[Page 292]

"These results ascertained, Buffon's next inquiry was how far they corresponded with those ascribed to the mirrors of Archimedes--the most particular account of which is given by the historians Zonaras and Tzetzes, both of the twelfth century.[H] 'Archimedes,' says the first of these writers, 'having received the rays of the sun on a mirror, by the thickness and polish of which they were reflected and united, kindled a flame in the air, and darted it with full violence on the ships which were anch.o.r.ed within a certain distance, and which were accordingly reduced to ashes.' The same Zonaras relates that Proclus, a celebrated mathematician of the sixth century, at the siege of Constantinople, set on fire the Thracian fleet by means of bra.s.s mirrors. Tzetzes is yet more particular. He tells us, that when the Roman galleys were within a bow-shot of the city-walls, Archimedes caused a kind of hexagonal speculum, with other smaller ones of twenty-four facets each, to be placed at a proper distance; that he moved these by means of hinges and plates of metal; that the hexagon was bisected by 'the meridian of summer and winter;' that it was placed opposite the sun; and that a great fire was thus kindled, which consumed the Roman fleet.

[Footnote H: Quoted by Fabricius in his "Biblioth. Graec.," vol. ii., pp.

551, 552.]

"From these accounts, we may conclude that the mirrors of Archimedes and Buffon were not very different either in their construction or effects.

No question, therefore, could remain of the latter having revived one of the most beautiful inventions of former times, were there not one circ.u.mstance which still renders the antiquity of it doubtful: the writers contemporary with Archimedes, or nearest his time, make no mention of these mirrors. Livy, who is so fond of the marvellous, and Polybius, whose accuracy so great an invention could scarcely have escaped, are altogether silent on the subject. Plutarch, who has collected so many particulars relative to Archimedes, speaks no more of it than the former two; and Galen, who lived in the second century, is the first writer by whom we find it mentioned. It is, however, difficult to conceive how the notion of such mirrors having ever existed could have occurred, if they never had been actually employed. The idea is greatly above the reach of those minds which are usually occupied in inventing falsehoods; and if the mirrors of Archimedes are a fiction, it must be granted that they are the fiction of a philosopher."

Supposing that Archimedes really did project the concentrated rays of the sun on the Roman vessels, one cannot help pitying the ignorance of the Admiral Marcellus. Had this officer been acquainted with the laws of the reflection of light, he might have laughed to scorn the power of Archimedes, and by receiving the unfriendly rays on one of the bright brazen convex shields of his soldiers, Marcellus could have scattered the concentrated rays, and prevented the burning of his vessels.

In these days of learning it therefore appears strange to find any one advocating the possible use of specula or reflecting mirrors for the purposes of offence or defence, but M. Peyrard a few years ago proposed [Page 293] to produce great effects by mounting each mirror in a distinct frame, carrying a telescope so that one person could direct the rays to the object intended to be set on fire, and he gravely calculated, presuming on the ignorance of the attacked, that with 590 gla.s.ses of about twenty inches in diameter, he could reduce a fleet to ashes at the distance of a quarter of a league! and with gla.s.ses of double that size at the distance of half a mile! What effect a sh.e.l.l or shot would produce upon this ancient weapon is not stated; this we may safely leave our readers to determine for themselves. The experiment of Archimedes has long been a favourite one with the boys. (Fig. 281.)

[Ill.u.s.tration: Fig. 281. One of the "miseries of _reflection_."]

The total internal reflection of light by a column of water is an experiment that admits of great variety so far as colour is concerned, and is one of the most novel and beautiful experiments with light presented to the public within the last few years. The author had the pleasure of introducing it in the first place at the Polytechnic Inst.i.tution, where the optical novelty excited the greatest attention, and received the approbation of her Most Gracious Majesty, and his Royal Highness the Prince Consort, with the Royal Family, who were pleased to pay a private evening visit to the Polytechnic, and amongst other things minutely examined the "Illuminated Cascade," which had been erected by Mons. Duboscq of Paris.

The illumination of the descending columns of water was obtained by converging the rays from a powerful electric light upon the orifice from [Page 294] which the water escaped, the Duboscq lantern already explained being employed, and in front of it were placed three cylinders, each having a circular window behind and opposite the lens, and an aperture of about one inch in diameter on the opposite side for the escape of water. The lantern used was of a peculiar shape, and had three sides, the electric light being in the centre of them, and pa.s.sing through three separate plano-convex lenses to the three cylinders from which the water escaped.

[Ill.u.s.tration: Fig. 282.--Fig. 1. A. The electric light. B C D. The three sides and lenses of the lantern. E F G. The three cylinders of water, each with a circular gla.s.s window and orifices at Z Z Z, from which the water and rays of light pa.s.s out.--Fig. 2. H. Section of one side of the Duboscq lantern. I I. Cylinder of water, which enters from below. K K. The stream of illuminated water. L L. Bit of coloured gla.s.s held between the lantern and the cistern of water.]

