438 
FOREST AND STREAM 
April 5, 1913 
A heav}’ arrow is, as a rule, also a stiff one, on 
account of its greater diameter. It would buckle, 
wobble and flirt less than a light one. Does 
this alone counterbalance the high initial ve¬ 
locity? Hardly. Would the advice of a man 
practically unknown to the archery world be 
sufficient if he were to advocate the use of 
arrows of a weight above that customarily used, 
or would it be up to him to give good and 
sufficient reasons for the faith that is in him? 
It was certainly up to me to prove the case, and 
for that reason 1 employed the equation that 
applies to all kinds of motion where a sudden 
force, or impact, acts on a body and produces 
a resulting motion. 
The equation given happens to be the second 
of Newton’s three fundamental laws of nature, 
and have been used by the scientific world dur¬ 
ing the last few centuries. No exceptions to it 
have ever been known. It is, therefore, reason¬ 
ably certain that the equation is correct. The 
■conclusions derived could not be deduced ex¬ 
cept through reference to and analysis of the 
ft. 
oquation v =: -—• 
in. 
That is why it was used. The mere state¬ 
ment of fact, without a clue to the process of 
reasoning employed would have been quite use¬ 
less. We must be shown in order to be con¬ 
vinced against our will, especially when w'e 
buck up against tradition and the custom of 
ages. 
Now that I have explained a few of the 
little matters where Dr. Hertig believed he dis¬ 
agreed with me, let us return to the question 
of our negroes. That, too, was simple. The 
older one was the mother of the younger. 
Dr. Hertig says; “When it comes to reduc¬ 
ing the beautiful total which comprises good 
archery to figures, I question the soundness of 
the analysis entering into the proposition.” 
In answ'er to this statement I am only ready 
to admit that it has not been customary, and 
that it is somewhat difficult or undesirable. The 
general principles of archery are in no way radi¬ 
cally different from those that enter in rifle 
■shooting, though more complicated and difficult 
to deduce. It would be impossible to analyze 
-what the archer frequently does, but it is a dif¬ 
ferent proposition to determine what he should 
•do. A man can become a good archer without 
understanding the fundamental principles that 
•enter in the various phases of his sport. He 
will merely be a well-trained automaton who 
would imitate spontaneously the motions to 
which he had become accustomed. For the high¬ 
est development of the game and the greatest 
■efficiency of which man is capable, a good knowl- 
•edge of the underlying principles is necessary, 
so that he can tell at once, or reason out, the 
■cause of his failure in the various phases of his 
shortcomings. Other things being equal, the man 
who understands the theory of his game is the 
one who wins in the long run. 
Mathematics can alwa3's be used to great 
advantage in anything that follows the regular 
law's of nature, or is in any sense of the word 
•methodical. It is not a hindrance except to the 
uninitiated, but gives the greatest imaginable aid 
to those in the habit of close and straight think¬ 
ing; in fact, mathematics, in its highest sense, 
is merely a shorthand method of reasoning, with 
the rules of the game so arranged that the fly¬ 
ing off a tangent, or the use of the unconstrained 
and rabid imagination, is avoided. 
It is not harsh and crabbed, as some would 
believe, but soft and musical as is Apollo’s lute. 
Though the hypothesis arrived at may sometimes 
be partially incorrect, nevertheless true progress 
only begins when facts are sought in at least 
the suggestion of a principle; for science con¬ 
sists not in a mere accumulation of facts, but 
in a generalization of knowledge, so as to ex¬ 
emplify known principles. The poet and the 
mathematical-physicist are thus nearly akin, as 
both employ the faculty of the imagination in 
its highest sense—that which the psychologists 
call the constructive imagination, as opposed to 
mere fancy. The philosopher's faculty is quite 
as pow'erful and important an agent in the de¬ 
velopment of archery as the mere gift of acquir¬ 
ing new knowledge by observation and experi¬ 
ment. Practically every discovery of physics 
and engineering was preceded by a mathematical 
analysis of the underlying theory. This is a 
matter of history and not mere supposition. No 
true progress will ever be made in archery, or 
in any physical science for that matter, unless 
mathematical and graphic analysis theoretically 
applied, though based on the known laws of 
nature, work hand in hand wdth practice, or else 
precede it. Without these our statements of 
archery technique are mcreh' an expression of 
personal belief, too frequently based on miscon¬ 
ceptions and prejudice. They lead nowhere, ex¬ 
cept to chaos. What we need in order to ad¬ 
vance our sport is a careful study of the prin¬ 
ciples of the various phases of the game. 
