The Physics
By Hugh S
i? (Copy right. 1V1J, bj
~*he first law of physics Is that all
goes up must, come down; always
excepting the cost of living. The
first law of baseball Is not to let It
come down.
The difference between the physics
of the classroom and of the diamond is
that the student learns the laws governing
inertia, velocity, dynamics, the
curvilinear trajectory of projectiles,
resisting power of air, attractive power
of masses; and the ball-player, by
experiment, deals only with the freak
variants of theso laws. Many times
the student who makes his college
team Is apt to think that the prof, was
stringing him when he laid down
the laws of motion, mass and velocity.
For a baseball under skilled
manipulation and control seems, like a
trust, to come as near violating all the
laws as possible. The ball always la
striving to do exactly what the laws
of Physics say it should do, with half
a dozen other forces striving to compel
It to do something else, and with
the bad boys In uniform trying to invent
new methods of making it violate
the law.
If the supreme court should flud the
law of gravitation unconstitutional,
or If the ball player could breathe In
an absolute vacuum, baseball would be
a simple proposition. The ball wo Id
keep on going In a straight line until
some one stopped It. Line hits would
continue to travel in a straight line
until some fielder, standing on the
needle point of infinity. Jumped and
pulled It down with one hand.
There Is a professor of physics In
a great eastern university who wrote
me inquiring as to the physics of the
spit ball, and who later lectured to his
classes upon the subject. I asked several
great pitchers to demonstrate for
the benefit of the professor how they
held the ball, swung their arms, released
It with their fingers, and how
much power they applied and to what
point on the surface of the sphere.
Among them was Clark Griffith, a master
In theory, who u aed to be past-master
in practice. I asked him to take
the professor to the grounds and show
him things. The result was a note
from Griffith, In which he said:
"Don't send any more bugs to see
me."
The point Is that the players do not
care what scientific phenomena they
develop so long as the opposing batsmen
take their healthles (i. e., swings)
at the ball and miss. The college professor
does not care much whether
Walsh strikes Collins out three times
with runners on bases so long as he
can demonstrate that the laws govemlnc
rntnflnn olr nroo,ii.?o *?1 -
tlon, retard and accelerated motion,
etc., etc.. are proved by the actions of
the ball. So physics and baseball as
studies have kept aloof from each
other.
Yet every move In a ball game affords
a problem. There are baBic conditions
which. In themselves, are
worthy of study. Consider atmospheric
pressure. Did you know that a man
Clarke Griffith.
who can throw a baseball 350 feet on
the Polo grounds. New York, on a
dead calm day, can throw the same
ball almost 400 feet on the Denver
br.ll park?
In studying the physics of baseball
let us commence with the chief Implements
of the game?the bat and ball.
The ball is composed of a small core,
with a heavy layer of highly treated
Para rubber, then wound with two
kinds of woolen yarn, over which is a
glue substance, upon which Is a horsehide
cover. The ball Is semi-pneumatic.
both the rubber and the glue upon
which the cover Is pasted tending to
hold air. The difference even of a
sixteenth of an Inch In the thickness |
of the rubber makes the ball so fast
L that It scarcely can bo handled. The !
I makers experimented for years to get *
I the ball tuned to the proper pitch of |
1 elasticity, and appear finally to have
I
of Baseball
. duller ton
' W. U. Chapman)
accomplished the aim of making a ball
not too "dead" and not too lively.
The shock of the bat against the ball
dispels the air gradually and at the
same time causes a molecular change
In the rubber so that a ball, after being
batted hard, loses much of Its resilient
power. The disarranging of
the molecular force causes a ball
which, to an outsider may seem as
firm and solid as ever, to become a
"mush," dead and llfelesB, and likely
to slow the entire game If permitted
to remain In play. The bats used are
almost all of second giowth ush of the
finest and stralghtest grain, and
carefully dried. They are supposed to
retain their resilient qualities Indefinitely,
but after a month or two of
hard usage the bat no longer possesses
the "drive" necessary for aard hitting.
Yet bats that have lost "life"
often will, when kept In storage a few
months, recover their lost "ring" and
be as good as ever, although the second
time they "die" more quickly.
This sense of feeling and hearing
among players Is a wonderful thing.
