lens, L, figs. 3 and 4, Plate I.; a parabolic conoid, a, truncated at its parameter; and a hemispherical mirror, b. The lens, when at its proper focal distance from the flame, subtends the same angle from it as the outer lips of the paraboloid. The hemispherical reflector occupies the place of the parabolic conoid which has been cut off behind the parameter. The flame is at once in the centre of the hemispherical mirror and in the common focus of the lens and paraboloid. Suppose the whole sphere of rays emanating from the flame to be divided into two portions, viz., the hemisphere of front rays and the hemisphere of back rays. Part of the anterior hemisphere of rays is intercepted by the lens and made parallel by its action, while the remainder is intercepted by the paraboloidal surface and made parallel by its action. The rays forming the posterior hemisphere, and which fall upon the hemispherical reflector, are sent back through the focus. in the same lines, but in directions opposite to those in which they came, whence passing onwards they are in part refracted by the lens, and the rest are made parallel by the paraboloid. The back rays thus finally emerge horizontally in union with the light from the anterior hemisphere. This instrument, therefore, fulfils the conditions prescribed by collecting the entire sphere of diverging rays into one parallel beam of light. The first instrument which I had constructed upon this principle, was for the North Harbour of Peterhead, and has been in use since August 1849. Mr A. Stevenson has also introduced an instrument of this kind, on a large scale, into HoY SOUND LIGHTHOUSE, one of the Northern Lights stations.*

Experiments were lately made at Gullane Hill on the comparative power of a brass reflector on this principle, and a highly finished silver reflector of the usual construction, both instruments being 25 inches in diameter at the lips. The lights were viewed at distances of from 7 to 12 miles every night during a week, and in every instance the brass reflector on the holophotal principle had the advantage of the silver

* At Hoy Sound there are two leading lights, the highest, which is of a red colour, requiring to be visible a great distance seaward. The Hoy reflector is of very great size. It measures 45 inches across the mouth, the lens is 11 inches in diameter, and the light is produced by a double wick-burner.

reflector, although it cost only about half as much as the other; and on one occasion, when the atmosphere was thick, the light from the holophotal brass reflector was alone visible. As the great objection to red, green, and other coloured lights, is the enormous loss by absorption, the holophotal arrangement seems specially adapted to all lights which pass through coloured media.

Another modification of the holophotal metallic reflector still remains to be described. The execution of such an instrument as that shewn in figs. 3 and 4, if of a large size, is necessarily attended with considerable difficulty. To remedy this evil, as well as to render the instrument smaller and more compact, I have recently had reflectors made of the form shewn in figs. 5 and 6. This plan consists of the union of two or more paraboloids, each having a different focal distance, with a spherical mirror and a lens. By this arrangement, the whole light is rendered parallel, in the same manner as in the instrument first described.*

Totally Reflecting Holophotal Apparatus, substituted for the

Metallic Paraboloid.

In so far as concerns the arrangement of the different parts, irrespective of the nature of the materials of which they are composed, the light emitted from any given flame by the instruments just described, should be the light of maximum intensity. But, as already stated, the most accurate experiments which have been undertaken by scientific observers, have shewn that reflection from the best silvered mirrors, and even from metallic specula made with the utmost care for experimental purposes, involves a loss of light by absorption of not less than about one-half of the whole incident rays.†

The advantage of employing as largely as possible the principle of total reflection from glass, in place of ordinary reflection from metallic specula, induced me to attempt further improvements in the Holophotal system of illumination. M. L. Fresnel found that the totally reflecting prisms p, figs. 11 and

* A small temporary light for Morecambe Harbour, Lancashire, is now being made of this form.

↑ Vide Brewster's Optics.

12, Plate II., of fixed lights were superior to the silvered mirrors which were formerly in use, in the proportion of 140 to 87.* It occurred to me that it might be possible to construct totally reflecting prisms so as to obtain a lenticular action in every plane. In the holophotal apparatus, figs. 3 and 4, Plate I., if we retain the lens and the spherical mirror, and in place of the paraboloid, we conceive the arc between the lens and the spherical mirror to be filled up with glass rings, which are the solids of revolution generated by the rotation of the cross section of the totally reflecting prisms used in fixed lights, round a horizontal axis passing through the flame, we shall then have succeeded in extending the action of the lens, so as to parallelize one-half of the whole sphere of incident rays.† Such an arrangement is shewn in figs. 7 and 8, Plate II., where L is the lens, p the totally reflecting prisms, and 6 is the spherical mirror. The distinguishing peculiarity of this arrangement is, that the prisms, instead of transmitting the light in parallel vertical plates, diverging all round as in the fixed light apparatus of Fresnel (figs. 11 and 12), produce an extension of the lenticular or quaquaversal action of the common annular lens, by assembling the light around its axis in the form of concentric hollow cylinders. In order to distinguish this system of prisms from those introduced by M. Fresnel, which have no lenticular action, they may therefore be termed "holophotal" or "catadioptric lenses."

