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them that the course of a reflected ray is the shortest | which he wishes to examine carefully. When he places possible.

The general nature of refraction also was known, with some of its special applications, such as, for instance, to burning-glasses and to magnifiers. These were probably either spherical glass shells filled with water or balls of rock crystal.

In the first century of our era Cleomedes pointed out how a coin at the bottom of an empty cup, where the eye cannot see it, can be made visible by filling the cup with water; and he showed that, in a similar way, the air may render the sun visible to us while it is still under the horizon. Shortly after this date Ptolemy (the celebrated astronomer) published his great work on Optics. He treats of vision, reflection, the theory of plane and concave mirrors, and refraction. He measured, with considerable accuracy, the angles of incidence and refraction, for rays passing from air into water and into glass, and from water into glass; it was not, however, till more than fifteen hundred years had passed that the true relation between these angles was discovered. In addition to what has just been mentioned, the ancients' knowledge of optics was limited to a very superficial acquaintance with some of the properties of But it was fragmentary rainbows, halos, mirage, etc. in the extreme, though it far surpassed in amount as well as in accuracy their knowledge of the other branches of physical science.

It is not easy to understand the ideas of the ancients about color. That it is a property of a body-just as its density, its hardness, or its smell is a property-was But they also imagined that a probably held by them. body could communicate its color to light; thus, for instance, the clouds were, by some of them, supposed to communicate their colors to the sunbeams which form a rainbow.

Our next glimpse of real progress dates from the
eleventh or twelfth century, when ALHAZEN (q.v.)
wrote a treatise on optics in Arabic, which for five hun-
dred years or more was a recognized authority on the
subject. It was, in many parts, founded on the work of
Ptolemy, but with considerable additions and improve-
ments. Alhazen gives an anatomical description of the
eye, and points out, fairly enough, how with two eyes
we see only one image. But he also points out that we
see each object, however small, by a pencil of diverging
rays-not (as the ancients imagined) by a single ray.
Alhazen accounts for twilight, and shows how by it to
measure the height of the atmosphere. He also gives
the now generally received explanation of the curious
The
fact that the sun and moon appear larger when rising or
setting than when they are high in the heavens.
farther progress of the subject we need not now trace.
From the end of the sixteenth century that progress has
been extremely rapid. Before we commence a more
rigorous treatment of the subject, it may be well to
make a few preliminary statements as to the nature of
vision and the condition for distinct vision. Properly
speaking these belong to OPTICS (q.v.), but it is impos-
sible to treat intelligibly any part of our subject without
presupposing some, generally very slight, knowledge of
other parts.
And the few preliminary statements we
have now to make are in no respect theoretical, while
they are so simple that anyone may at once test their
truth for himself.

Except in the case of a very abnormal eye (extremely
short-sighted or long-sighted as the case may be) there
is a distance from it-usually somewhere about ten
inches-at which, if an object be placed, it is seen more
Almost
distinctly than if placed at any other distance.
everyone, perhaps without his knowing it, habitually
places at or about that distance from his eye an object

it at a smaller distance he becomes conscious of the e-
fort required to see it distinctly. He has, in fact, to
alter the form of the optical machinery of the eye, by a
muscular effort, so that it may become capable of bring-
those for which the parts were in their unstrained state
ing to a focus on the retina rays more divergent than
adapted. A corresponding effort, but usually much
more slight, is commonly felt to be required if the ob-
we arrive at the conclusion that, for the minimum of
ject be at a distance greater than ten inches. Hence
strain on the eye, rays should fall on it diverging as if
for all ordinary eyes any divergence from double of this
they came from a point about ten inches distant. But
(i.c., divergence as if from a distance of five inches) to
zero (i.., parallel rays) is consistent with the possibility
former limits, or convergent, are unfit to produce dis-
of distinct vision. Rays either more divergent than the
tinct vision. Hence every optical instrument, whatever
be the reflections or refractions to which light has been
subjected in passing through it, must finally allow the
light to escape either in parallel rays or with a diver-
The comparatively
gence within the above specified limits, if it is to be
employed by an ordinary eye.
slight differences which exist among ordinary eyes are
easily compensated by the rack-work, or screw adjust-
good telescope and to the body of a good microscope.
ment, which is invariably attached to the eyepiece of a
Every motion of this rack-work alters the divergence of
the rays as they finally escape from the instrument.
Any eye, however abnormal, if it be capable of produc-
ing distinct vision at all, has only to be furnished with
does a normal eye. This statement, however, refers
suitable spectacles in order that it may behave exactly as
color. The deficiency which causes color-blindness can-
A definite
only to sharpness of definition, not in any degree to
conceivable process.
not be supplied by any
part of the ordinary organ of vision is wanting (or inact-
ive) in such cases-while the merely optical parts of the
eye are usually in perfect order.