Attention may be directed to the fact that the light merely pa.s.ses out of the orifices as a diverging beam of light until the flow of water commences, when the rays are immediately taken up and reflected from [Page 295] point to point inside the arched column of water, and illuminating the latter in the most lovely manner, it appears sometimes like a stream of liquid metal from the iron furnace, or like liquid ruby gla.s.s, or of an amethyst or topaz colour, according to the colours of the plates of gla.s.s held between the mouths of the lantern and the circular windows in the cylinders of water. The same experiment created quite a _furore_ at the Crystal Palace when it was introduced in one of the author's lectures delivered in that n.o.ble place of amus.e.m.e.nt. In order that our readers may understand the arrangement of the apparatus, we have given at page 294 a ground plan view of it, as also the appearance of the cascade when exhibited at the Polytechnic to the Royal party. (Fig. 284.)

[Ill.u.s.tration: Fig. 283. A B. The sides of the cascade. The dotted lines show the reflection of only two rays of the beam of light pa.s.sing down inside the water.]

Another curious effect observed with the illuminated cascade, is the descent of b.a.l.l.s of light as the reflection is cut off for a moment by pa.s.sing the finger through the stream of water, showing that a certain time is occupied in the reflection of light from one end of the cylinder of water to the other; indeed the best idea of the _rationale_ of the experiment is formed by subst.i.tuting in imagination a silver tube highly polished in the interior, for the descending jet of water. The reflection of sound takes place precisely in the same manner, and the vibrations of the air are reflected from plane, concave, and convex surfaces. It is on this principle that waves of sound thrown off from different surfaces (as of hard rocks), produce the effect of the _echo_.

The sounds arrive at the ear in succession, those reflected nearest the ear being first, and the reflecting surfaces at the greatest distance sending the waves of sound to the ear after the former. At Lurley Falls on the Rhine, there is an echo which repeats seventeen times. Whispering galleries, again, ill.u.s.trate the reflection of sound from continuous curved surfaces, just as the arched column of water reflects from its interior curved surfaces the rays of light.

Speaking-tubes are well known in which the waves of sound are successively reflected from the sides, exactly like the "Illuminated Cascade" (Fig. 283). The speaking-trumpet is also another and familiar example of the same principle. Probably when Albertus Magnus constructed the brazen head, which had the power of talking, it was nothing more than a metallic head with a few wheels and _visible_ mechanism inside, but connected with a lower apartment by a hollow metal tube, where Albertus Magnus descended, and astonished the ignorant with [Page 296]

the then unknown principle of the speaking tube. Light entering at one end of a bright metallic tube is reflected from the sides of the tube till it reaches the other, and precisely the same effect occurs in the interior of the cascade of water. (Fig. 284).

[Ill.u.s.tration: Fig. 284. End of Polytechnic Hall, where the illuminated cascade was displayed to her Majesty, H.R.H. the Prince Consort, and Royal party. The cascades issued from behind some artificial rock-work.]

THE KALEIDOSCOPE.

If this article on light and optics had gone minutely into the mathematical and purely scientific portion of the subject, we should have had frequent occasion to mention the name of Sir David Brewster, a distinguished philosopher, whose name is peculiarly identified with this interesting branch of physics. It is always pleasing to find men of such standing not only devoting themselves to arguments which college wranglers would study with pleasure, but also descending to a lower level, and inventing optical instruments that delight and amuse the non-scientific and juvenile part of the community. The names of Sir David Brewster and Professor Wheatstone have been connected during the last few years with the invention of the stereoscope, an instrument [Page 298] that will be noticed in another part of this book, but here we shall describe one of the most original optical instruments ever devised, and although it is now regarded as a mere toy, its merits are very great. The t.i.tle of the instrument is borrowed from the Greek [Greek: _kalos_], beautiful, [Greek: _eidos_], a form or appearance, [Greek: _skopeo_], to see; and the public certainly endorsed the name when they purchased 200,000 of these instruments in London and Paris during the s.p.a.ce of three months. It is said that the sensation it excited in London, throughout all ranks of the community, was astonishing, and people were everywhere seen, even at the corners of the streets, looking through the kaleidoscope. The essential parts of this instrument are two mirrors of unsilvered black parallel gla.s.s, or plate gla.s.s painted black on one side, which should be from six to ten inches in length, and from one inch to an inch and a half in breadth at the object end, while they are made narrower at the other end, to which the eye is applied. The mirrors are united at their lower edges by a strip of black calico fixed with common glue, and are left open at the upper edges, and retained at the proper angle by a bit of cork properly blackened. The angles are 36, 30, 25-5/7, 22, 20, 18, which divide the circ.u.mference into 10, 12, 14, 16, 18, 20 parts, thus 36 10 = 360, or 18 20 = 360, and the strictest attention must be paid to this part of the adjustment, or the figures produced will not be symmetrical. After the mirrors are adjusted to [Page 298] the proper angle, the s.p.a.ce between the two upper edges should be covered across with black velvet and the mirrors placed in a tin or bra.s.s tube, so that the broad ends shall barely project beyond the end, while the narrow end is placed so that the angle formed by the junction of the mirrors shall be a little below the middle of that end of the tube. A cover with a circular aperture in the centre is then to be fitted to the narrow end of the mirrors, which should in general be furnished with a convex lens whose focal length is an inch or two greater than the length of the mirrors. A case for holding the objects, and for communicating to them a revolving motion, is fitted to the object end of the tube. The objects best suited for producing pleasing effects are small fragments of coloured gla.s.s, wires of gla.s.s, both spun and twisted, and of different colours and shades of colours, and of various shapes, in curves, angles, circles; also, beads, bugles, fine needles, small pieces of lace, and fragments of fine sea-weed are very beautiful. M. Sturm, of Prague, has lately fixed the images of the kaleidoscope, so that they are available for the production of patterns in every branch of silk, cotton, and mixed fabrics. Photographs could be taken of the most beautiful of these accidental designs, which only occur once, and if not copied are lost.

