Part 21

Picture to yourself an apparatus for detecting optical striæ set up in a dark room. In order not to make the description too complicated, I shall give the essential features only of the apparatus, leaving out of account altogether the minuter details which are rather of consequence for the technical performance of the experiment than for its understanding. We suppose the projectile speeding on its path, accordingly, through the field of our differential optical apparatus. On reaching the centre of the field (Fig. 51) the projectile disengages an illuminating electric spark _a_, and the image of the projectile, so produced, is photographically impressed upon the plate of the camera behind the intercepting slide _b_. In the last and best experiments the lens _L_ was replaced by a spherical silvered-glass mirror made by K. Fritsch (formerly Prokesch) of Vienna, whereby the apparatus was naturally more complicated than it appears in our diagram. The projectile having been carefully aimed passes in crossing the differential field between two vertical isolated wires which are connected with the two coatings of a Leyden jar, and completely filling the space between the wires discharges the jar. In the axis of the differential apparatus the circuit has a second gap _a_ which furnishes the illuminating spark, the image of which falls on the intercepting slide _b_. The wires in the differential field having occasioned manifold disturbances were subsequently done away with. In the new arrangement the projectile passes through a ring (see dotted line, Fig. 51), to the air in which it imparts a sharp impulse which travels forward in the tube _r_ as a sound-wave having the approximate velocity of 340 metres per second, topples over through the aperture of an electric screen the flame of a candle situated at the other opening of the tube, and so discharges the jar. The length of the tube _r_ is so adjusted that the discharge occurs the moment the projectile enters the centre of the now fully clear and free field of vision. We will also leave out of account the fact that to secure fully the success of the experiment, a large jar is first discharged by the flame, and that by the agency of this first discharge the discharge of a second small jar having a spark of very short period which furnishes the spark really illuminating the projectile is effected. Sparks from large jars have an appreciable duration, and owing to the great velocity of the projectiles furnish blurred photographs only. By carefully husbanding the light of the differential apparatus, and owing to the fact that much more light reaches the photographic plate in this way than would otherwise reach it, we can obtain beautiful, strong, and sharp photographs with incredibly small sparks. The contours of the pictures appear as very delicate and very sharp, closely adjacent double lines. From their distance from one another, and from the velocity of the projectile, the duration of the illumination, or of the spark, is found to be 1/800000 of a second. It is evident, therefore, that experiments with mechanical snap slides can furnish no results worthy of the name.

Let us consider now first the picture of a projectile in the rough, as represented in Figure 52, and then let us examine it in its photographic form as seen in Figure 53. The latter picture is of a shot from an Austrian Mannlicher rifle. If I were not to tell you what the picture represented you would very likely imagine it to be a bird's eye view of a boat _b_ moving swiftly through the water. In front you see the bow-wave and behind the body a phenomenon _k_ which closely resembles the eddies formed in the wake of a ship. And as a matter of fact the dark hyperboloid arc which streams from the tip of the projectile really is a compressed wave of air exactly analogous to the bow-wave produced by a ship moving through the water, with the exception that the wave of air is not a surface-wave. The air-wave is produced in atmospheric space and encompasses the projectile in the form of a shell on all sides. The wave is visible for the same reason that the heated shell of air surrounding the candle flame of our former experiments is visible. And the cylinder of friction-heated air which the projectile throws off in the form of vortex rings really does answer to the water in the wake of a vessel.

Now just as a slowly moving boat produces no bow-wave, but the bow-wave is seen only when the boat moves with a speed which is greater than the velocity of propagation of surface-waves in water, so, in like manner, no wave of compression is visible in front of a projectile so long as the speed of the projectile is less than the velocity of sound. But if the speed of the projectile reaches and exceeds the velocity of sound, then the head-wave, as we shall call it, augments noticeably in power, and is more and more extended, that is, the angle made by the contours of the wave with the direction of flight is more and more diminished, just as when the speed of a boat is increased a similar phenomenon is noticed in connexion with the bow-wave. In fact, we can from an instantaneous photograph so taken approximately estimate the speed with which the projectile is travelling.

The explanation of the bow-wave of a ship and that of the head-wave of a body travelling in atmospheric space both repose upon the same principle, long ago employed by Huygens. Conceive a number of pebbles to be cast into a pond of water at regular intervals in such wise that all the spots struck are situate in the same straight line, and that every spot subsequently struck lies a short space farther to the right. The spots first struck will furnish then the wave-circles which are widest, and all of them together will, at the points where they are thickest, form a sort of cornucopia closely resembling the bow-wave. (Fig. 54.) The resemblance is greater the smaller the pebbles are, and the more quickly they succeed each other. If a rod be dipped into the water and quickly carried along its surface, the falling of the pebbles will then take place, so to speak, uninterruptedly, and we shall have a real bow-wave. If we put the compressed air-wave in the place of the surface-waves of the water, we shall have the head-wave of the projectile.

You may be disposed to say now, it is all very pretty and interesting to observe a projectile in its flight, but of what practical use is it?

It is true, I reply, one cannot _wage war_ with photographed projectiles. And I have likewise often had to say to medical students attending my lectures on physics, when they inquired for the practical value of some physical observation, "You cannot, gentlemen, cure diseases with it." I had also once to give my opinion regarding how much physics should be taught at a school for millers, supposing the instruction there to be confined _exactly_ to what was necessary for a miller. I was obliged to reply: "A miller always _needs_ exactly as much physics as he _knows_." Knowledge which one does not possess one cannot use.