The object of each batter Is to "hit
It on the trade mark" with that part
of his bat between four and six Inches
from the end. He does not express It
that way, but he alms to hit the center
of mass of the ball with tho center
of percussion of the bat?so he
says, "square on the nose." The center
of percussion of the bat varies according
to the grip of the batter'B
hands, and it is the object of the
pitcher to force the ball to revolve so
as to avoid meeting the ceuter of percussion.
A ball weighing five and eight
ounces and with a circumference of
nine inches, pitched at an approximate
velo *lty of 280 feet a second
over a distance of 60 feet, is struck
squarely upon the center of percussion
of a bat weighing 40 ounces and
swinging at a velocity of 1.250 feet
per second, will travel how far? Perhaps
the professor of physics can
figure it out, but if he doec he is
wrong. He would have to know more
than these statistics before he could
make the correct calculation. He
should know the forearm strength of
the batter, the muscle leverage, the
meeting angle of ball and bat, the rotary
motion of the ball, the condition
of the atmosphere, dlrectlou of wind
and a few other things. It is much
easier to have Vean Gregg shoot up
a fast one, let Larry Lajoie hit it, and
measure the distance, than to take a
post-graduate coursa and calculate it.
Every ball that is pitched, or
thrown, or batted has some rotary or
oscillatory movement all its own further
to complicate attempts to solve
nr/ihlotna I n Kr? orvKn 11 ?
|/iuuivuit) tu uuocuail OILS. | Uu
ball h&8 a wonderful ability to absorb
and retain motion no matter how
Imparted. The spit ball, which was
so fully and exhaustively treated In
the lectures of my friend the professor
that 1 expect to see about 120
Walshes graduate from his school In
the next two years. Is the result of
skillful applying of an unnatural force
to counteract the natural rotation of
the ball. The professor disputes this.
Possibly he does not know that a ball,
gripped with the thumb and two
lingers, and thrown directly overhand.
has a natural tendency to rotate
upward and "hop," as the pitchers
say. All good fast balls rotating
this way take a sudden jump In
the air. The spit ball pitcher wets
the surface of the ball, grips the lower
side tightly with his thumb, lets
the ball slide off the lingers. The effect
is that two conflicting forces
cause the ball to "wobble" for a distance.
and then, yielding to the influence
of the thumb pressure and the
attraction of gravity, it darts downward.
When a bull thus pitched is
hit it still refuses to surrender its inclination
to rotate. It sturts toward
the infield with two forces still
struggling for mastery. Each time the
ball touches the earth it takes a different
English. The inflelder scoops
the ball and throws If he clutches
the ball hard enough to kill all motion.
all is well. If he seizes it lieln
ly and throws with the same motion
the ball takes fresh and renewed English
as it leaves his hand and Is more
likely to shoot out of reach of the
batsman toward whom he throws.
The pitched ball, manipulated so aB
to revolve unnaturally, takes "English"
In the air just as a billiard ball
does against cloth and cushion. Many
persons have told me that the atmos'
phere on a still day offers practically
a uniform resistance to a projectile.
It does not. We know now that the
air is filled with eddies, currents and
pockets, even on the calmest of days.
But admitting that it is uniform in
density, a ball does not follow the
physical law of constant decrease in
speed in ratio to the resistance of the
air. It even is capable of accelerated
motion, and of both in the same 00
feet. That is. a ball may be made to
slow up and then resume a faster
rate of speed. The professor of physics
doubts this, yet it is a fact that
any experienced ball player will vouch
for. They have seen a ball seem to
hesitate, and then proceed at an accelerated
gait. It.may sound impossible
but at some spot in the path
of every spit ball, slow ball or knuckle
ball, it suddenly changes pace.
I 0
*
Wo experimented once with n pneumatic
gun the ritllng in the barrel of
which gave It fiuavy rotation In any
desired direction. It was merely an
exaggeration of the curve. We shot
balls under 30 pounds of pressure, making
them curve sometimes a hundred
feet. Putting the up curve motion on
the ball (which always tends to curve
In the direction of Its rotation), we
aimed the gun at a target exactly on
a Straight lino nnH thu ho 11 pnlncr
straight for perhaps a hundred feet,
suddenly Reemed to slacken speed,
then It leaped upward and rose at
a terrific rate until It passed over the
cross bar of the Hag-pole In the center
field. 70 feet above tho ground.
Yet tho ball was not disobeying tho
laws of physics, rather proving them.