Another fact which must be stated' here is that, to
produce vision of a body in its natural position, the
image on the retina, as seen from the back, must be in-
as regards right and left. Thus, in the ordinary astro-
verted-not merely as regards up and down, but also
A third is
and we, therefore, see an inverted image.
nomical telescope the image on the retina is not inverted,
that our judgment of the relative distances of objects
One eye, kept still, can inform us only of rel-
is formed mainly by the use of the two eyes simulta-
ative distance in virtue of the greater or less effort to
neously.
see distinctly (already spoken of). With both eyes,
or with one eye moved from side to side, parallax comes
This power of judging distance is, of course, greater as
in, and gives us the stereoscopic effect, as it is called.
the eyes are set more widely apart. There is, practi-
cally, no limit to the effective distance between the eyes
when the proper instrumental methods (as with the tel-
estereoscope) are employed.

It is also necessary to premise a few words about The various homogeneous rays of the solar color. To such a quesspectrum have each a color of its own which no refraction can modify. But what about the many colors tion as "What is yellow?" the answer is, " Each partic which do not occur in the spectrum? ular kind of yellow may be any one of an infinite number the same is true, in general, of all other colors. Clerk of different combinations of homogeneous rays." And Maxwell found that a yellow equivalent to that of the spectrum can be obtained by mixing in proper proportions certain homogeneous red and green rays. This single example is sufficient to show that the color-sense

cent. It is probable that the light of nebulæ and the proper light of comets are due to this cause. The proximate cause, in all these cases, is the kinetic energy of the fragments before impact. To this class, therefore, can be reduced the light given out when a target is struck by a cannon shot.

The Kinetic Energy of Current Electricity or of an Electric Discharge. Here we have lightning, the electric light, and probably also the light of the aurora.

The Potential Energy of Chemical Affinity.-The limelight, gaslight, candle and lamplight, firelight, the magnesium light, etc.; also phosphorus, dead fish (?), etc., glowing in the dark.

is of a very singular nature. This question will be the formation of the sun and stars, heat enough is gentreated in OPTICS (PHYSIOLOGICAL); but for our pres-erated by impact to render the whole vividly incandesent purpose it is only necessary to say that we now know that the normal eye has only three color-sensations -a red, a green, and a violet-and that the apparent color of any light which falls on it depends merely on the relative intensities of the excitement produced by the light on the three organs of sense corresponding to these sensations. This is true, however, only within certain limits of intensity; for extremely bright light, whatever be its real color, seems to excite all the three sensations simultaneously, much as white light does; and with very feeble light (as, for instance, that of an ordinary aurora or of a lunar rainbow) we are sometimes scarcely conscious of colors. In color-blindness one or more of these organs of sense is wanting, or imperfect. The most common form, Daltonism, depends on the absence of the red sense. Great additions to our knowledge of this subject, if only in confirmation of results already deduced from theory, have been obtained in the last few years by Holmgren, who has experimented on two persons, each of whom was found to have one color-blind eye, the other being nearly normal. In this way was obtained, what could otherwise have been matter of conjecture only, a description of colorblind vision in terms of (at least approximately) normal vision.

|

Friction, as in the trains of sparks from a grindstone or brake; though here, in general, chemical affinity also has a share. Sudden Great Compression of a Gas, as of air by meteoric stones and falling stars.