[Ill.u.s.tration: Fig. 285. A B. The tube containing the two mirrors, shown by dotted lines. A. is the small end where the eye is placed. B. The object end. C D. Another view of the mirrors arranged to place in the tube; the shaded portion represents the black velvet. E. Double convex lens. F. Box to contain objects, and usually fitted with ground gla.s.s outside.]

CHAPTER XXII.

THE REFRACTION OF LIGHT.

This term appears to be often confounded with that of reflection, and signifies the bending or breaking back of a ray of light (_re_, back, and _frango_, to break); and it will be remembered that when light falls on the surface of a solid (either liquid or gaseous) body, it may be reflected (_re_, back, and _flecto_, to bend), refracted, polarized, or absorbed. In the previous chapter the property of the reflection of light has been fully investigated, and in this one refraction only will be considered. It is a property which has been, and will continue to be, of the greatest practical utility in its application to the construction of all magnifying gla.s.ses, whether belonging to the telescope, microscope, magic lantern, or the dissolving views; or the minor refracting instruments--such as spectacles, opera-gla.s.ses, &c.; and it should be remembered that their magnifying power depends solely on the property of refraction.

If substances such as gla.s.s had not been endowed with this property, it would be difficult to understand how the great discoveries in the science of astronomy could have been made, or what information we could have gained respecting those interesting truths so constantly revealed by the aid of the microscope. Numerous instances might be quoted of the value of this latter instrument in the detection of adulteration, and the examination of organic structures. When so many talented and industrious scientific men are at work with this [Page 299] instrument, it is perhaps invidious to point to one singly, though we must make an exception in favour of Professor Ehrenberg, of Berlin, whose microscope did such good service in procuring undeniable proof of the Simonides'

fraud; he has made use of it again to detect the thief that stole a barrel of specie, which had been purloined on one of the railways. One of a number of barrels, that should have contained coin, was found on arrival at its destination to have been emptied of its precious contents, and re-filled with sand. On Professor Ehrenberg being consulted, he sent for samples of sand from all the stations along the different lines of railway that the specie had pa.s.sed, and by means of his microscope identified the station from which the sand must have been taken. The station once discovered, it was not difficult to hit upon the culprit in the small number of _employes_ on duty there.

[Ill.u.s.tration: Fig. 286.]

The simplest case of refraction occurs in tracing the course of a ray of light through the air, and into the medium water; in this case it pa.s.ses from a rare to a dense medium, and the fact itself is well ill.u.s.trated by the next diagram, in which the shaded portion represents water, and the paper that it is drawn upon the air. The line A B is a perpendicular ray of light, which pa.s.ses straight from the air into and through the water, without being changed in its direction. The line C D is another ray, inclined from the perpendicular, and entering the water at an angle, does not pa.s.s in the straight line indicated by the dotted line, but is refracted or bent towards the perpendicular at D E.

This fact reduced to the brevity of scientific laws is thus expressed:--When a ray of light falls perpendicularly on a refracting surface, _it does not experience any refraction or change of direction_.

When light pa.s.ses out of a rare into a dense medium, as from air into water, _the angle of incidence is greater than the angle of refraction_.

And when light pa.s.ses from a dense into a rare medium, as out of water into air, _the reverse takes place_, and _the angle of incidence is smaller than the angle of refraction_.

