quarter of an hour, and that the trains proceed with a common and
uniform velocity of, say, one mile per minute. Now, a person who remains
stationary, at any point on the railway, observes the trains passing at
regular intervals of fifteen minutes, no matter at what part of the line
he may be placed. But now, let us imagine that a train having that very
instant passed him, he begins to walk along the line towards the place
from which the trains are dispatched: it is plain that he will meet the
next train before fifteen minutes—he would, in fact, meet it a mile
higher up the line than the point from which he began his walk fourteen
minutes before; but the train, taking a minute to pass over this mile,
would pass his point of departure just fifteen minutes after its
predecessor. And our imaginary pedestrian, supposing him to continue his
journey at the same rate, would meet train after train at intervals of
fourteen minutes. Similarly, if he walked away from the approaching
trains, they would overtake him at intervals of sixteen minutes. And
again, it would be easy for him to calculate the speed of the trains,
knowing that they passed over each point of the line every fifteen
minutes. Thus, suppose him to pass _down_ the line a distance known to
be, say, a quarter of a mile; suppose he leaves his station at noon, the
moment a train has passed, and that he takes, say an hour, to arrive at
his new station a quarter of a mile lower; here, observing a train to
pass at fifteen seconds after one o’clock, and knowing that it passed
his original station at one, he has a direct measure of the speed of the
trains. Here we have been explaining a discovery two centuries old; but
our purpose is to prepare the reader for an account of how the velocity
of light has been recently measured in a direct manner, and it certainly
appears a marvellous achievement that means have been found to measure a
velocity so astounding, not in the spaces of the solar system, or along
the diameter of the earth’s orbit, but within the narrow limits of an
ordinary room! The reliance with which the results of these direct
measures will be received, will be greatly increased by the knowledge of
the astronomical facts with which they show an entire concordance. In
taking leave of Roemer, we may mention that his discovery, like many
others, and like some inventions which have been described in this book,
did not for some time find favour with even the scientific world, nor
was the truth generally accepted, until Bradley’s discovery of the
aberration of light completely confirmed it.
[Illustration:
FIG. 192.
]
To two gifted and ingenious Frenchmen we are indebted for independent
measurements of the velocity of light by two different methods. The
general arrangement of M. Fizeau’s method is represented in Fig. 192, in
which the rays from a lamp, L, after passing through a system of lenses,
fall upon a small mirror, M N, formed of unsilvered plate-glass inclined
at an angle of 45° to the direction of the rays; from this they are
reflected along the axis of a telescope, T, by the lens of which being
rendered parallel, they become a cylindrical beam, B, which passes in a
straight line to a station, D, at a distance of some miles (in the
actual experiment the lamp was at Suresnes and the other station at
Montmartre, 5½ miles distant) whence the beam is reflected along the
same path, and returns to the little plate of glass at M N, passing
through which it reaches the eye of the observer at E. At W is a toothed
wheel, the teeth of which pass through the point F, where the rays from
the lamp come to a focus; and as each tooth passes, the light is stopped
from issuing to the distant station. This wheel is capable of receiving
a regular and very rapid rotation from clockwork in the case, C,
provided with a register for recording the number of its revolutions. If
the wheel turns with such a speed that the light permitted to pass
through one of the spaces travels to the mirror and back in exactly the
same time that the wheel moves and brings the next space into the tube,
or the second space, or the third, or any _space_, the reflected light
will reach the spectator’s eye just as if the wheel were stationary; but
if the speed be such that a _tooth_ is in the centre of the tube when
the light returns from the mirror, then it will be prevented from
reaching the spectator’s eye at all, so long as this particular speed is
maintained, but either a decrease or an increase of velocity would cause
the luminous image to reappear. Speeds between those by which the light
is seen, and those by which it entirely disappears, cause it to appear
with merely diminished brilliancy. It is only necessary to observe the
speed of the wheel when the light is at its brightest, and when it
suffers complete eclipse, for then the time is known which is required
for space and tooth respectively to take the place of another space—and
hence the time required for the light to pass to the mirror and back is
found.
M. Foucault’s method is similar in principle to that used by Wheatstone
in the measurement of the velocity of electricity. He used a mirror
which was made to revolve at the rate of 700 or 800 turns _per second_,
and the arrangement of the apparatus was such as to admit of the
measurement of the time taken by light to pass over the short space of
about four yards! More recently, however, he has modified and improved
his apparatus by adopting a most ingenious plan of maintaining the speed
of the mirror at a determined rate, which he now prefers should be 400
turns per second, while the light is reflected backwards and forwards
several times, so that it traverses a path of above 20 yards in length.