Another very curious source, not (so far as is known), reducible to incandescence, is the giving out (usually in an altered form) of light previously absorbed-fluorescence, phosphorescence, etc.

A third source is physiological-fireflies, glowworms, Medusa, dead fish (?), etc., the eye of a cat.

Any not black and not transparent body, exposed to any of these sources of light, becomes in its turn what may for our purpose also be treated as a source.

As will be shown in RADIATION, the only bodies which, when incandescent, give every constituent of white light, are bodies which are black in the sense of absorbing each and every ray which falls upon them. Such bodies are not necessarily solids—though the best examples we have of them are lampblack, and (somewhat less perfect) charcoal and gas-coke.

GEOMETRICAL OPTICS.-It is approximately true that, in any homogeneous medium, light moves in straight lines. If an opaque body be placed anywhere in the straight line between the eye and an object the object is concealed. Through a long straight tube no objects can be seen but those situated in the direction of its axis produced. This is so fundamental a fact, or it is so evident a result of experienɔe, that it is the foundation of every process which involves the direction in space of one object as regards another-whether it be for the aiming with a rifle, the pointing of a telescope, or for the delicate observations of a geodetic survey. But we must carefully observe the restrictions under which the statement is made. Not merely is it said to be only approximately true, but it is so only in a homogeneous medium.

Finally, the sensation of sight is not limited to the duration of the mechanical action on the eye. It is known that we do not see a sudden flash (an electric spark, for instance) until a measurable, though very short, period has elapsed. This depends on the rate at which an excitation is propagated along the optic nerve. But the familiar experiment of whirling a red-hot stick in a dark room shows that the sensation of sight lasts for a short period after the mechanical action which produced it has ceased. This period is probably different for different eyes, and for different amounts of excitement even in the same eye. (If the light be very intense the effect lasts much longer, but completely changes its character.) For our present purpose it may be assumed that the duration is somewhere about of a second. Thus, if the end of the red-hot stick describes a circle once in of a second, we see the complete circle; if in a longer period, we only see at once such a part of it as was described in of a second. Connected with this is the remarkable result obtained experimentally by Swan, that the amount of sensation is, for flashes of short duration, directly proportional, not only to the brightness of the flash, but also to its duration. A flash which lasts for of a second produces the full effect on the eye; but an (a) On this is founded the geometrical theory of electric spark, as a flash of lightning, which certainly shadows-a subject of some importance, especially as does not endure for more than 1000 of a second, | regards eclipses. In this application the results may be produces at most only Toooo of the effect it would considered as absolutely true, though the statement is produce if it lasted of a second. On this short liable in certain delicate cases to somewhat startling exduration of visual impressions depends the action of the ceptions. When an opaque body is placed between a thaumatrope, the wheel of life, etc. By various kinds screen and a luminous point it casts a shadow on the of machinery a succession of views of an object in dif- screen. (The sun's image formed by a lens or burning. ferent positions or forms is presented to the eye, each glass of short focus is our best mode of attempting to for a brief interval. The result is that we fancy we see realize the conception of a luminous point; but a fair one and the same object going through a species of con- approximation may be made by piercing a very small tinuous motion, or of change of form, which would pre-needle-hole in a large plate of thin metal, and placing it sent it to the eye in these successive positions or forms. Thus, a tadpole may be represented as wiggling about, or as developing continuously into a frog, etc.

10

The main source of light is incandescence. (It is usually understood that to be incandescent a body must be at a high temperature.) This may be due to any of a number of causes, such as the following:

The Potential Energy of Gravitation of Scattered Fragments of Matter.-When these fall together, as in

close to any bright flame or incandescent body.) The outline of the shadow is, of course, to be found by drawing straight lines from the luminous point so as to touch the opaque body all around. These lines form a cone. The points of contact form a line on the opaque body separating the illuminated from the non-illuminated portion of its surface. Similarly, when these lines are produced to meet the screen, their points of intersection with it form a line which separates

the illuminated from the non-illuminated parts of the

screen.

