II. On the Bands formed by the Superposition of Paragenic Spectra produced by the Grooved Surfaces of Glass and Steel*.-Part I. By Sir DAVID BREWSTER, K.H., F.R.S.L. & E.†

[With a Plate.]

IN N examining the colours produced by thin laminæ of the crystalline lens of fishes, I observed a series of rectilineal serrated fringes perpendicular to the direction of the fibres, and produced by inclining the laminæ in a plane cutting these fibres at right angles. I was thus led to imitate these fringes or bands by combining grooves or striæ cut upon glass or steel surfaces, or grooves taken from these surfaces upon isinglass or gums.

In my first experiments I combined a system of grooves on glass, executed for me by Mr. Dollond, with a similar system on steel executed by Sir John Barton, both of them containing 2000 divisions in an inch. The plate of glass was placed above the plate of steel, and slightly inclined to it, as shown in Plate I. figs. 1 and 2. The glass plate A B C D, fig. 2, was covered with grooves, but the steel plate below it was grooved only on the shaded portion a bed, the parts AacC, Bbd D being polished so as to reflect to the eye at E (fig. 1), the grooves on the glass when illuminated by rays, Rr, proceeding from the first pair of the paragenic spectra produced by the grooves.

When the direction of the grooves ac is nearly parallel to the plane of reflexion, and to one another, a series of minute serrated bands is seen on the space abcd, where the light has been. transmitted twice through the grooves on glass, and reflected once from those on steel; but no bands are seen upon A ac C, Bbd D, where the steel was only polished.

When the grooves were slightly inclined to the plane of reflexion, large serrated bands appeared upon the spaces A a c C, BbdD; and when this inclination was increased, these large bands became smaller and more numerous, crowding towards Cc and d D. On the other hand, they become larger and larger as the direction of the grooves returned into the plane of reflexion. In the azimuth of 0° they become straight, and by increasing the azimuth, they pass, as it were, to the right hand, as shown in fig. 3.

When the direction of the grooves is inclined to the plane of

* In a very interesting paper on the Spectra produced by Gratings or Grooved Surfaces, M. Babinet has given them the appropriate name of paragenic, in order to distinguish the spectra produced by refraction from those produced by the lateral propagation of light. "Sur la Paragénie ou propagation latérale de la lumière." Paris, 1864. Extrait du Cosmos.

f From the Transactions of the Royal Society of Edinburgh, vol. xxiv.

reflexion, the minute serrated bands upon a bed become smaller and less serrated.

When the inclination m n N M of the grooved plates is increased, the large bands become smaller and smaller; and when it is diminished, they become larger and larger, getting inclined as in fig. 3, and becoming parallel at 0° of inclination.

Having been provided, by the kindness of Sir John Barton, with two grooved plates of glass containing 500 divisions in an inch, I was enabled to examine the fringes on the paragenic spectra under different circumstances.

When the grooved surfaces of the plates were placed in contact, and the grooves formed a small angle with one another, the middle or principal image, A (fig. 4), when observed with a lens whose anterior focus coincided with the grooves, had no bands, but the paragenic spectra a, c, b, d on each side had numerous serrated bands or fringes perpendicular to the direction of the grooves, the number on the first spectra a, b being at the rate of 19 in an inch of the luminous disk, and increasing in arithmetical progression.

When the luminous object is rectangular, and the rectangular paragenic spectra are brought nearly into contact, as at ab and cd (fig. 5), the bands, as seen at nearly a perpendicular incidence, are shown in this figure.

When the incident light is inclined to the direction of the grooves, the bands suffer no change, and appear immoveable on the surface of the glass plates.

When the ray of light is perpendicular to the direction of the grooves, and the surface of the glass on which they are cut is inclined to the ray of light, the bands all descend from a to b (fig. 5), moving off, as it were, at b and d and succeeded by others when the angle of incidence increases, while they ascend from b to a and from d to c, moving off at a and c, when the angle of incidence diminishes. In this case the grooves of the plate next the eye are turned to the left, the opposite motions taking place when they are turned to the right*.

The bands correspond to the intersection of the one set of grooves with the other set; and consequently they diminish in nuniber and recede from one another when the inclination of the one set of grooves to the other diminishes, becoming parallel to the grooves when the grooves on both plates are parallel.

Interference bands parallel to the grooves may be seen by transmitted light upon the paragenic spectra when two systems of grooves are placed parallel to each other, and when the grooves in the one system are parallel to those in the other.

* This motion of the bands is not seen when the grooved surfaces are perfectly parallel.