The time taken by the light to travel this short distance is, of course,
extremely small, but it is accurately measured by the clockwork
mechanism, and found to be about the 1/150000000th of a second! The
results of these experiments of Foucault’s make the velocity of light
several thousand miles per second less than that deduced from the
astronomical observation of Roemer and Bradley, in which the distance of
the earth from the sun formed the basis of the calculations; and hence
arose a surmise that this distance had been over-estimated. That such
had, indeed, been the case was confirmed almost immediately afterwards
by a discussion among the astronomers as to the correctness of the
accepted distance, the result of which has been that the mean distance,
which was formerly estimated at 95 millions of miles, has, by careful
astronomical observations and strict deductions, been now estimated at
between 91 and 92 millions of miles. The famous transit of Venus
December 9th, 1873–-to observe which the Governments of all the chief
nations of the world sent out expeditions—derived its astronomical and
scientific importance from its furnishing the means of calculating, with
greater correctness than had yet been attained, the distance of the
earth from the sun.
[Illustration:
FIG. 193.
]
[Illustration:
FIG. 194.
]
[Illustration:
FIG. 195.
]
_REFLECTION OF LIGHT._
Long before plate glass backed by brilliant quicksilver ever reflected
the luxurious appointments of a drawing-room; long before looking-glass
ever formed the mediæval image of “ladye fair”; long before the haughty
dames of imperial Rome were aided in their toilettes by _specula_; long
before the dark-browed beauties of Egypt peered into their brazen
mirrors; long, in fact, before men knew how to make glass or to polish
metals, their attention and admiration must have often been riveted by
those perfect and inverted pictures of the landscape, with its rocks,
trees, and skies, which every quiet lake and every silent pool presents.
Enjoyment of the spectacle probably prompted its imitation by the
formation artificially of smooth flat reflecting surfaces; and no doubt
great skill in the production of these, and their application to
purposes of utility, coquetry, and luxury, preceded by many ages any
attempt to discover the laws by which light is reflected. The most
fundamental of these laws are very simple, and for the purpose we have
in view, it is necessary that they should be borne in mind. Let A B,
Fig. 193, be a _plane reflecting surface_, such as the surface of pure
quicksilver or still water, or a polished surface of glass or metal, and
let a ray of light fall upon it in the direction, I O, meeting the
surface at O, it will be reflected along a line, O R,—such that if at
the point O we draw a line, O P, perpendicular to the surface, the
incident ray, I O, and the reflected ray, O R, will form equal angles
with the perpendicular—in other words, the angle of incidence will be
equal to the angle of reflection, and the perpendicular, the incident
ray, and the reflected ray, will all be in one plane perpendicular to
the reflecting plane. It would be quite easy to prove from this law that
the luminous rays from any object falling on a plane reflecting surface
are thrown back just _as if_ they came from an object placed behind the
reflecting surface symmetrically to the real object. The diagrams in
Figs. 194 and 195 will render this clear. In the second diagram, Fig.
195, it will be noticed that only the portion of the mirror between Q
and P takes any part in the action, and therefore it is not necessary,
in order to see objects in a plane mirror, that the mirror should be
exactly opposite to them; thus the portion O Q might be removed without
the eye losing any part of the image of the object A B.
[Illustration:
FIG. 196.
]
There are many very interesting and important scientific instruments in
which the laws of reflection from plane surfaces are made use of—such,
for example, as the _sextant_ and the _goniometer_; but passing over all
these, we may say a word about the formation of several images from one
object by using two mirrors. It has already been explained that the
action of a plane mirror is equivalent to the placing of objects behind
it symmetrically disposed to the real object. The reflections, or
_virtual images_ in the mirror, behave optically exactly _as if_ they
were themselves real objects, and are reflected by other mirrors in
precisely the same manner. From this it follows that two planes inclined
to each other at an angle of 90° give three images of an object placed
between them, the images and the object apparently placed at the four
angles of a rectangle. When the mirrors are inclined to each other at an
angle of 60°, five images are produced, which, with the original object,
show an hexagonal arrangement. The formation of these by the principle
of symmetry is indicated in Fig. 196. It was these symmetrically
disposed images which suggested to Sir David Brewster the construction
of the instrument so well known as the _kaleidoscope_, in which two—or,
still better, three—mirrors of black glass, or of glass blackened on one
side, are placed in a pasteboard tube inclined to each other at 60°: one
end of the tube is closed by two parallel plates of glass; the outer one
ground, but the inner transparent, leaving between them an interval, in
which are placed fragments of variously-coloured glass, which every
movement of the instrument arranges in new combinations. At the other
end of the tube is a small opening—on applying the eye to which one sees
directly the fragments of glass, with their images so reflected that
beautifully symmetrical patterns are produced; and this with endless
variety. When this instrument was first made in the cheap form in which
it is now so familiarly known, it obtained a popularity which has
perhaps never been equalled by any scientific toy, for it is said that
no fewer than 200,000 kaleidoscopes were sold in London and Paris in one
month.