This line is called the boundary of the geometrical shadow. A common but beautiful instance of it is seen when a very small gas-jet is burning in a ground-glass shade, near the wall of a room. In this case the cone, above mentioned, is usually a right cone with its axis vertical. Thus the boundary of the geometric shadow is a portion of a circle on the roof, but a portion of an hyperbola on the vertical wall. If the roof be not horizontal, we may obtain in this way any form of conic section. Interesting and useful hints in projection may be obtained by observing the shadows of bodies of various forms cast in this way by rays which virtually diverge from one point: e.g., how to place a plane quadrilateral of given form so that its geometric shadow may be a square; how to place an elliptic disk, with a small hole in it, so that the shadow may be circular, with a bright spot at its center, etc.

When there are more luminous points than one, we nave only to draw separately the geometrical shadows due to each of the sources, and then superpose them. A new consideration now comes in. There will be, in general, portions of all the separate geometrical shadows which overlap one another in some particular regions of the screen. In such regions we still have full shadow; but around them there will be other regions, some illuminated by one of the sources alone, some by two, etc., until finally we come to the parts of the screen which are illuminated directly by all the sources. There will evidently be still a definite boundary of the parts wholly unilluminated, i.e., the true shadow or umbra, and also a definite boundary of the parts wholly illuminated. The region between these boundaries-i.e., the partially illumined portion-is called the penumbra.

in air is to that of the tooth, at the first disappearance of the reflected light, as the distance of the mirror from the disk is to the half breadth of the tooth. It is not to be supposed that the description we have just given embodies all the details of this remarkable experiment. On the contrary, telescopes were used at each station to prevent loss of light as much as possible, and many other precautions were adopted. This method and its first results were published in 1849 in the Comptes Ren dus. The experiments gave, on their very careful repetition by Cornu in 1874, the value 186,700 miles for the velocity in vacuo. It is interesting to observe that, as the nearest fixed star is probably about 200,000 times farther from us than the sun is, we now see such a star by light which left it more than three years ago. If, as is now supposed, variable stars (such as Mira Ceti) owe their rapid periodical changes of brightness to eclipses, and if different homogeneous rays travel with different velocities in free space, it is evident that such stars would show a gradual change of color as they wax, and an opposite change as they wane. Nothing of the kind has as yet been observed, though it has been carefully sought for. Hence we have every reason to conclude that, in free space, all kinds of light have the same velocity.

LIGHTFOOT, JOHN, an eminent rabbinical scholar, was the son of Thomas Lightfoot, vicar of Uttoxeter, Staffordshire, was born at Stoke-upon-Trent, England, in 1602, and died in 1657.