I have attempted something of that nature. 
My inexperience as an archer may have led me 
astray in some minor details, but I maintain that 
the general method of procedure is correct, 
rather than our more fashionable, though popu¬ 
lar, method of hit. miss and come again. But 
for goodness sake avoid modern scientific 
methods, even if in every other case they have 
proved the only correct method of procedure. 
There is a member of the Chicago Archery 
Club w'ho has the habit of striking his arm guard 
with annoying frequency. His club mates can¬ 
not understand why, and claim that he should be 
one of the world's leading archers, as “his left 
arm is held firm as a rock, and cannot be seen 
to move one particle w'hen the arrow is shot.” 
He has shot for years with the same fault, and 
the “human factor,” which causes his defect and 
which Dr. Hertig says “is subject to a non- 
mathematical process and not one of figures and 
signs,” has never been discovered either by him¬ 
self or others. Let us examine this as a specific 
case to illustrate that the method of “figures, 
signs and equations” may after all be of some 
little value. 
The study of the two (correct) force dia¬ 
grams, in my article on “The Toxophilites Para¬ 
dox” (Forest and Stream, Feb. 8, 1913), showed 
that there were five different and distinct ele¬ 
ments, or effects, that enter in order to shoot 
an arrow without lateral divergence to the left. 
These followed strictly from the study of the 
diagrams and were not based on mere personal 
belief. What did the analysis show? First, that 
the explanation of Ford, Butt, Walrond and 
others, which had been accepted as satisfactory 
by all of us up to the present day, were not 
sufficient to account for the phenomenon. For¬ 
tunately, I was able to refer to Dr. Elmer’s 
machine as a laboratory proof of this insuffi¬ 
ciency. Second, the existence of a force (A, 
Fig. II.) at the nock of the arrow which moved 
the string to the left and tended to rotate the 
plane of the bow in the same direction. Third, 
the more than probable existence of a compen¬ 
satory motion of the archer’s arm to the left, 
which motion is somewhat delayed at the in¬ 
stant of release, but comes into play and in¬ 
creases after the center of gravity of the arrow 
passes the point of contact with the bow. Fourth, 
the explanation why all the arrows of a set 
should have a uniform configuration of their 
center of gravity and also be of equal stiff¬ 
ness in the shaft. 
Now, if the left arm is held “steady as a 
rock,” as we have always been told that it must, 
the third of the above effects, which is one of 
the two compensating factors where the “human 
equation” enters, will be eliminated. The arrow 
through its tendency, caused by inertia, of mov¬ 
ing forward without angular divergence will 
thus throw the burden of rectification on the 
second of the above mentioned effects, i. e., cause 
the plane of the bow and string to rotate to the 
left with a greatly increased and totally un¬ 
necessary force, thus striking the string against 
the arm guard and keeping a man who should 
be an e.xpert archer from attaining the proficiency 
and success that his latent abilities merit. 
The argument in favor of the heavy arrow, 
the explanation of Dr. Elmer's machine, the 
solution of the arrow not diverging to the left, 
the need of a uniform rigidity, the probability 
that the left arm should not be held “firm as a 
rock.” the prediction of the apparent cause of 
the Chicago archer (whom I have not even met) 
striking his arm guard, and a few other minor 
conclusions follow directly as a consequence of 
feet 
an equation v = -, and from two force 
inches 
diagrams. These conclusions have not been con¬ 
troverted. If such results follow as a logical 
analysis of equations and diagrams, it would al¬ 
most seem that the “reducing of the beautiful 
total which comprises good archery to figures” 
is not such a bad method after all. The proof 
of the pudding is in its eating. 
The trouble with archery is that it is suf¬ 
fering either from too much apathy, neglect and 
fetish worship of things that are accepted mere¬ 
ly because the halo of ages surrounds them with 
too much reverence: or else too much hot air, 
with little serious thinking, and not sufficient 
consideration of the methods of modern thought. 
We idealize our sport, but do not put it on a 
scientific basis. The development of the essen¬ 
tial ideas, the underlying principles, and the con¬ 
sequent application is a job for a full-sized man. 
They are difficult to present, hard to under¬ 
stand, but infinitely more perplexing to develop. 
When they are assimilated by the chosen few, 
and transmitted in expurgated form to the re¬ 
maining devotees of the sport, our game will 
have a chance; it is handicapped enough by 
existing conditions. 
A great work can be done along these lines, 
but it is a thankless job. 
Let us give the men who make an honest 
effort our sympathy and consideration. 
Finis coronat opus. 
