glasses viewed them under oblique illumination, usually at a
considerable distance, so as to give full scope to the aberrations, and
had recourse for greater exactitude to a telescope. But the method was
carried to its highest pitch of perfection in 1867 by Toepler who
employed the following procedure: A small luminous source _a_ (Fig. 49)
illuminates a lens _L_ which throws an image _b_ of the luminous source.
If the eye be so placed that the image falls on the pupil, the entire
lens, if perfect, will appear equally illuminated, for the reason that
all points of it send out rays to the eye. Coarse imperfections of form
or of homogeneity are rendered visible only in case the aberrations are
so large that the light from many spots passes by the pupil of the eye.
But if the image _b_ be partly intercepted by the edge of a small slide,
then those spots in the lens as thus partly darkened will appear
brighter whose light by its greater aberrations still reaches the eye in
spite of the intercepting slide, while those spots will appear darker
which in consequence of aberration in the other direction throw their
light entirely upon the slide. This artifice of the intercepting slide
which had previously been employed by Foucault for the investigation of
the optical imperfections of mirrors enhances enormously the delicacy of
the method, which is still further augmented by Toepler's employment of
a telescope behind the slide. Toepler's method, accordingly, enjoys all
the advantages of the Huygens and the Foucault procedure combined. It is
so delicate that the minutest irregularities in the air surrounding the
lens can be rendered distinctly visible, as I shall show by an example.
I place a candle before the lens _L_ (Fig. 50) and so arrange a second
lens _M_ that the flame of the candle is imaged upon the screen _S_. As
soon as the intercepting slide is pushed into the focus, _b_, of the
light issuing from _a_, you see the images of the changes of density and
the images of the movements induced in the air by the flame quite
distinctly upon the screen. The distinctness of the phenomenon as a
whole depends upon the position of the intercepting slide _b_. The
removal of _b_ increases the illumination but decreases the
distinctness. If the luminous source _a_ be removed, we see the image of
the candle flame only upon the screen _S_. If we remove the flame and
allow _a_ to continue shining, the screen _S_ will appear uniformly
illuminated.
[Illustration: Fig. 50.]
After Toepler had sought long and in vain to render the irregularities
produced in air by sound-waves visible by this principle, he was at last
conducted to his goal by the favorable circumstances attending the
production of electric sparks. The waves generated in the air by
electric sparks and accompanying the explosive snapping of the same, are
of sufficiently short period and sufficiently powerful to be rendered
visible by these methods. Thus we see how by a careful regard for the
merest and most shadowy indications of a phenomenon and by slight
progressive and appropriate alterations of the circumstances and the
methods, ultimately the most astounding results can be attained.
Consider, for example, two such phenomena as the rubbing of amber and
the electric lighting of modern streets. A person ignorant of the myriad
minute links that join these two things together, will be absolutely
nonplussed at their connexion, and will comprehend it no more than the
ordinary observer who is unacquainted with embryology, anatomy, and
paleontology will understand the connexion between a saurian and a bird.
The high value and significance of the co-operation of inquirers through
centuries, where each has but to take up the thread of work of his
predecessors and spin it onwards, is rendered forcibly evident by such
examples. And such knowledge destroys, too, in the clearest manner
imaginable that impression of the marvellous which the spectator may
receive from science, and at the same time is a most salutary
admonishment to the worker in science against superciliousness. I have
also to add the sobering remark that all our art would be in vain did
not nature herself afford at least some slight guiding threads leading
from a hidden phenomenon into the domain of the observable. And so it
need not surprise us that once under particularly favorable
circumstances an extremely powerful sound-wave which had been caused by
the explosion of several hundred pounds of dynamite threw a directly
visible shadow in the sunlight, as Boys has recently told us. If the
sound-waves were absolutely without influence upon the light, this could
not have occurred, and all our artifices would then, too, be in vain.
