plate, P, at the proper angle with the perpendicular. On one end, R, lay a piece of good looking-glass the size of the end; and in the other end cut a hole in which the Nicol, N, or other analyser, can be rotated (Fig. 158). The object can

N

F

B

FIG. 158.-Simple Doubler.

be held between P and R, or even laid on the looking-glass itself in many cases. For most purposes of the "doubler" no focusing lenses will be required. I have even laid a piece of looking-glass on the table, and arranged over it a plate of clear glass at the proper angle by means of the Bunsen universal holder (Fig. 12), holding the Nicol in my hand.

NOTE ON ARTIFICIAL NICOL PRISMS.

The second half of a Nicol having no doubly-refracting effect, I have sometimes thought that large spar might be made to do double duty by making the second half of glass of the proper density. MM. Jamin and Soleil have employed an oblong cell with glass ends filled with bisulphide of carbon, across which was slanted a mere film of calcite. The bisulphide might be brought to exactly the higher index by benzol, and it will be seen that with this apparatus the action of the Nicol is precisely reversed, the total reflection taking place in the calcite. But though theoretically perfect, this apparatus is dangerous, owing to the heat of the lantern.

CHAPTER XII.

CHROMATIC PHENOMENA OF

PLANE-POLARISED LIGHT. LIGHT AS AN ANALYSER OF MOLECULAR CONDITION.

Resolution of Vibrations-Interference Colours-Why Opposite Positions of the Analyser give Complementary Colours-Coloured Designs in Mica and Selenite-Demonstrations of InterferenceCrystallisations-Organic Films-Effects of Strain or TensionEffects of Heat-and of Sonorous Vibration.

134. Resolution of Vibrations.-We could have formed no conclusion as to the precise orbits of the molecules of ether in our polarised waves, apart from the phenomena; but if we have rightly interpreted these, then any one acquainted with elementary mechanics and the "resolution of forces" will see that we can test such a theory by experiment. Dealing with motions whose direction we are supposed to know, if we are correct we can "resolve" those motions. Taking a perpendicular plane of vibration, for instance, and supposing our ether-atoms move solely in the plane orbit A B, B A (Fig. 159), if we interpose a plate of crystal which only permits of vibrations in the directions в C, B D, the perpendicular plane must be resolved into two planes at an angle of 45° with the original plane.

It seems evident already that we have done this, from the duplication of our images when the two double-image prisms

were at an angle of 45° with one another, and from the transmission of half the light through our two tourmalines at the same angle. But if we are right, the two oblique planes must be also capable of resolution in their turn, by the analyser, into perpendicular and horizontal planes; and when our polariser and analyser are crossed and the "field," therefore, quite dark, if we interpose between them a tourmaline at 45° we ought to restore the light. Cross therefore the Nicol or other analyser till the screen is dark, and insert the rotating tourmaline. Sure enough, as we rotate it, though the tourmaline is really a brown tint

FIG. 159.-Effect of a Crystalline Film.

mounted on a clear glass, it appears as a light image on the dark field.

We have, however, learnt that the tourmaline stops one of the rays, and we wish to see beyond doubt if the original plane really is resolved into two planes. We therefore want a slice of some crystal which allows both halves of the doubly-refracted ray to pass, and either selenite or mica is convenient, as splitting easily into thin plates, which contain both planes of vibration at right angles to a ray transmitted through them. A crucial test suggests itself. In F, Fig. 132, we re-compounded one beam out of the two beams from our first doubly refracting prism. We see, on reflection, that if each of the first two beams is really again split by a

properly adjusted film into two, vibrating in planes at 45° angle with them, that is no longer possible, and there must remain at least three images. We find, then, by experiment with polariser and analyser crossed, the position of the slice of selenite which still leaves the field dark, and which, of course, gives us its polarising planes. We then mount a circular disc of it in a position at 45° angle with that, in a wooden slider an inch wide, and 4 inches long, with a circular hole in the centre for the slice, protected between two discs of glass. With the two double-image prisms giving the single beam F, we introduce the slider into the slit s provided for it in our Huyghens' apparatus, Fig. 131. Our expectation is justified to the letter; for three images at once appear on the screen.

135. Interference Colours of Polarised Light.— But here we have another beautiful phenomenon. If the slice of mica or selenite be thin, these are coloured images, and each pair presents complementary colours; for if the images overlap anywhere, we get there white light. These coloured images are singularly beautiful as the front prism is rotated; and that is why the Huyghens' apparatus was recommended to be arranged as described.

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We can readily understand, this colour. In every bifurcation of the ray, it is doubly refracted because of unequal elasticity, and one ray is more retarded than the other. We can see" this in a large piece of Iceland spar, for one of the images of a black spot seen through it appears nearer than the other. The two rays, while they vibrate in planes at right angles to each other, cannot of course interfere; but the analyser brings portions from each again into the same plane. Now in the rigid plane orbit of our original polarised beam we have that identity of origin we have already learnt (§ 96) is necessary for two rays to interfere; and in the absolute plane into which the rays separated by

the selenite are again united by the analyser we have that identity of path, or nearly so, we also found to be necessary. We bring together again, then, into the same plane (that of the analyser) two originally identical rays, one of which, during separation, has got behind the other in passing through the film by a given distance, depending on the thickness of the film of crystal. But whilst in reflection from a "thin film," one ray is retarded by twice the thickness of the film; in this case one ray is retarded by the difference in velocity, whilst both traverse the same film. Of course a much thicker film is required in this latter case; and, of course also, the greater the difference in the two indices of refraction, the thinner the film must be to produce a given colour. Too great a thickness, of course, gives no colour; for the same reasons too thick a "thin film" gives none (§ 101).

136. Cause of Complementary Colours. To explain the "complementary" colours, we must take into account the direction as well as the plane of vibration of the ether-atoms, at each moment of bifurcation or resolution into two planes at 45° angle with their path at that moment. Let us suppose the original plane-polarised ray a, Fig. 160, is at the phase when the atoms are moving downwards when it meets the selenite with its planes at 45°. The bifurcated rays must obviously travel in the directions B and C. Now B, when again resolved by the analyser, must take the directions D and E, and c of F and G. A double-image prism would transmit both, but by our Nicol analyser when crossed or parallel one plane or other is stopped. It is readily seen that when in the position which allows the two perpendicular vibrations to get through, these two (D F) are in the same phase of their orbits, and so coincide with or strengthen each other; but if the horizontal vibrations get through, E and G are in contrary phases, or destroy each other. However, therefore,