In Its terrific speed It had encountered
an air UJUow which It could not
penetrate, and It had bounced off this
denser bunch of air and rolled upward.
One would think that If a baseball
Is hit Into the air Is will follow a ballistic
curve in ratio to the angle of
ascension reduced by the amount of
air pressure. Physics says It should.
It will not, and no man can draw the
ballistic curve that any fly ball will
follow. The greatest range of any
projectile In theory. Is gained by an
angle of 45 degrees. Military authorities
know that, owing to air resistance,
the greatest distance Is attained
at an angle Just under 40 degrees.
Having both the theory and the practice,
therefore, baU players to make
home runs should hit the ball at an
angle of 40 degrees minus. One of
' \ \
I
John Kling.
Frank Baker's world's series home
runs was near that angle, the othei
scarcely 30 degrees. It went farther
As a matter of fact, even. If a ball
player could hit a ball at any desired
angle, he could not be certain where
It would go. It would depend too muct
upon the rotary motion of the ball
l,ast summer I saw- a hard line hil
driven straight at Charlie Herzog ol
the Giants. He put up his hands tc
catch the ball, then suddenly threw
his head aside Just In time to avoid
being hit In the face, the ball missing
his hands by two feet. The ball had
"shot" suddenly from Its true path
In a game between Washington and
Chicago late last fall. Walter Johnson
hit a ball at an angle of close to 4(
degrees, and with terrific force. 1
should estimate that It was nearly 9C
feet high, at Its greatest elevation
Had It followed the true ballistic
curve, It would have passed over the
center held fence. The ball sudden
ly stopped, started to drop straight
downward then caught In anothei
current of air, and Bodie, who was
running after the ball, overtook It com
lng toward him, as if the batter had
hit It from center field. Under condi
tions such as these a study of aero
nautlcs would help players more than
physics would.
The outfielder who "gets the Jump'
or. the ball at the crack of the bat
figures its trajectory at a glance
sprints denperately outward and turns
exactly upon the spot where the ball
will alight, then catches it, has all
the calculations ever devised beaten
Physics assumes that balls, thrown
with equal force, following the same
angle of projection over the sarin
range, will be allk". 1 never doubted
It until I practiced at second base with
Malachl Kittrldgo and the lamented
Jim Donohue throwing the ball down
to me. Donohue threw faster, and
seemed harder, yet the ball came intc
the hands as lightly as If tossed Kltt
ridge's thrown ball came more slowly
but It jarred and bruised the hands
This peculiarity of throwers is un
derstood well by players, and one ol
the first Inquiries concerning a new
player Is whether he throws a light
or a heavy ball, which refers to tin
striking force of the ball, and not its
weight. A ball revolving naturally
aim iiiiuwii over uii- linger lips, as ii
fast ball is thrown, has a tendency u
lift, is light. One that loses its ro
tary motion, and oscillates rather than
rotates, is "dead" and heavy. Every
player throws a different kind of ball
the variations depending upon the siz?
of the hands, the length of the fingers
and the manner of holding the ball
The man who knew enough about
physics, and also about baseball, could
fill a book on the physics of pitching
It is 'simple, while seeming complex
It was not so very long ago that
Tyng, the Harvard pitcher, developed
a curve ball that started a protract
ed argument which finally resulted in
a group of learned professors gath
ering to decide whether a ball actual
!y could be made to curve in the air
The profeseors who doubted the poa
sibtllty of a ball curving bA.sed their
doubts upon the alleged Insufficiency
of air resistance. They admitted the
. - - , t .* ? '
I
theory, and doubted the fact. Every
curve, shoot, "hook." "fadeaway." and
Blow ball depends upon the same principles.
revolution and air pressure. The
way a ball curves depends upon the
force with which It Is thrown and the
amount of rotation. Its direction depends
upon the amount of friction applied
by the lingers to a given point on
the surface of the ball. The ball al- 1
ways curves In the direction of the
heaviest friction applied by the band,
and away from the heaviest air
friction. The curve Increases In the
ratlc of the amount of Its revolution.
Perhaps the most frequent question
nsked of a baseball writer Is. "How
far can a ball be made to curve?"
Of course they meat} by a normal
pitcher not using mechanical assistance.
I never have been able to find
the limit of the curve, nor. Indeed, to |
calculate the curve accurately, although
I have mnde some experiments.
