them form an extremely complicated problem, which can be reasoned out
very simply and prettily as a matter of pure philosophy but practice
offers not a few difficulties. The same body having the velocity 2, 3, 4
... displaces in the same interval 2, 3, 4 ... times the same mass of
air, or the same mass of fluid, and imparts to it _in addition_ 2, 3, 4
... times the same velocity. But for this, plainly, 4, 9, 16 ... times
the original force is required. Hence, the resistance, it is said,
increases with the square of the velocity. This is all very pretty and
simple and obvious. But practice and theory are at daggers' points here.
Practice tells us that when we increase the velocity, the law of the
resistance changes. For every portion of the velocity the law is
different.
The studies of the talented English naval architect, Froude, have thrown
light upon this question. Froude has shown that the resistance is
conditioned by a combination of the most multifarious phenomena. A ship
in motion is subjected to the friction of the water. It causes eddies
and it generates in addition waves which radiate outward from it. Every
one of these phenomena are dependent upon the velocity in some different
manner, and it is consequently not astonishing that the law of the
resistance should be a complicated one.
The preceding observations suggest quite analogous reflexions for
projectiles. Here also we have friction, the formation of eddies, and
the generation of waves. Here, also, therefore, we should not be
surprised at finding the law of the resistance of the air a complicated
one, nor puzzled at learning that in actuality the law of resistance
changes as soon as the speed of the projectile exceeds the velocity of
sound, for this is the precise point at which one important element of
the resistance, namely, the formation of waves, first comes into play.
No one doubts that a pointed bullet pierces the air with less resistance
than a blunt bullet. The photographs themselves show that the head-wave
is weaker for a pointed projectile. It is not impossible, similarly,
that forms of bullets will be invented which generate fewer eddies,
etc., and that we shall study these phenomena also by photography. I am
of opinion from the few experiments which I have made in this direction
that not much more can be done by changing the form of the projectile
when the velocity is very great, but I have not gone into the question
thoroughly. Researches of the kind we are considering can certainly not
be detrimental to practical artillery, and it is no less certain that
experiments by artillerists on a large scale will be of undoubted
benefit to physics.
No one who has had the opportunity of studying modern guns and
projectiles in their marvellous perfection, their power and precision,
can help confessing that a high technical and scientific achievement has
found its incarnation in these objects. We may surrender ourselves so
completely to this impression as to forget for a moment the terrible
purposes they serve.
Permit me, therefore, before we separate, to say a few words on this
glaring contrast. The greatest man of war and of silence which the
present age has produced once asserted that perpetual peace is a dream,
and not a beautiful dream at that. We may accord to this profound
student of mankind a judgment in these matters and can also appreciate
the soldier's horror of stagnation from all too lengthy peace. But it
requires a strong belief in the insuperableness of mediæval barbarism to
hope for and to expect no great improvement in international relations.
Think of our forefathers and of the times when club law ruled supreme,
when within the same country and the same state brutal assaults and
equally brutal self-defence were universal and self-evident. This state
of affairs grew so oppressive that finally a thousand and one
circumstances compelled people to put an end to it, and the cannon had
most to say in accomplishing the work. Yet the rule of club law was not
abolished so quickly after all. It had simply passed to other clubs. We
must not abandon ourselves to dreams of the Rousseau type. Questions of
law will in a sense forever remain questions of might. Even in the
United States where every one is as a matter of principle entitled to
the same privileges, the ballot according to Stallo's pertinent remark
is but a milder substitute for the club. Nor need I tell you that many
of our own fellow-citizens are still enamored of the old original
methods. Very, very gradually, however, as civilisation progresses, the
intercourse of men takes on gentler forms, and no one who really knows
the good old times will ever honestly wish them back again, however
beautifully they may be painted and rhymed about.
In the intercourse of the nations, however, the old club law still
reigns supreme. But since its rule is taxing the intellectual, the
moral, and the material resources of the nations to the utmost and
constitutes scarcely less a burden in peace than in war, scarcely less a
yoke for the victor than for the vanquished, it must necessarily grow
more and more unendurable. Reason, fortunately, is no longer the
exclusive possession of those who modestly call themselves the upper ten
thousand. Here, as everywhere, the evil itself will awaken the
intellectual and ethical forces which are destined to mitigate it. Let
the hate of races and of nationalities run riot as it may, the
intercourse of nations will still increase and grow more intimate. By
the side of the problems which separate nations, the great and common
ideals which claim the exclusive powers of the men of the future appear
one after another in greater distinctness and in greater might.
FOOTNOTES:
[Footnote 110: A lecture delivered on Nov. 10, 1897.]
[Footnote 111: Christiansen, _Wiedemann's Annalen_, XXIII. S. 298,
XXIV., p. 439 (1884-1885).]
