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A beam of light is directed by the silvered plane mirror of a heliostat (A) into a darkened room.

It is received on an achromatic lens (B) 10 centims. in diameter; focal distance from posterior surface 70 centims.

A slit (C) is then placed within the focus of this lens, the distance being 48 centims. from the lens (B).

After passing through the narrow slit, which is about one tenth of a millimetre wide, the light is received upon a second achromatic lens (D), of the same diameter as the first, but with a focal





distance of 115 centims. The distance of this lens from the slit is 164 centims.; and the focusing of the lines of the spectrum on a paper screen or on the ground glass of the camera is accomplished by moving the lens (D) nearer to or further from the slit (C), or by moving the camera or screen (F) itself.

The grating (E), mounted on a suitable stand, is placed at a distance of 80 centims. from the second lens. All parts of the apparatus being carefully adjusted, so that A, B, C, D, E are on the same horizontal axis, the grating is then arranged on its vertical axis, to throw the centre of its reflected image on the opening of the slit (C).

The lines of the grating being accurately parallel to the sides of the slit, a series of beautiful spectra are produced on each side of the slit, any or all of which may be received on suitably adjusted screens, one of which is represented at F. In all of these spectra, if the slit is very narrow, the prominent Fraunhofer, with numerous other lines, appear sharply defined.

Of the spectra described above, only the first, second, and third orders on each side of the image of the slit are available for general use, on account of the overlapping of those that follow. Of those that are available, I have preferred to use the second order, since in this the dispersion is much greater than in the first, and by the apparatus described above a spectrum of a length of more than 30 centims. is obtained.

For the projection of the prismatic spectrum a prism is substituted in place of the grating, when a very fine spectrum is produced, the focus of the violet end of which is very much closer to the prism than that of the red end.

In the diffraction-spectra, also, it is necessary to vary the angle at which the screen is placed to define sharply the lines at the

extremities of each spectrum. In the spectra of the first order on each side, the screen is placed very nearly at right angles to a line drawn from the grating to B in the spectrum. As each order in succession is examined, the divergence from this angle is greater and greater, and at the same time the focal distance of the lines moves nearer to the grating.

The lenses I have employed were those of a very fine photographic combination; they give with the rest of the arrangement a spectrum in which the definition of the lines is perfect, and they are present by hundreds. Though the lenses are 10 centims. in diameter, only the central portion of each is used, a diaphragm with a circular aperture of 5 centims. or less being placed in front of B.

To form the absorbent spectra of any organic substance, a suitable solution of the same is poured into a cell with parallel sides. This is placed at any convenient point between A and B, care being taken that the faces of the cell are at right angles to the course of the ray A, B. The slit may in this case be opened wider, when each spectrum will show the characteristic absorbent bands of the substance employed, the position being indicated (and, if required, recorded) by their relation to the lines of the solar spectrum in which they are produced.

When the calcium or electric light is to be used for lectureroom demonstration of diffraction-spectra, the lens (B) should have as short a focus and as large a diameter as possible. The grating may also be so arranged on its vertical axis as to throw its image at a right angle to the line B E, to be there received on a screen. Though by this device the spectra on one side of the image of the grating are greatly elongated, and those on the other compressed, it presents the advantage of enabling the audience to see all the spectra at once, and also the optical contrivances by which they are produced.

XIX. Proceedings of Learned Societies.


[Continued from vol. xlviii. p. 541.]

May 7, 1874.-William Spottiswoode, M.A., Treasurer and VicePresident, in the Chair.

HE following communication was read :—


Addition to the Paper, "Volcanic Energy: an attempt to develop its true Origin and Cosmical Relations"*. By Robert Mallet, A.M., C.E., F.R.S., M.R.I.A., &c.

Referring to his original paper (Phil. Trans. 1873), the author

* Phil. Mag. vol. xliv. p. 468.

remarks here that, upon the basis of the heat annually dissipated from our globe being equal to that evolved by the melting of 777 cubic miles of ice at zero to water at the same temperature, and of the experimental data contained in his paper, he had demonstrated, in terms of mean crushed rock, the annual supply of heat derivable from the transformation of the mechanical work of contraction available for volcanic energy, and had also estimated the proportion of that amount of heat necessary to support the annual vulcanicity now active on our globe; but, from the want of necessary data, he had refrained from making any calculation as to what amount in volume of the solid shell of our earth must be crushed annually, in order to admit of the shell following down after the more rapidly contracting nucleus. This calculation he now makes upon the basis of certain allowable suppositions, where the want of data requires such to be made, and for assumed thicknesses of solid shell of 100, 200, 400, and 800 miles respectively.