I refer to the actual curvo of
the ball due to its rotary motion and
air resistance. I do not think that
the real curve of the ball In 56 feet
^distance from the pitcher's hand
when he releasee the ball, to the home
plate) can be more than 20 Inches.
I have heard ball players declare the
ball curves from six Inches to tlve
feet. I tried It once with Orval Overall,
who had, I believe, the most
sweeping and widest fast curve ball
I ever Baw.
We placed 12 big sheetB of tissue
paper between slats, 8 of them at
short Intervals over the llrst 15 feet
In front of the plate, the rest scattered
at wider Intervals until the last
one was 0 feet In front of the pitcher's j
slab, and, to my surprise, his hand
struck the paper as the ball was released.
proving the actual distance
?of tho pitch is much shorter than
usually supposed. Of course Overall's
reach wras much greater than
the average, but I do not think the actual
pitching distance, from hand to
plate, is more than 56 feet.
Overall pitched Ills wide overhand
curve. The ball entered tho first
sheet four feet to the right of tho
string, which was placed through tho
center of the two plates at a height of
five feet, and almost six feet above the
ground (he was pitching off a slight
elevation). Ills hand hit the paper
and tore a hole a foot lower, showing
he had released tho ball before his
arm reached the extreme limit of Its
swing Tho ball went through tho second
sheet, which was 10 feet from tho
llrst Just four Inches lower than
through the llrst, and a little over
two and a half feet from the right of
the line. It w us less than a foot from
the line when It struck the first of the
eight sheets placed closely together In
front of the plate, and It tore through
1 the next one a trllle higher. Then It
" began Its true curve. Nine feet In
front of the plate It "broke" and shot
downward and outward and crossed
' the sheet at the home plate ten inches
5 above the ground and nearly twelve
1 Inches to the "outside" (that is, for a
right-handed batter) of the center ol
I the plate. The ball had dropped five
f feet two Inches downward, through the
rorce or gravity, the angle at which It
r was pitched and the curve, and had
' angled and curved practically five feet.
> The closest calculation we could make
' was that the ball actually curved, as
a result of Its rotary motion, approxl'
mately 17 inches.
1 The air resistance, which was dls'
puted at Tyng's experiments, has, of
' course, became a known facter with
' the study of the science of aeronautics.
The amount of resistance can
5 bo computed closely by the use of the
! barometer. The ball curves in the direction
in which it revolves. The
amount of the curve depends upon the
l r? ? -1
Christy Mathewson.
i rate of rotation and the weight of air.
i The entire science of pitching consists
in the deft application of fric- ,
tion upon some point of the hall which
I makes it rotate in a certain direction,
or, which counteracts its natural ro.
i tation and cause it to "wabble" or
float with little revolving motion. The
I slow balls, fadeaways, knuckle balls,
all have as their object the preveni
tion of rotary motion, or to gi 'e false
rotary motion of "feverse English "
The ball that | resents the moBt air
surface to the resistance of the atmosphere
slows up quickest and yields
more rapidly to gravitation. The one I
that spins oftenest (not necessarily
i fastest; curves most.
glMHI
VETERANS TO MEET
ON BATTLEFIELT
Big Reunion of Survivors of Civ
War at Gettysburg on
July 1.
J A ?? -
?kj,uuu LArtUItU TO ATTENI
Men Who Wore the Blue and Gra
to Again Gather on Ground
Made Memorable by Hietorlc
Conflict.
By EDWARD B. CLARK.
WASHINGTON. ? During th
first four days of July th
battlefield of Gettysburg, Pa
will again be the scene of
meeting of the Blue and th
Gray, but this time they will meet 1
amity and affection. A half-century wl
have passed since last these men of tw
great American armies met on thl
northern field. Then they were fac
to face In deadly conflict, for the Jssu<
It was well understood to both cor
tending forces, was the success of th
southern cause, or the beginning of It
defeat, to be followed by the restorr
tlon of tho Union as It had been befor
the first shot was fired at Fort Sutr
ter.