[Footnote 112: The German phrase is _Schlierenmethode_, by which
term the method is known even by American physicists. It is also
called in English the "shadow-method." But a term is necessary which
will cover all the derivatives, and so we have employed
alternatively the words _striate_ and _differential_. The etymology
of _schlieren_, it would seem, is uncertain. Its present use is
derived from its technological signification in glass-manufacturing,
where by _die Schlieren_ are meant the wavy streaks and
imperfections in glass. Hence its application to the method for
detecting small optical _differences_ and faults generally.
Professor Crew of Evanston suggests to the translator that
_schlieren_ may be related to our _slur_ (L. G., _slüren_, to trail,
to draggle), a conjecture which is doubtless correct and agrees both
with the meaning of _schlieren_ as given in the large German
dictionaries and with the intransitive use of our own verb _slur_,
the faults in question being conceived as "trailings," "streakings,"
etc.--_Trans._]
ON INSTRUCTION IN THE CLASSICS AND THE SCIENCES.[113]
Perhaps the most fantastic proposition that Maupertuis,[114] the
renowned president of the Berlin Academy, ever put forward for the
approval of his contemporaries was that of founding a city in which, to
instruct and discipline young students, only Latin should be spoken.
Maupertuis's Latin city remained an idle wish. But for centuries Latin
and Greek _institutions_ exist in which our children spend a goodly
portion of their days, and whose atmosphere constantly surrounds them,
even when without their walls.
For centuries instruction in the ancient languages has been zealously
cultivated. For centuries its necessity has been alternately championed
and contested. More strongly than ever are authoritative voices now
raised against the preponderance of instruction in the classics and in
favor of an education more suited to the needs of the time, especially
for a more generous treatment of mathematics and the natural sciences.
In accepting your invitation to speak here on the relative educational
value of the classical and the mathematico-physical sciences in colleges
and high schools, I find my justification in the duty and the necessity
laid upon every teacher of forming from his own experiences an opinion
upon this important question, as partly also in the special circumstance
that in my youth I was personally under the influence of school-life for
only a short time, just previous to my entering the university, and had,
therefore, ample opportunity to observe the effects of widely different
methods upon my own person.
Passing now, to a review of the arguments which the advocates of
instruction in the classics advance, and of what the adherents of
instruction in the physical sciences in their turn adduce, we find
ourselves in rather a perplexing position with respect to the arguments
of the first named. For these have been different at different times,
and they are even now of a very multifarious character, as must be where
men advance, in favor of an institution that exists and which they are
determined to retain at any cost, everything they can possibly think of.
We shall find here much that has evidently been brought forward only to
impress the minds of the ignorant; much, too, that was advanced in good
faith and which is not wholly without foundation. We shall get a fair
idea of the reasoning employed by considering, first, the arguments that
have grown out of the historical circumstances connected with the
original introduction of the classics, and, lastly, those which were
subsequently adduced as accidental afterthoughts.
* * * * *
Instruction in Latin, as Paulsen[115] has minutely shown, was introduced
by the Roman Church along with Christianity. With the Latin language
were also transmitted the scant and meagre remnants of ancient science.
Whoever wished to acquire this ancient education, then the only one
worthy of the name, for him the Latin language was the only and
indispensable means; such a person had to learn Latin to rank among
educated people.
The wide-spread influence of the Roman Church wrought many and various
results. Among those for which all are glad, we may safely count the
establishment of a sort of _uniformity_ among the nations and of a
regular international intercourse by means of the Latin language, which
did much to unite the nations in the common work of civilisation,
carried on from the fifteenth to the eighteenth century. The Latin
language was thus long the language of scholars, and instruction in
Latin the road to a liberal education--a shibboleth still employed,
though long inappropriate.
For scholars as a class, it is to be regretted, perhaps, that Latin has
ceased to be the medium of international communication. But the
attributing of the loss of this function by the Latin language to its
incapacity to accommodate itself to the numerous new ideas and
conceptions which have arisen in the course of the development of
science is, in my opinion, wholly erroneous. It would be difficult to
find a modern scientist who had enriched science with as many new ideas
as Newton has, yet Newton knew how to express those ideas very correctly
and precisely in the Latin language. If this view were correct, it would
also hold true of every living language. Originally every language has
to adapt itself to new ideas.
It is far more likely that Latin was displaced as the literary vehicle
of science by the influence of the nobility. By their desire to enjoy
the fruits of literature and science, through a less irksome medium
than Latin, the nobility performed for the people at large an
undeniable service. For the days were now past when acquaintance with
the language and literature of science was restricted to a caste, and in
this step, perhaps, was made the most important advance of modern times.