[Illustration:
FIG. 197.—_Polemoscope._
]
By way of contrast to the mirrors of the kaleidoscope harmlessly
producing beautiful designs, by symmetrical images of fragments of
coloured glass, we show the reader, in Fig. 197, mirrors which are
reflecting quite other scenes, for here is seen the manner in which even
the plane mirror has been pressed into the service of the stern art of
war. The mirrors are employed, not like those of Archimedes, to send
back the sunbeams from every side, and by their concentration at one
spot to set on fire the enemy’s works, but to enable the artillerymen in
a battery to observe the effect of their shot, and the movement of their
adversaries, without exposing themselves to fire by looking over the
parapet of their works. The contrivance has received the appropriate
name of _Polemoscope_ (πολεμος, _war_, and σκοπεω, _to view_), and it
consists simply, as shown in the figure, of two plane mirrors so
inclined and directed, that in the lower one is seen by reflection the
localities which it is desired to observe.
[Illustration:
FIG. 198.—_Apparatus for Ghost Illusion._
]
We return once more to the arts of peace, in noticing the advantage
which has been lately taken of plane mirrors for the production of
spectral and other illusions, in exhibitions and theatrical
entertainments, the improvement in the manufacture of plate-glass having
permitted the production of enormous sheets of that substance. Among the
most popular exhibitions of this class was that known as “Pepper’s
Ghost,” the arrangement of the mirrors having been the subject of a
patent taken out by Mr. Pepper and Mr. Dircks jointly. The principle on
which the production of the illusion depends, may be explained by the
familiar experience of everybody who has noticed that, in the twilight,
the glass of a window presents to a person inside of a room the images
of the light or bright objects in the apartment, while the objects
outside are also visible through the glass. As, by night coming on, the
reflections increase in brilliancy, the darkness outside is almost
equivalent to a coat of black paint on the exterior surface of the
glass; but, on the contrary, in the daylight no reflection of the
interior of the room is visible to the spectator inside, on looking
towards the window. The reflections are present, nevertheless, in the
day-time as well as at night, only they are overpowered and lost when
the rays which reach the eye _through_ the glass are relatively much
more powerful. Even in the day-time the image of a lighted candle is
usually visible, in the absence of direct sunshine, against a dark
portion of the exterior objects as a back-ground. The visibility, or
otherwise, of the internal objects by reflection, and of the external
objects seen through the glass, depends entirely on the relative
intensities of the illumination, for the more illuminated side
overpowers and conceals the other, just as the rising sun causes the
stars “to pale their ineffectual fires.” Hence, on looking through the
window on a dark night, we cannot see objects out of doors unless we
screen off the reflection of the illuminated objects in the room. If the
rays transmitted through the glass, and those which are reflected, have
intensities not very different, we see then the reflected images mixed
up in the most curious manner with the real objects. It is exactly in
this way that the ghosts are made to appear in the illusion of which we
are speaking. The real actors are seen through a large plate of
colourless and transparent glass, and from the front surface of this
glass rays are reflected which apparently proceed from a phantom taking
a part in the scene among the real actors. The arrangement is shown in
Fig. 198, where E G is the stage, separated from the auditorium, h, by a
large plate of transparent glass, E F, placed in an inclined position,
and not visible to the spectators, for the lights in front are turned
down, and the stage is also kept comparatively dark. Parallel to the
large plate of glass is a silvered mirror, C D, placed out of the
spectators’ sight, and receiving the rays from a person at A, also out
of sight of the spectators, and strongly illuminated by an oxy-hydrogen
lime-light at B. The manner in which the rays are reflected from the
silvered mirror to the plate-glass, and hence reflected so as to reach
the spectators and give them the impression of a figure standing on the
stage at G, is sufficiently indicated by the lines drawn in the diagram.