In order to ill.u.s.trate these laws, a zinc-worker or tinman may construct a little tank, with gla.s.s windows in the front and sides, the latter being as deep as the half-circle described on the back metal plate of the tank, which of course rises higher, in order to show the full circle; this should be j.a.panned white, and a perpendicular and horizontal black line described upon it--the whole, with the exception of the circle, being j.a.panned black. If the Duboscq lantern is arranged with the little mirror, as described in fig. 276, page 287, the ray of light may be thrown perpendicularly, or at an angle, through the water, [Page 300] and the actual breaking back of the ray of light is rendered distinctly apparent. (Fig. 287.)

[Ill.u.s.tration: Fig. 287. A. Duboscq lantern. B. The mirror. B C. The incident ray. C D. The refracted ray. E F. Tank, containing water up to the horizontal line of the circle.]

The refraction of light is also well displayed by Duboscq's apparatus, with the plano-convex lens, and a bra.s.s arrow as an object, with another double convex lens to focus it. When a good sharp outline of the arrow is obtained on the disc, a portion of the rays of light producing it may then be truly broken out or refracted by laying across the bra.s.s arrow a square bar of plate gla.s.s. (Fig. 288).

[Ill.u.s.tration: Fig. 288. A. Rays of light from the electric light. B.

The cap, with figure of arrow cut out. C. The bar of plate gla.s.s. D. The double convex gla.s.s to focus E, the image on the disc, and portion refracted at B.]

There are many simple ways in which the refraction of light is displayed, such as the apparent breaking of an oar where it enters the water, or the remarkable manner in which the bottom is lifted up when we look, at any angle, through the clear water of a deep river or lake; the latter circ.u.mstance has unhappily led to most serious accidents, in consequence of children being induced by the apparent shallowness of [Page 301] the water to get in and bathe. Fish, again, unless seen perpendicularly from a boat, always appear nearer than their true position, and the Indians, when they spear fish, always take care to strike as near the perpendicular as possible; experienced shots know they must aim a little lower and nearer than the apparent position of a fish in order to hit it.

Having learnt that light is bent from its course, it might be supposed that all objects looked at through plate gla.s.s should appear distorted; but it must be remembered that the sides of the gla.s.s being nearly parallel, an equal amount of refraction occurs in every direction--so that, unless the window is glazed with uneven wavy gla.s.s, the object, for all practical purposes, does not apparently change its position, being neither moved to the right or the left, or upward or downward. In order to bend the rays of light in the required direction, the gla.s.s must be cut into certain figures called prisms, plane gla.s.ses, spheres, and lenses, some of which are shown in the annexed cut. (Fig. 289.)

[Ill.u.s.tration: Fig. 289.]

[Ill.u.s.tration: Fig. 290. A B. A double convex lens. C is a ray of light, which falls perpendicularly on A B, and therefore pa.s.ses on straight to F, the focus. D D. Rays falling at an angle on A B, refracted to focus, F.]

It would be tedious to trace out, by a regular series of diagrams, the pa.s.sage of light through the variety of combinations of lenses; and as the plane, convex, and concave surfaces have been examined with respect to their effect on the reflection of light, they may be referred to again with regard to their influence in refracting light. In the latter it will be found that convex and concave lenses have just the opposite properties of mirrors; thus, a convex lens receiving parallel rays will cause them to converge to a focus. (Fig. 290.) The case of _short-sighted_ persons arises from too great a convexity of the eye, which makes a very near focus; and that of old people is a flattening of the eye, by which the focus is thrown to a greater distance. The remedy for the latter is a convex spectacle-gla.s.s, whilst a concave lens is required for the former, to scatter the rays and prevent their coming to a point too soon.

[Page 302]

The action of a concave refracting surface is again the opposite to a concave reflecting surface--the former disperses the rays of light, whilst, the latter collects them. A concave lens, as might be expected, produces exactly the contrary effect on light to that of a concave mirror. (Fig. 291.)

[Ill.u.s.tration: Fig. 291. A B. A double concave lens. C., is a ray of light which falls perpendicularly on A B, and pa.s.ses through without any alteration of its course. D D. Rays falling at an angle on A B, are refracted and diverged.]

These facts are well shown with the aid of the lantern and electric light. The rays of light are refracted in a visible manner when received on a concave or convex lens, provided a little smoke from paper is employed, as in the mirror experiments. (Fig. 292.)

[Ill.u.s.tration: Fig. 292. A. The electric light. B. The lens.]

Bearing these elementary truths in mind, it will not be difficult to follow out a complete set of ill.u.s.trations explanatory of the construction and use of various popular optical contrivances.

[Page 303]

CHAPTER XXIII.