To-day, when international intercourse is firmly established in spite of
the many languages employed, no one would think of reintroducing
Latin.[116]
The facility with which the ancient languages lend themselves to the
expression of new ideas is evidenced by the fact that the great majority
of our scientific ideas, as survivals of this period of Latin
intercourse, bear Latin and Greek designations, while in great measure
scientific ideas are even now invested with names from these sources.
But to deduce from the existence and use of such terms the necessity of
still learning Latin and Greek on the part of all who employ them is
carrying the conclusion too far. All terms, appropriate and
inappropriate,--and there are a large number of inappropriate and
monstrous combinations in science,--rest on convention. The essential
thing is, that people should associate with the sign the precise idea
that is designated by it. It matters little whether a person can
correctly derive the words _telegraph_, _tangent_, _ellipse_, _evolute_,
etc., if the correct idea is present in his mind when he uses them. On
the other hand, no matter how well he may know their etymology, his
knowledge will be of little use to him if the correct idea is absent.
Ask the average and fairly educated classical scholar to translate a few
lines for you from Newton's _Principia_, or from Huygens's _Horologium_,
and you will discover at once what an extremely subordinate rôle the
mere knowledge of language plays in such things. Without its associated
thought a word remains a mere sound. The fashion of employing Greek and
Latin designations--for it can be termed nothing else--has a natural
root in history; it is impossible for the practice to disappear
suddenly, but it has fallen of late considerably into disuse. The terms
_gas_, _ohm_, _Ampère_, _volt_, etc., are in international use, but they
are not Latin nor Greek. Only the person who rates the unessential and
accidental husk higher than its contents, can speak of the necessity of
learning Latin or Greek for such reasons, to say nothing of spending
eight or ten years on the task. Will not a dictionary supply in a few
seconds all the information we wish on such subjects?[117]
It is indisputable that our modern civilisation took up the threads of
the ancient civilisation, that at many points it begins where the latter
left off, and that centuries ago the remains of the ancient culture were
the only culture existing in Europe. Then, of course, a classical
education really was the liberal education, the higher education, the
ideal education, for it was the _sole_ education. But when the same
claim is now raised in behalf of a classical education, it must be
uncompromisingly contested as bereft of all foundation. For our
civilisation has gradually attained its independence; it has lifted
itself far above the ancient civilisation, and has entered generally new
directions of progress. Its note, its characteristic feature, is the
enlightenment that has come from the great mathematical and physical
researches of the last centuries, and which has permeated not only the
practical arts and industries but is also gradually finding its way into
all fields of thought, including philosophy and history, sociology and
linguistics. Those traces of ancient views that are still discoverable
in philosophy, law, art, and science, operate more as hindrances than
helps, and will not long stand before the development of independent and
more natural views.
It ill becomes classical scholars, therefore, to regard themselves, at
this day, as the educated class _par excellence_, to condemn as
uneducated all persons who do not understand Latin and Greek, to
complain that with such people profitable conversations are not to be
carried on, etc. The most delectable stories have got into circulation,
illustrative of the defective education of scientists and engineers. A
renowned inquirer, for example, is said to have once announced his
intention of holding a free course of university lectures, with the word
"frustra"; an engineer who spent his leisure hours in collecting insects
is said to have declared that he was studying "etymology." It is true,
incidents of this character make us shudder or smile, according to our
mood or temperament. But we must admit, the next moment, that in giving
way to such feelings we have merely succumbed to a childish prejudice. A
lack of tact but certainly no lack of education is displayed in the use
of such half-understood expressions. Every candid person will confess
that there are many branches of knowledge about which he had better be
silent. We shall not be so uncharitable as to turn the tables and
discuss the impression that classical scholars might make on a scientist
or engineer, in speaking of science. Possibly many ludicrous stories
might be told of them, and of far more serious import, which should
fully compensate for the blunders of the other party.
The mutual severity of judgment which we have here come upon, may also
forcibly bring home to us how really scarce a true liberal culture is.
We may detect in this mutual attitude, too, something of that narrow,
mediæval arrogance of caste, where a man began, according to the special
point of view of the speaker, with the scholar, the soldier, or the
nobleman. Little sense or appreciation is to be found in it for the
_common_ task of humanity, little feeling for the need of mutual
assistance in the great work of civilisation, little breadth of mind,
little truly liberal culture.
A knowledge of Latin, and partly, also, a knowledge of Greek, is still a
necessity for the members of a few professions by nature more or less
directly concerned with the civilisations of antiquity, as for lawyers,
theologians, philologists, historians, and generally for a small number
of persons, among whom from time to time I count myself, who are
compelled to seek for information in the Latin literature of the
centuries just past.[118] But that all young persons in search of a
higher education should pursue for this reason Latin and Greek to such
excess; that persons intending to become physicians and scientists
should come to the universities defectively educated, or even
miseducated; and that they should be compelled to come only from schools
that do _not_ supply them with the proper preparatory knowledge is going
a little bit too far.