Let us forego entirely the consideration that as a general thing every scientific advance, every new problem elucidated, every extension or enrichment of our knowledge of facts, affords a better foundation for practical pursuits. Let us rather put the special question, Is it not possible to derive some really practical knowledge from our theoretical acquaintance with the phenomena which take place in the space surrounding a projectile?

No physicist who has ever studied waves of sound or photographed them will have the least doubt regarding the sound-wave character of the atmospheric condensation encompassing the head of a flying projectile. We have therefore, without ado, called this condensation the head-wave.

Knowing this, it follows that the view of Melsens according to which the projectile carries along with it masses of air which it forces into the bodies struck, is untenable. A forward-moving sound-wave is not a forward-moving mass of matter but a forward-moving form of motion, just as a water-wave or the waves of a field of wheat are only forward-moving forms of motion and not movements of masses of water or masses of wheat.

By interference-experiments, on which I cannot touch here but which will be found roughly represented in Figure 55, it was found that the bell-shaped head-wave in question is an extremely thin shell and that the condensations of the same are quite moderate, scarcely exceeding two-tenths of an atmosphere. There can be no question, therefore, of explosive effects in the body struck by the projectile through so slight a degree of atmospheric compression. The phenomena attending wounds from rifle balls, for example, are not to be explained as Melsens and Busch explain them, but are due, as Kocher and Reger maintain, to the effects of the impact of the projectile itself.

A simple experiment will show how insignificant is the part played by the friction of the air, or the supposed conveyance of the air along with the moving projectile. If the photograph of the projectile be taken while passing through a flame, i. e., a visible gas, the flame will be seen to be, not torn and deformed, but smoothly and cleanly perforated, like any solid body. Within and around the flame the contours of the head-wave will be seen. The flickering, the extinction of the flame, etc., take place only after the projectile has travelled on a considerable distance in its path, and is then affected by the powder gases which hurry after the bullet or by the air preceding the powder-gases.

The physicist who examines the head-wave and recognises its sound-wave character also sees that the wave in question is of the same kind with the short sharp waves produced by electric sparks, that it is a _noise_-wave. Hence, whenever any portion of the head-wave strikes the ear it will be heard as a report. Appearances point to the conclusion that the projectile carries this report along with it. In addition to this report, which advances with the velocity of the projectile and so usually travels at a speed greater than the velocity of sound, there is also to be heard the report of the exploding powder which travels forward with the ordinary velocity of sound. Hence two explosions will be heard, each distinct in time. The circumstance that this fact was long misconstrued by practical observers but when actually noticed frequently received grotesque explanations and that ultimately my view was accepted as the correct one, appears to me in itself a sufficient justification that researches such as we are here speaking of are not utterly superfluous even in practical directions. That the flashes and sounds of discharging artillery are used for estimating the distances of batteries is well known, and it stands to reason that any unclear theoretical conception of the facts here involved will seriously affect the correctness of practical calculations.

It may appear astonishing to a person hearing it for the first time, that a single shot has a double report due to two different velocities of propagation. But the reflexion that projectiles whose velocity is less than the velocity of sound produce no head-waves (because every impulse imparted to the air travels forward, that is, ahead, with exactly the velocity of sound), throws full light when logically developed upon the peculiar circumstance above mentioned. If the projectile moves faster than sound, the air ahead of it cannot recede from it quickly enough. The air is condensed and warmed, and thereupon, as all know, the velocity of sound is augmented until the head-wave travels forward as rapidly as the projectile itself, so that there is no need whatever of any additional augmentation of the velocity of propagation. If such a wave were left entirely to itself, it would increase in length and soon pass into an ordinary sound-wave, travelling with less velocity. But the projectile is always behind it and so maintains it at its proper density and velocity. Even if the projectile penetrates a piece of cardboard or a board of wood, which catches and obstructs the head-wave, there will, as Figure 56 shows, immediately appear at the emerging apex a newly formed, not to say newly born, head-wave. We may observe on the cardboard the reflexion and diffraction of the head-wave, and by means of a flame its refraction, so that no doubt as to its nature can remain.

Permit me, now, to illustrate the most essential of the points that I have just adduced, by means of a few rough drawings taken from older and less perfect photographs.

In the sketch of Figure 57 you see the projectile, which has just left the barrel of the rifle, touch a wire and disengage the illuminating spark. At the apex of the projectile you already see the beginnings of a powerful head-wave, and in front of the wave a transparent fungiform cluster. This latter is the air which has been forced out of the barrel by the projectile. Circular sound-waves, noise-waves, which are soon overtaken by the projectile, also issue from the barrel. But behind the projectile opaque puffs of powder-gas rush forth. It is scarcely necessary to add that many other questions in ballistics may be studied by this method, as, for example, the movement of the gun-carriage.

A distinguished French artillerist, M. Gossot, has applied the views of the head-wave here given in quite a different manner. The practice in measuring the velocity of projectiles is to cause the projectile to pass through wire screens placed at different points in its path, and by the tearing of these screens to give rise to electro-magnetic time-signals on falling slabs or rotating drums. Gossot caused these signals to be made directly by the impact of the head-wave, did away thus with the wire screens, and carried the method so far as to be able to measure the velocities of projectiles travelling in high altitudes, where the use of wire screens was quite out of the question.

The laws of the resistance of fluids and of air to bodies travelling in 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.

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