Tho United States government am
the government of nearly every stat
In the Union have combined to mak
the Gettysburg reunion of the soldier
of the north and south one of the grea
peace events of the century. The stat
of Pennsylvania some time ago aj
pointed a "Fiftieth Anniversary of th
Battle of Gettysburg commission" t
make preparations for the four dayt
reunion, at which Pennsylvania as
state was to act as host to the vel
erans of the war between the state
and to the thousands of visitors wh
would follow their march to the flel
of battle, and appropriated $150,000 fo
tho purpose of entertaining the vel
erans.
40.000 Veterans Expected.
It Is expected that 40,000 veteran
of the war, not all of them, howevei
survivors of the Gettysburg battle, wll
be found encamped upon the fieli
when reveille sounds on the mornlni
of July 1. It will be a different. r?
veille than that which the fife am
drum corps of the two great armie
sounded fifty years ago. The call t
awakening will be a call to a peacefu
celebration while the call to the awal
enlng In July, 1863, wan a call o
armies to conflict and, to thousands o
men, a call to death.
For years the veterans have beei
looking forward to this reunion. It i
probable that there will be presen
many thousands of survivors of th
batMe. The United States governmen
under an act of congress has apprc
priated money for the preparation o
the camps and for the messing of th
soldier visitors. The average age o
the men engaged in the Civil war wa
only eighteen years, but fifty year
have passed since these soldier boy
fought at Gettysburg, and so if th
computation of age was a true one th
average years of the veterans who wii
meet in Pennsylvania in July will b
about sixty-eight years. Many of then
of course, will be much older and
good many of them, men who entere
at ages ranging from fourteen to sei
enteen years, will be younger, but a
will be old men as the world view
ago.
Many of the states of the ITnlot
north as well as south, have made a]
propriations to send their veterans t
the Gettysburg reunion and to pay a
other expense?. The battle of Gettyi
burg is recognized as the turnihg poin
of the war between the states. It ha
been called time and again one of th
decisive battles of the world. Gene:
ally it is recognized that Gettysbur
decided the great conflict, helped 1
the decision probably by the fall c
Vicksburg on the Mississippi, whic
took place virtually at the momen
that the conflict on the Pennsylvani
field was decided in favor of the nortl
ern arms.
The preparations which the goverr
rnent i? making to care for the vetei
ana at Gettysburg are interestlnj
They have been under the charge c
James H. Aleshire. quarter master ger
eral of the I'nitod States army, an
Henry G. Sharpe, commissary genera
of the United States army. Two year
ago last March 14,000 regular troop
were gathered in camp at Texas. Th
health of the soldiers throughout th
Texas encampment was almost pei
feet, made so by the plane which ha
been carefully laid to nee that perfec
sanitation was maintained. The Uni
ed States uriny was taught a lesso
by the Spanish war, when lack c
proper sanitary precautions and unpri
paredness in other ways cost the go^
eminent the lives of more men tha
were sacrificed to the bullets of th
Spaniard.
The estimates of the commissar
and quartermaster authorities ar
based upon an attendance of 40,000 ve
erans. It probably will cost the got
ernment about $360,000 to act in pai
as host to the survivors of the battl
and other veterans who attend th
Gettysburg reunion.
Big Task to Feed Men.
The survivors of toe war from th
north and south who will be presen
being old men, must be cared for i
a way which would not have been net
essary fifty years ago. The messing c
the veterans will require 400 arm
ranges, 1 great field bakery, 40,00
mess kits, 800 cooks, 800 kitchen hel]
ers and 130 bakers. This helping pe,
sonnel will be required to be in cam
for at least seven days, and aian) c
Wr'
'<? :r.~; ~
- Vj -4f
them for a longer period, for the purpose
of Installing the field bakery, the
field ranges and in dismantling, cleaning,
packing and storing material after
Ithe encampment la orar.
The old soldiers are to be supplied
with fresh meat directly from refrig>
erator cars drawn upon the field. They
will be given fresh vegetables and spe*
j| cial bread with the besV^offee and tee
which the market affords. For them it
will not be a case of hardtack, bootleg
and poor bacon.
The Battle of Gettysburg commission
of the state of Pennsylvania has
3 a large sum of money at its disposal
for the entertainment of the visiting
veterans, and the thousands of persons
who will accompany them. Hospitality
1b to mark the days. Fifty years
ago Pennsylvania aided in the work of
repelling the visitors from the south.