Holophotal Apparatus, consisting entirely of Glass, and acting by refraction and total reflection only.

I shall now describe a method of replacing the hemispherical reflector of metal or silvered glass, by means of a polyzonal totally reflecting hemisphere of glass, vide fig. 9, Plate II. By this arrangement reflection from metallic specula is abolished from every part of the system, and the principles of total reflection and simple refraction are substituted.

* Vide Treatise on Illumination of Lighthouses, by Alan Stevenson, LL.B., F.R.S.E., Civil Engineer.

†These prisms might perhaps be extended in number so as to take in even more than the half sphere of rays.

The action of these glass zones will be best understood by referring to fig. 10, which gives the cross section of one of them; shews the flame or centre of the system, and the diverging rays are represented by dotted lines, the arrows indicating the direction of one diverging ray before and after being altered by the prism. The side b c is concave, the centre of curvature being in f the centre of the flame. The surfaces of the other sides, a b, and a c, are portions of parabolas whose common focus is f, or of circles osculating the parabolic curves. Those parabolic surfaces face each other, and their tangents form an angle of 90° with each other at the vertex of the prism. Any ray proceeding from the centre ƒ will be received as a normal to the surface bc, and will consequently pass on without suffering any deviation from e, where it meets the prism, to its incidence on the surface a b, where it will be totally reflected in the direction rr, tangential to the sphere at the axis of each zone. At it again suffers total reflection, and finally emerges in a radial direction without deviation at the point e'. An exactly similar action will take place simultaneously with another ray in the same path from the flame, though passing in an opposite direction. The concentric zones, a, which compose the dome, vide fig. 9, are solids of revolution, generated by the rotation round the horizontal axis of the instrument of triangles similar to a b c, fig. 10, with a radius equal to a f. The angle formed by the radius with the horizontal axis of the instrument varies from nearly 90° down to zero, as shewn in fig. 9. Where those angles vanish at a', a conoid will result, having the radius of its base equal to the semichord of its inner surface. The formule for calculating such zones, by Mr William Swan, who has kindly rendered me much assistance in prosecuting this part of the subject, are printed in the Society's Transactions.* The prisms b a c, resemble in their action that of the drops of rain which give rise to the natural phenomenon of the rainbow. From this peculiarity, these zones may be distinguished by the name of "Rainbow Prisms." In fig. 9, which shews the whole

* Page 20. (Vol. iv.)

instrument complete, L represents the common lens acting on the rays by refraction only; p, the catadioptric portion of the lens acting by refraction and total reflection; and a a' a, the "rainbow prisms" acting by total reflection only. Should the execution of the hemispherical dome be attended with success, the effect will be striking, as no direct light from the flame should be visible behind the apparatus, although the screen interposed is but of transparent crystal. When in Paris, in March 1850, I had an opportunity of shewing a model and drawings of this apparatus to M. Fresnel, and also to M. Letourneau, the manufacturer of the French lenses. M. Fresnel was of opinion that theoretically, it was wholly without defect, although the execution might be found troublesome.* Mr John Adie, optician, is at present engaged in the construction of a complete apparatus on this principle, the diacatoptric lenses having been already finished.

Alteration of the Common Parabolic Lighthouse Reflector

to the Holophotal System.

To render holophotal the ordinary reflectors which are still much used in lighthouses, let there be cut off, vide fig. 2, Plate I., a small portion, a', a', behind the parameter, substituting a portion of a spherical mirror behind, and adding a lens, L, with three diacatoptric lenticular rings. The Horsburgh lighthouse, now being constructed on the Pedro Branca rock, near Singapore, according to plans by Mr J. T. Thomson, Government Surveyor, was lately fitted up with apparatus on this principle, under the direction of Mr A. Stevenson. It consists of a frame having nine holophotal reflectors of this kind. A similar apparatus is now being made for the new harbour light of Pulteneytown.†

It is worthy of remark that in this instrument there is no loss of light by superficial reflection.

†The reflector for Pulteneytown is constructed of zinc, which forms a cheap substitute for silver. I have also had made for me a porcelain reflector, 6} inches diameter, of what is called "lustre ware," which gives a good light, and requires no polishing. Were plane circular discs or portions of hollow spheres (which are the best forms) constructed of this material, and fixed in the top or cover of our street lamps, the light which now escapes upwards might, at a very trifling cost, be usefully directed downwards to the street.