wise directed his attention to the advantages which would theoretically result from having a reflector, whose section should not be the arc of circle, but of a parabola; in which case, by a property of that curve, all rays falling parallel to the axis would be accurately brought to convergence at the focus. He devised methods for forming such surfaces; but the practical difficulties encountered were so great that no advantage could be derived from the idea. Subsequent artists have experienced the same difficulties; and all attempts to prosecute such a plan have long since been abandoned; and after all, perhaps, the advantages have been overrated, since a very slight deviation from exact parallelism to the axis, would occasion considerable aberration from the true focus.

Gregory was a man of highly acute and original mind; and in a remote situation supplied the want of intercourse with the scientific world from the powerful resources of his own genius. Having no communication with the Continent, he had never seen the works of Snell or Des Cartes; but he deduced for himself the law of refraction, by an independent investigation.

Double Refraction.

Erasmus Bartholinus, in 1669, first observed the singular fact, that a small object seen through a transparent crystal of the Iceland spar appeared double. He pursued the subject, however, but little further than to give some very general description of it. It was evident that the ray was divided into two within the crystal, following different laws of refraction.

Huyghens soon after directed his attention to the phenomena of the doubly refracting crystal; by a series of accurate measurements, he determined the directions assumed by the two rays under all varieties of direction of the incident ray. One of the rays was found to follow the ordinary law of the sines in the plane of in cidence; the other followed a variable law of deviation,

and this, too, in a variable plane. Huyghens, however, succeeded in tracing the law of these changes, which is somewhat complex. He illustrated it by a geometrical construction, which represents the position of the ray in all cases; but of which it would be impossible to give any general description. It was, however, intimately connected with a theory of which we must now proceed to give some account.

Theory of Undulations.

Perhaps the most curious portion of Huyghens's investigation consists in his very remarkable theory of light, which, framed in the first instance upon the simplest conceptions, and admirably applying to the representation of the ordinary phenomena, was soon found to be no less beautifully applicable to the morè complex case of double refraction. This theory was first communicated to the Academy of Sciences at Paris in 1678; but afterwards published in a separate form in 1690, under the title of "Traité de la Lumière." Propounded, in the first instance, to explain the limited range of optical phenomena then known, this theory, with a few modifications, has been found in the hands of subsequent philosophers to afford by far the most complete and satisfactory representation of nearly all the varied and complicated results which optical experiments have disclosed. The original idea of Huyghens was simply this: that an inconceivably subtile and elastic medium, or æther, pervades all space and all bodies, existing within denser media in a state of greater condensation. Waves, pulsations, or undula tions excited in this medium are propagated in different directions, according to the impulse originally commu nicated by some peculiar action of those bodies which we call luminous; and these pulsations reaching our eyes, affect us with the sensation of vision. Under ordinary circumstances these undulations are propagated from the original centre of excitation in a regular cir

cular or spherical form, somewhat like the circles produced on dropping a stone into the water.

By an application of these views by no means difficult, he gave a complete explanation of the ordinary phenomenon of reflection and refraction. In reflection the waves rebound in a way easily imagined; in the case of refraction, owing to the increased density, the undulations are propagated more slowly within the transparent medium than in the air. Hence, in order to pass in the same time, the waves must take a shorter course; that is, (impinging obliquely) must proceed in a direction nearer to the perpendicular, and this in proportion to the increase of density. The ratio is that of the refracting power of the medium; and it easily follows, that it is the same as that of the sines of the angles which the incident and refracted rays (or direction of the radius of the front of the waves) make with the perpendicular to the surface. This agreed exactly with Fermat's reasoning, before referred to.

The undulatory theory thus admirably applying to the ordinary refraction of a single ray, Huyghens proceeded to enquire into its applicability to the phenomena of double refraction. The ordinary ray was admitted to follow the ordinary law of the sines, and to be represented by spherical undulations. The extraordinary refraction could be expressed by no simple law (as before observed), but it might be represented by a complicated construction, in which its position is assigned by means of a plane always touching a spheroid. This geometrical theory corresponded exactly with the physical theory of a set of undulations propagated no longer in a spherical, but in a spheroidal form. By assuming, then, undulations of this kind in certain crystallised media, by which one portion of the light proceeded, whilst the other was propagated in common spherical undulations, a faithful presentation was given of the phenomena of double refraction. The theory thus far, then, was assigned purely as an hypothesis which explained the phenomena. It was further to be tried, to be received or

rejected, as it might apply or not to such new phenomena as might afterwards be discovered. Though, as we shall see, several facts in optics were brought to light soon after, yet it does not appear that any attempt was made to apply this theory to their explanation.

Inflection of Light.

Grimaldi, a learned Jesuit, published at Bologna in 1665 an account of some remarkable phenomena in optics, which have subsequently acquired a high degree of interest and importance. Indeed, considering the very singular and even paradoxical nature of one of the results, it is astonishing that they did not attract more attention at the time.

The main fact, which he examined with great care, was this: On placing a narrow opaque body, such as a wire or hair, in a beam of the sun's light, admitted through a pin-hole into a dark room, he found the shadow received on a screen at different distances considerably broader than, upon a geometrical construction of rectilinear rays, it ought to be at those distances. The width of the shadow was defined accurately by certain bright lines, which appeared running parallel to the edges of the hair: all within these being considered as shadow, though the darkness gradually diminishes from the central part towards the boundaries. He also noticed, that when the breadth of the opaque body does not exceed a certain amount, the middle part of the shadow, instead of being uniformly dark, is streaked with several parallel bright and dark bands, in the direction of its length, the centre band being always bright, the number varying with the breadth and dis

tance.

He considered all these phenomena due to a certain bending or inflection, as he called it, which he supposed the rays to undergo in passing near the edges of the opaque body; and that these stripes within the shadow were due to the joint action of the two portions of light

coming from each side. The result he broadly announced by saying, that in this case the joint action of two portions of light produced darkness.

Dr. Hooke appears to have tried similar experiments, without any knowledge of what Grimaldi had done. In 1672 and 1674, he communicated two papers to the Royal Society on the subject. From some of his expressions, it would seem that he adopted a theory of light resembling that of Huyghens, and gave a sort of general explanation of the facts by supposing a prin= ciple analogous to that since termed interference, and which has been most extensively applied in optics.

Mechanics.

The mechanical researches of Huyghens are of great value. In addition to those on collision, before mentioned, he was the first to demonstrate the relation between the length of a pendulum and the time of its vibrations, as also between this and the time of rectilinear descent down the length of the pendulum.

His practical application of these principles is that which has introduced the great improvement in clocks by the use of a pendulum as the regulating power. This grand invention is explained in his “ his "Horologium Oscillatorium," published in 1670, though the date of the actual invention is 1656.

The common pendulum vibrates only in circular arcs ; but so long as these are not extended beyond very small limits, the times of all the vibrations are precisely equal. If the arcs be greater, this equality is no longer preserved. It was one of Huyghens's investigations to find a curve, in which, if a body moved as a pendulum, ́ the vibrations in all arcs should be equal; and it was a mathematical result, that that curve must be the cycloid. By the ordinary mode of suspending a pendulum, it necessarily performs its vibrations in circular arcs; but Huyghens devised a method, founded on a geometrical property of the cycloid, for making a pen