In early July next the same state will
have its arms wide open in welcome
to the men wearing the gray. Entei^
talnments of various kinds will be of*
fered the visiting veterans, but it is
pretty well understood that their deep
interest in revisiting the scenes where
e they fought, Little Round Top, Oak
n Ridge, Cemetery Hill. Culp'e Hill,
Rock Creek, the Stone Wall and other
^ nlnrna mill hnM
r ..... uuiu .ucui ittigoi} IU Ult)
pleasures and to the Badnesses of per*
sonal reminiscences. Arm In arm with
?* the Union soldiers the Confederate sol|
dlere will retramp the battleground.
8 They will look over the field of Pickett's
desperate charge. They will rel*
trace the marching steps of Longstreet's
corps. They will go to the
1 place where Meade had his headquarj
ters and to the place from which Lee
' directed his southern forces In battle.
' Pennsylvania Is going to make a
'' great celebration of peace of this flf8
tleth anniversary of what probably
was tho decisive battle of the war, although
it was fought nearly two years
before the war ended. Other states
8 will help Pennsylvania In Its work, and
, from every section of the country,
north, east, south and west, the veta
erans will assemble, most of them
probably to see for the last time In
life the field upon which they were
" willing to die for the sake of their re1
spectlve causes.
r The veterans will not be directly encamped
In the Gettysburg park, which
is dotted with monuments to the various
commands which took part In the
* fight and which is laid out In approved
' park fashion, with fine drives and
beautifully kept lawns. There will be
' two camps, known as No. 1 and No. 2.
* No. 1 will cover 149 acres and No. 2
will cover 44 acres. The layouts of
1 these camps are based on the use of
H conical tents, each of which will, without
crowding, accommodate eight per1
sons. Inasmuch as accommodations
lf are to be furnished for 40,000 visitors
5,000 tents will be required to give
quarters to the visiting hoBts.
Visitors to Be Cared For.
H Every possible care Is to be taken
t of the visitors. The sanitary arrangeQ
ments which have been made are said
t to be the best that are possible and
} they are the result of careful study by
f medical officers of the service. All the
experience of the past has been drawn
f upon to make It certain that the Lealth
of the veterans will be conserved while
s they are In camp.
H With so many thousands of old sol0
dlers In attendance, and taking Into
e consideration the probability that the
U weather will be warm. It Is expected
B that there will be sickness, but the
j United States government and the
^ state of Pennsylvania are preparing
(l for a hospital service which shall be
adequate to any contingency. There
II will bo hospital corps detachments
H present ready to render first aid to
the injured, and there will be many
j field hospitals with surgeons in attendance,
where the sick can receive
0 instant attendance. j
11 It is said that this contemplated re3.
union has induced more interest
,t among the old soldiers of the north
^ and the south than any event which
e has happened since the day that the
r. war closed. There is today at GettysK
burg a great national park, in which
n is included a cemetery where thou,f
sands of soldier dead are burled. The
h United States government and the legislature
of Pennsylvania worked tort,
gether to make a park of the battlei
field and to mark accurately every
point in it which hae historic interest,
j. When one goes to the field he can tell
r. JuBt where this brigade or that brlgade
was engaged, Just where this
,f charge or that charge was made and
i. just where the desperate defenses of
d positions were maintained until the
d tide of battle brought either victory or
H defeat to one of the immediate com*
mands engaged.
e It wan in 1895 that congress estabe
lished a national park at Gettysburg
r- and gavo the secretary of war authord
lty to name a commission "to superinit
tend the opening of additional roads,
i- nun k. uiu Dounuaries, ascertain and
n definitely mark the lines of battle of
>f troopB engaged, to acquire lands which
?- were occupied by infantry, cavalry and
artillery, and such other adjacent
n lands as the secretary of war may
e deem necessary to preserve the important
topographical features of the baty
tlefleld."
e When the Union and the Confeder*
t- ate veterans reach Gettysburg on June
r- 30 next they will find on the scene of
t the old conflict between five and six
e hundred memorials raised in commeme
oration of the deeds of their commands
on the great fields of the Pennsylvania
battlefield. There are, moree
over, 1,000 markers placed to destgt,
nate historic spots. There are great
n towers built upon the field by the gov:
ernment so that bird's-eye views can
if be obtained of the entire scene of the
y battle. Fine roade have been con0
structed and everywhere attention has
>- been paid to every detail of the least
r- importance in setting forth the history
p of one of the greatest battles ever
>f known tc warfare.