The apparitional and unsubstantial character of the image is derived
from its seeming transparency, and from the manner in which it may be
made to melt away, by diminishing the brightness of the light which
falls on the real person. The introduction of the second mirror was a
great improvement, for by this the phantom is made to appear erect,
while its original stands in a natural attitude. Whereas, with only the
plate-glass, E F, the _ghost_ could not be made to appear upright,
unless, indeed, as was sometimes done, the plate was inclined at an
angle of 45°, and the actor of the ghost lay horizontally beneath it. A
scene of the kind produced by the improved apparatus, is represented in
Fig. 198_a_.
[Illustration:
FIG. 198_a_.—_The Ghost Illusion._
]
Another illusion is produced by the help of a large silvered mirror,
placed at an inclination of 45°, sloping backwards from the floor, and,
in consequence, presenting to the spectators the image of the ceiling,
which appears to them the back of the scene. The mirror is perforated
near the centre by an opening, through which a person passes his head,
and, all his body being concealed by the mirror, the effect produced is
that of a head floating in the air. Means are provided of withdrawing
the mirror, when necessary, while the curtain is down, and then the real
back of the scene appears, which, of course, is exactly similar to the
false one painted on the ceiling. Fig. 199 represents a scene produced
at the Polytechnic by a somewhat similar arrangement of mirrors, under
the management of Mr. Pepper. Plane mirrors were employed in another
piece of natural magic which this gentleman exhibited to the public, who
were shown a kind of large box, or cabinet, raised from the floor, and
placed in the middle of the stage, so that the spectators might see
under it and all round it. Inside of the box were two silvered mirrors
the full height of it, and these were hinged to the farther angles, so
that each one being folded with its face against a side of the box,
their backs formed the apparent sides, and were painted exactly the same
as the real interior of the box. When the performer enters the box, the
door is closed for an instant, while he, stepping to the back, turns the
mirrors on their hinges until their front edges meet, where an upright
post in the middle of the box conceals their line of junction. The
performer thus places himself behind the mirrors in the triangular space
between them and the back of the box, while the mirrors, now inclined at
angles of 45° to the sides, reflect images of these to the spectators
when the door is opened, and the spectators see then the box apparently
empty, for the reflection of the sides appears to them as the back of
the cabinet. The entertainment was sometimes varied by a skeleton
appearing, on the door being opened, in the place of the person who
entered the cabinet. It is hardly necessary to say that the skeleton was
previously placed in the angle between the mirrors where the performer
conceals himself.
[Illustration:
FIG. 199.—_Illusion produced by Mirrors._
]
[Illustration:
FIG. 200.—_A Stage Illusion._
]
To the same inventive gentleman, whose ingenious use of plane mirrors
has thus largely increased the resources of the public entertainer, is
due another stage illusion, the effect of which is represented in Fig.
200; and, although it does not depend on reflection, it may be
introduced here as showing how the perfection of the manufacture of
plate-glass, which makes it available for the ghost exhibition, can be
applied in another way in dramatic spectacles. The female form, here
supposed to be seen in a dream by the sleeper, is not a reflection,
although she appears floating in mid-air, strangely detached from all
supports, but the real actress. This is accomplished by making use of
the transparency of plate-glass, a material strong enough to afford the
necessary support, and yet invisible under the circumstances of the
exhibition.
But it is not behind the turned-down footlights, or in the exhibitions
of the showman, that we find the most beautiful illustrations of the
laws of reflection. In the quiet mountain mere, amid the sweet freshness
of nature, we may often see tree, and crag, and cliff, so faithfully
reproduced, that it needs an effort of the understanding to determine
where substance leaves off and shadow begins, a condition of the liquid
surface indicated in two lines by Wordsworth:
“The swan, on still St. Mary’s Lake,
Floats double, swan and shadow.”
The landscape painter is always gratified if he can introduce into his
picture some piece of water, and it can hardly be doubted that much of
the charm of lakes and rivers is due to their power of reflecting. Look
on Fig. 201, a view of some buildings at Venice; and, in order to see
how much of its beauty is owing to the quivering reflections, imagine
the impression it would produce were the place of the water occupied by
asphalte pavement, or a grass lawn. The condition of the reflections
here represented is perhaps even more pleasing than that produced by
perfect repose: they are in movement, and yet not broken and confused:
“In bright uncertainty they lie,
Like future joys to Fancy’s eye.”
[Illustration:
FIG. 201.—_View of Venice—Reflections._
]
_REFRACTION._