penetration is equal to 1.2
inch, the wound is very dangerous. A plate of wrought iron
three-sixteenths of an inch thick, is sufficient to resist a
rifle-musket bullet at distances varying from 20 to 200 yards. Iron of
thickness, however, will not resist bullets of the present day. That a
rope mantlet may give full protection against rifle-musket bullets, it
should be composed of five layers (three vertical and two horizontal) of
4¹⁄₂-inch rope.
=Projection.= In mathematics, the action of giving a projectile its
motion. It is also used to signify a scheme, plan, or delineation.
=Proking-spit.= A large Spanish rapier.
=Prolongation.= An extension of leave of absence, or a continuation of
service.
=Prolongation of the Line.= Is effected by parallel movements at the
right or left of any given number of men on a front division.
=Prolonge.= See IMPLEMENTS.
=Prolonge-hooks.= See ORDNANCE, CARRIAGES FOR, NOMENCLATURE OF ARTILLERY
CARRIAGE.
=Promotion.= This word signifies, in military matters, the elevation of
an individual to some appointment of greater rank and trust to the one
he holds.
=Promulgation.= The act of promulgating; publication; open declaration;
as, the promulgation of the sentence of a court-martial.
=Proof.= A term applied to the testing of powder, and also of ordnance,
which are always fired with a regulated charge of powder and shot, to
test their strength and soundness.
=Proof.= Conclusive evidence.
=Proof.= Capable of withstanding; as, bomb-proof, shot-proof.
=Propel.= To drive forward; to urge or press onward by force; to move or
cause to move; balls are _propelled_ by the force of gunpowder.
=Proper.= A term which serves to mark out a thing more especially and
formally. Thus, the _proper form of a battalion_ is the usual continuity
of line given to the formation of a battalion, and which remains
unaltered by the wheelings of its divisions; or if altered, is restored
by the same operation. _Proper right_, is the right of a battalion,
company, or subdivision, when it is drawn up according to its natural
formation. _Proper pivot flank_, in column, is that which, when wheeled
up to, preserves the division of the line in the natural order, and to
their proper front. The other may be called the _reverse_ flank.
=Proper.= In heraldry, a charge borne of its natural color, is said to
be _proper_. An object whose color varies at different times and in
different examples, as a rose which may be white or red cannot be borne
proper.
=Prosecute.= To carry on; to continue; as, to prosecute the war. Also,
to accuse of some crime or breach of law, or to pursue for punishment
before a legal tribunal; to proceed against judicially.
=Prosecutor.= In courts-martial the judge-advocate is usually the
prosecutor; but if an officer prefers a charge, he sometimes appears to
sustain the prosecution. No person can appear as prosecutor not subject
to the articles of war, except the judge-advocate.--_Hough._
=Proveditor.= One employed to procure supplies for an army; a purveyor.
=Proving-ground.= Ground used for testing powder or ordnance.
=Provision.= Properly to victual; to furnish with provisions.
=Provost.= The temporary prison in which the military police confine
prisoners till they are disposed of.
=Provost Cells.= Also called regimental or garrison cells, in the
British service are those certified cells under a provost or acting
provost-sergeant, in which court-martial prisoners may be imprisoned up
to forty-two days.
=Provost-Marshal.= In the army, is an officer appointed to superintend
the preservation of order, and to be, as it were, the head of the police
of any particular camp, town, or district. He has cognizance of all
camp-followers, as well as members of the army. His power is summary,
and he can punish an offender, taken _flagrante delicto_, on the spot,
according to the articles of war.
=Provost-Sergeant.= Is a sergeant who is charged with the military
police of a corps. He is generally given one or two non-commissioned
officers as assistants. In the British service he also is charged with
the custody of all prisoners in the cells.
=Prowess.= Valor; bravery in the field; military gallantry.
=Prowlers.= Are persons who steal within the lines of a hostile army for
the purpose of robbing, killing; or destroying bridges, roads, mails, or
other means of communication. Such persons are not entitled to the
privileges usually accorded to prisoners of war.
=Prussia.= A kingdom of the new German empire. The people of Prussia
first appear in history in the 10th century, under the name of Borussi;
from these the country derives its name. Some historians, however,
derive the name from _Po_, signifying near, and _Russia_. The Prussians
were subjected by Boleslaus of Poland in 1018; they made a successful
stand against Boleslaus IV. of Poland in 1161, and for a time maintained
a rude and savage kind of independence. The Teutonic Knights were
engaged in war for half a century with the people,--winning lands and
souls by hard fighting,--until at length, in 1283, they found themselves
undisputed masters of the country, having almost exterminated the pagan
population. During this period the knights founded many cities and
repeopled the country with German colonists. In 1454 the municipal and
noble classes, with the co-operation of Poland, rose in open rebellion
against the knights, who were forced to cede West Prussia and Ermland to
Poland. Albert (or Albrecht) of Brandenburg was acknowledged duke of
East Prussia in 1525; his son-in-law, John Sigismund, created elector of
Brandenburg and duke of Prussia in 1608. The reign of John Sigismund’s
successor, Georg-Wilhelm (1619-1640), was distracted by the miseries of
the Thirty Years’ War, and the country was alternately the prey of
Swedish and imperial armies. The electorate was raised by the genius of
Frederick William, the great elector, to the rank of a great European
power. His successor, Frederick III. (1688-1713), was proclaimed king of
Prussia by the title of Frederick I. in 1701. During the reign of
Frederick William IV., Prussia co-operated powerfully in putting down
the insurrections in Poland and Baden. In the war of the
Schleswig-Holstein duchies, the Prussians acted in concert with the
disaffected against their sovereign, the king of Denmark, occupying the
ducal provinces in the name and on behalf of the diet. A treaty of peace
was concluded between Prussia and Denmark, on July 2, 1850. In 1863 the
allied Prussian and Austrian armies entered the duchies of
Schleswig-Holstein and defeated the Danes; the duchies were separated
from Denmark. Warm disputes with Austria respecting Schleswig-Holstein
arose in the beginning of 1866. The vote of the majority of the diet of
the Germanic Confederation supported Austria; Prussia announced her
withdrawal from the confederation, and its dissolution; the diet
declared itself indissoluble, and continued its functions, June 14,
1866. War was declared by Prussia, June 18, 1866, which ended in the
total defeat of Austria and her allies. A treaty of peace between
Austria and Prussia was signed at Prague on August 23, 1866. By its
articles Austria consented to the breaking up of the Germanic
Confederation, and to Prussia’s annexing Hanover, Hesse-Cassel, Nassau,
and Frankfort-on-the-Main, and gave up Holstein and her political
influence in North Germany. For further history, see FRANCO-PRUSSIAN
WAR.
=Pruth.= A river of Europe, which rises in the Carpathian Mountains. It
forms a portion of the boundary-line between Russia and Turkey, and by
crossing it, in 1853, the Russians gave rise to the war with Turkey and
the subsequent Crimean war.
=Psiloi.= Among the Greeks, were light-armed men who fought with arrows
and darts, or stones and slings, but were unfit for close fight. They
were in honor and dignity inferior to the heavy-armed soldiers.
=Publish.= To make known. In a garrison orders are published by being
read at parade. Orders are also published by circulating written copies.
=Puebla=, or =La Puebla de los Angeles=. Capital of the department of
Puebla, in Mexico, 80 miles southeast from the city of Mexico. It was
taken by the French on May 17, 1863, after a siege of several weeks’
duration, the Mexican general Ortega, with 18,000 men, surrendering to
Gen. Forey. This event threw open the road to Mexico, and was the
immediate precursor of the overthrow of the government of Juarez.