From the curve of total contraction (plate x. Phil. Trans. part i. 1873) obtained by his experiments on the contraction of slags, he has now deduced partial mean coefficients of contraction for a reduction in temperature of 1° Fahr., for intervals generally of about 500° for the entire scale, between a temperature somewhat exceeding that of the blast-furnace and that of the atmosphere, or 53° Fahr. And applying the higher of these coefficients to the data of his former paper, and to the suppositions of the present, he has obtained the absolute contraction in volume of the nuclei appertaining to the respective thicknesses of solid shell above stated. In order that the shell may follow down and remain in contact with the contracted nucleus, either its thickness must be increased, its volume remaining constant, or the thickness being constant, a portion of the volume must be extruded. The former supposition is not admissible, as the epoch of mountain-building has apparently ceased; adopting the second, the author calculates the volume of matter that must be crushed and extruded from the shell in order that it may remain in contact with the nucleus. He tabulates these results for the four assumed thicknesses of shell, and shows that the amount of crushed and extruded rock necessary for the heat for the support of existing volcanic action is supplied by that extruded from the shell of between 600 and 800 miles thickness, and that the volume of material, heated or molten, annually blown out from all existing volcanic cones, as estimated in his former paper, could be supplied by the extruded matter from a shell of between 200 and 400 miles in thickness.

On data which seem tolerably reliable the author has further been enabled to calculate, as he believes for the first time, the actual amount of annual contraction of our globe, and to show that if that be assumed constant for the last 5000 years, it would amount to a little more than a reduction of about 3.5 inches on the earth's mean radius. This quantity, mighty as are the effects it produces as the efficient cause of volcanic action, is thus shown to be so small as to elude all direct astronomical observation, and, Phil. Mag. S. 4. Vol. 49. No. 323. Feb. 1875. L

when viewed in reference to the increase of density due to refrigeration of the material of the shell, to be incapable of producing, during the last 2000 years, any sensible effect upon the length of the day. The author draws various other conclusions, showing the support given by the principal results of this entirely independent investigation to the verisimilitude of the views contained in his previous memoir.

May 21.-William Spottiswoode, M.A., Treasurer and Vice-President, followed by Dr. Sharpey, Vice-President, in the Chair.

The following communications were read :



On Combination of Colour by means of Polarized Light." By W. Spottiswoode, M.A., Treas. and V.P.R.S.

The results of combining two or more colours of the spectrum have been studied by Helmholtz, Clerk Maxwell, Lord Rayleigh, and others; and the combinations have been effected sometimes by causing two spectra at right angles to one another to overlap, and sometimes by bringing images of various parts of a spectrum simultaneously upon the retina. Latterly also W. v. Bezold has successfully applied the method of binocular combination to the same problem (Poggendorff, Jubelband, p. 585). Some effects, approximating more or less to these, may be produced by chromatic polarization.

Complementary Colours.-First, as regards complementary colours. If we use a Nicol's prism, N, as polarizer, a plate of quartz, Q, cut perpendicularly to the axis, and a double-image prism, P, as analyzer, we shall, as is well known, obtain two images whose colours are complementary. If we analyze these images with a prism, we shall find, when the quartz is of suitable thickness, that each spectrum contains a dark band, indicating the extinction of a certain narrow portion of its length; these bands will simultaneously shift their position when the Nicol N is turned round. Now, since the colours remaining in each spectrum are complementary to those in the other, and the portion of the spectrum extinguished in each is complementary to that which remains, it follows that the portion extinguished in one spectrum is complementary to that extinguished in the other; and in order to determine what portion of the spectrum is complementary, the portion suppressed by a band in any position we please, we have only to turn the Nicol N until the band in one spectrum occupies the position in question, and then to observe the position of the band in the other spectrum. The combinations considered in former experiments are those of simple colours; the present combinations are those of mixed tints, viz. of the parts of the spectrum suppressed in the bands. But the mixture consists of a prevailing colour, corresponding to the centre of the band, together with a slight admixture of the spectral colours immediately adjacent to it on each side.

The following results, given by Helmholtz, may be approximately verified :—

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When in one spectrum the band enters the green, in the other a band will be seen on the outer margin of the red and a second at the opposite end of the violet-showing that to the green there does not correspond one complementary colour, but a mixture of violet and red, i. e. a reddish purple.

Combination of two Colours.-Next as to the combination of two parts of the spectrum, or of the tints which represent those parts. If, in addition to the apparatus described above, we use a second quartz plate, Q, and a second double-image prism, P,, we shall form four images, say OO, OE, EO, EE; and if A, A' be the complementary tints extinguished by the first combination QP alone, and B, B' those extinguished by the second Q, P, alone, then it will be found that the following pairs of tints are extinguished in the various images:

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It is to be noticed that in the image OE the combination Q, P, has extinguished the tint B' instead of B, because the vibrations in the image E were perpendicular to those in the image O formed by the combination QP. A similar remark applies to the image E E. The total number of tints which can be produced by this double combination Q P, Q, P, is as follows:

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Collateral Combinations.-The tints extinguished in the overlap 00+EO will be B, A, B', A; but since B and B' are complementary, their suppression will not affect the resulting tint except as to intensity, and the overlap will be effectively deprived of A alone; in other words, it will be of the same tint as the image O would be if the combination Q, P, were removed. Similarly the overlap OE+EE will be deprived effectually of A' alone; in other words, it will be of the same tint as E, if Q, P, were removed. If therefore

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