And so, similarly, the phenomenon accompanying projectiles which I am
about to show you was once in a very imperfect manner incidentally seen
by a French artillerist, Journée, while that observer was simply
following the line of flight of a projectile with a telescope, just as
also the undulations produced by candle flames are in a weak degree
directly visible and in the bright sunlight are imaged in shadowy waves
upon a uniform white background.
_Instantaneous illumination_ by the electric spark, the method of
rendering visible small optical differences or striæ, which may hence be
called the _striate_, or _differential_, method,[112] invented by
Foucault and Toepler, and finally the _recording_ of the image by a
_photographic_ plate,--these therefore are the chief means which are to
lead us to our goal.
I instituted my first experiments in the summer of 1884 with a
target-pistol, shooting the bullet through a striate field as described
above, and taking care that the projectile whilst in the field should
disengage an illuminating electric spark from a Leyden jar or Franklin's
pane, which spark produced a photographic impression of the projectile
upon a plate, especially arranged for the purpose. I obtained the image
of the projectile at once and without difficulty. I also readily
obtained, with the still rather defective dry plate which I was using,
exceedingly delicate images of the sound-waves (spark-waves). But no
atmospheric condensation produced by the projectile was visible. I now
determined the velocity of my projectile and found it to be only 240
metres per second, or considerably less than the velocity of sound
(which is 340 metres per second). I saw immediately that under such
circumstances no noticeable compression of the air could be produced,
for any atmospheric compression must of necessity travel forward at the
same speed with sound (340 metres per second) and consequently would be
always ahead of and speeding away from the projectile.
I was so thoroughly convinced, however, of the existence of the supposed
phenomenon at a velocity exceeding 340 metres per second, that I
requested Professor Salcher, of Fiume, an Austrian port on the Gulf of
Quarnero, to undertake the experiment with projectiles travelling at a
high rate of speed. In the summer of 1886 Salcher in conjunction with
Professor Riegler conducted in a spacious and suitable apartment placed
at their disposal by the Directors of the Royal Imperial Naval Academy,
experiments of the kind indicated and conforming in method exactly to
those which I had instituted, with the precise results expected. The
phenomenon, in fact, accorded perfectly with the _a priori_ sketch of it
which I had drafted previously to the experiment. As the experimenting
was continued, new and unforeseen features made their appearance.
It would be unfair, of course, to expect from the very first experiments
faultless and highly distinct photographs. It was sufficient that
success was secured and that I had convinced myself that further labor
and expenditure would not be vain. And on this score I am greatly
indebted to the two gentlemen above mentioned.
The Austrian Naval Department subsequently placed a cannon at Salcher's
disposal in Pola, an Adriatic seaport, and I myself, together with my
son, then a student of medicine, having received and accepted a
courteous invitation from Krupp, repaired to Meppen, a town in Hanover,
where we conducted with only the necessary apparatus several experiments
on the open artillery range. All these experiments furnished tolerably
good and complete pictures. Some little progress, too, was made. The
outcome of our experience on both artillery ranges, however, was the
settled conviction that really good results could be obtained only by
the most careful conduct of the experiments in a laboratory especially
adapted to the purpose. The expensiveness of the experiments on a large
scale was not the determining consideration here, for the size of the
projectile is indifferent. Given the same velocity and the results are
quite similar, whether the projectiles are large or small. On the other
hand, in a laboratory the experimenter has perfect control over the
initial velocity, which, provided the proper equipment is at hand, can
be altered at will simply by altering the charge and the weight of the
projectile. The requisite experiments were accordingly conducted by me
in my laboratory at Prague, partly in conjunction with my son and partly
afterwards by him alone. The latter are the most perfect and I shall
accordingly speak in detail here of these only.
[Illustration: Fig. 51.]
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.
[Illustration: Fig. 52.]
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.
[Illustration: Fig. 53. Photograph of a blunted projectile.]
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.
[Illustration: Fig. 54.]
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.
[Illustration: Fig. 55.]
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.
[Illustration: Fig. 56.]
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.
[Illustration: Fig. 57.]
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.