LIGHTHOUSE. The primary and most important consideration relating to the design and construction of a lighthouse tower which is to be built within the tidemark is the force of the waves which may be expected to assail it, and the directions and heights at which that force will act on the building. The great waves which are found in the open ocean cannot be generated in VELOCITY OF LIGHT.-Light moves with a velocity smaller seas; and, with a due regard to economy in of nearly 186,000 miles per second. To illustrate by far construction, ought not, therefore, to be provided the most convincing popular proof of the finite velocity of against. What is wanted is to ascertain in such shorter light, suppose a person looking at himself in a mirror bescas the height of waves in relation to the length of fore which is moving a screen with a number of aper-"fetch" in which they are generated, and next to detures, the breadth of each aperture being equal to the termine their energy when on reaching the shore or a distance between any two of them. If the screen be at sunken rock, and so ceasing to be waves of oscillation, rest with an aperture before the mirror, the light from the they enormously increase their destructive force by beobserver's face passes through the aperture and is re- coming waves of translation. The law of increase in flected back, so that he sees himself as if the screen were the height of waves was found by Mr. T. Stevenson to not present. Suppose the screen to be moving in such be proportional to the square root of the distance from a way that, when the light which passed through the the windward shore, and the greatest force recorded aperture returns to the screen after reflection, the un- on rocks exposed to the ocean was three and one-half pierced part of the screen is in its way, it is evident tons per square foot. The relative forces of summer that the observer cannot see himself in the mirror. If and winter gales were found to be as one to three, and the screen pass twice as fast, the light that escaped by || the vertical force, after acting on a curved sea-wall, was one aperture will, after reflection, return by the next, eighty-four times greater than the horizontal force at a so that he will see his image as at first. If three times height of twenty-three feet above high water. The hisas fast, the second unperforated part of the screen will tory of the ancient lighthouses is of so scanty a nature stop the returning light; so he cannot see his image. that we may pass at once to more modern works, comTo apply this practically a thin metallic disk had a set mencing with Winstanley's Eddystone light. of teeth cut on its circumference so that the breadth of The Eddystone Rocks, which lie about fourteen miles a tooth was equal to that of the space between two teeth. off Plymouth, are fully exposed to the southwestern This disk could be set in very rapid rotation by a train seas. The lighthouse was completed by Winstanley in of wheelwork, and the rate of turning could easily be four seasons. In 1698 it was finished at a height of determined by Savart's method. Light passed between eighty feet and the light exhibited; but in 1699, in contwo teeth to a mirror situated at ten miles' distance, sequence of damage by storms, the tower was increased which sent it back by the same course, so that when the by an outer ring of masonry four feet thick, and made wheel was at rest the reflected light could be seen. On solid from the foundation to nearly twenty feet above turning the disk with accelerated velocity the light was the rock. The height was increased to nearly 120 feet, observed to become more and more feeble up to a cer- and completed in 1700. During the well-known hurritain velocity, at which it was extinguished; turning cane of November 20, 1703, the tower was destroyed. faster it reappeared, growing brighter and brighter till In general design as well as in details this work must the velocity was doubled; then it fell off, till it vanished be placed among the vetanda of maritime engineering. when the velocity was trebled, and so on. It is evident For example, in plan it was polygonal instead of circufrom the first illustration above that the velocity of light lar. In his blind devotion to ornamentation Winstanley

There are a great many other lighthouses in Ireland, The demands which are made on a light that has to India, and America which merit more attention than our revolve are not nearly so great as on one that is fixed, space admits of, and we shall therefore conclude with for the revolving light does not, like the fixed, require directing the attention of the engineer to the important to illuminate the whole horizon simultaneously, but influence of the configuration of rocks in modifying the only each point of it at successive intervals of time. breaking waves. It cannot excite surprise that some of When the dark intervals occur, the rays from the flame the structures which were erected on the Eddystone which are then pointing in the direction of the dark should have withstood the waves so long as they did. spaces should therefore have their direction so altered This fact seems to lead to the conclusion that the Eddy- laterally as to pass into the adjoining light spaces and stone Rock, at one time at least, acted to some extent thus to increase the power of the luminous flashes. A as a shelter to the structures which were built on it. | revolving light, though supplied by a flame of the same During a summer gale when Dhu Heartach lighthouse power as a fixed, will thus necessarily be far more intense, was being erected fourteen stones each of two tons as it does not lose its power by diffusing the rays constantly weight, which had been fixed on the tower by joggles over the whole horizon, but gathers them up into a numand Portland cement at the level of 37 feet above high ber of separate bundles or beams of great intensity. water, were torn out and swept off into deep water. At The apparatus of a revolving light has consequently the Bell Rock stones of two tons weight were several more optical work to do than that of a fixed, for the rays times swept away during the construction of the tower, must be bent not only in the vertical plane but laterally while it is a remarkable fact that no stones were ever in the horizontal and in all intermediate planes as well. moved at the Eddystone. But what is more striking, the thin glass panes of Winstanley's first tower stood successfully through a whole winter's storms at the same