* * * * *
After the conditions which had given to the study of Latin and Greek
their high import had ceased to exist, the traditional curriculum,
naturally, was retained. Then, the different effects of this method of
education, good and bad, which no one had thought of at its
introduction, were realised and noted. As natural, too, was it that
those who had strong interests in the preservation of these studies,
from knowing no others or from living by them, or for still other
reasons, should emphasise the _good_ results of such instruction. They
pointed to the good effects as if they had been consciously aimed at by
the method and could be attained only through its agency.
One real benefit that students might derive from a rightly conducted
course in the classics would be the opening up of the rich literary
treasures of antiquity, and intimacy with the conceptions and views of
the world held by two advanced nations. A person who has read and
understood the Greek and Roman authors has felt and experienced more
than one who is restricted to the impressions of the present. He sees
how men placed in different circumstances judge quite differently of the
same things from what we do to-day. His own judgments will be rendered
thus more independent. Again, the Greek and Latin authors are
indisputably a rich fountain of recreation, of enlightenment, and of
intellectual pleasure after the day's toil, and the individual, not less
than civilised humanity generally, will remain grateful to them for all
time. Who does not recall with pleasure the wanderings of Ulysses, who
does not listen joyfully to the simple narratives of Herodotus, who
would ever repent of having made the acquaintance of Plato's Dialogues,
or of having tasted Lucian's divine humor? Who would give up the glances
he has obtained into the private life of antiquity from Cicero's
letters, from Plautus or Terence? To whom are not the portraits of
Suetonius undying reminiscences? Who, in fact, would throw away _any_
knowledge he had once gained?
Yet people who draw from these sources only, who know only this culture,
have surely no right to dogmatise about the value of some other culture.
As objects of research for individuals, this literature is extremely
valuable, but it is a different question whether it is equally valuable
as the almost exclusive means of education of our youth.
Do not other nations and other literatures exist from which we ought to
learn? Is not nature herself our first school-mistress? Are our highest
models always to be the Greeks, with their narrow provinciality of mind,
that divided the world into "Greeks and barbarians," with their
superstitions, with their eternal questioning of oracles? Aristotle with
his incapacity to learn from facts, with his word-science; Plato with
his heavy, interminable dialogues, with his barren, at times childish,
dialectics--are they unsurpassable?[119] The Romans with their apathy,
their pompous externality, set off by fulsome and bombastic phrases,
with their narrow-minded, philistine philosophy, with their frenzied
sensuality, with their cruel and bestial indulgence in animal and man
baiting, with their outrageous maltreatment and plundering of their
subjects--are they patterns worthy of imitation? Or shall, perhaps, our
science edify itself with the works of Pliny who cites midwives as
authorities and himself stands on their point of view?
Besides, if an acquaintance with the ancient world really were attained,
we might come to some settlement with the advocates of classical
education. But it is words and forms, and forms and words only, that are
supplied to our youth; and even collateral subjects are forced into the
strait-jacket of the same rigid method and made a science of words,
sheer feats of mechanical memory. Really, we feel ourselves set back a
thousand years into the dull cloister-cells of the Middle Ages.
This must be changed. It is possible to get acquainted with the views of
the Greeks and Romans by a shorter road than the intellect deadening
process of eight or ten years of declining, conjugating, analysing, and
extemporisation. There are to-day plenty of educated persons who have
acquired through good translations vivider, clearer, and more just views
of classical antiquity than the graduates of our gymnasiums and
colleges.[120]
For us moderns, the Greeks and the Romans are simply two objects of
archæological and historical research like all others. If we put them
before our youth in fresh and living pictures, and not merely in words
and syllables, the effect will be assured. We derive a totally different
enjoyment from the Greeks when we approach them after a study of the
results of modern research in the history of civilisation. We read many
a chapter of Herodotus differently when we attack his works equipped
with a knowledge of natural science, and with information about the
stone age and the lake-dwellers. What our classical institutions
_pretend_ to give can and actually will be given to our youth with much
more fruitful results by competent _historical_ instruction, which must
supply, not names and numbers alone, nor the mere history of dynasties
and wars, but be in every sense of the word a true history of
civilisation.
The view still widely prevails that although all "higher, ideal
culture," all extension of our view of the world, is acquired by
philological and in a lesser degree by historical studies, still the
mathematics and natural sciences should not be neglected on account of
their usefulness. This is an opinion to which I must refuse my assent.
It were strange if man could learn more, could draw more intellectual
nourishment, from the shards of a few old broken jugs, from inscribed
stones, or yellow parchments, than from all the rest of nature. True,
man is man's first concern, but he is not his sole concern.