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 more 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 communicated 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 direc tion 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 principle 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 "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

dulum oscillate in that curve; in which case, its motions in all arcs, great or small, would be strictly isochronous.* The property referred to was, that the involute of a cycloid is a cycloid: hence the thread sustaining the weight being unwound from the arc or surface of a cycloid, the body which it carries will at the same time move in the arc of another cycloid. The weight was, therefore, suspended between two pieces of wood or cheeks, cut in the shape of cycloids. When it hung motionless, the string was a tangent to both the cheeks at the point of suspension, where they also touched each other. In any other position the string was partially wound upon one of the cheeks, while the remainder formed a tangent to the curve.

This method is, however, inapplicable in practice, and can only be regarded as an elegant theoretical speculation. For practical purposes, a pendulum simply suspended and vibrating in small circular arcs, possesses every requisite, even for purposes of the utmost exact

ness.

In these researches, several eminent mathematicians communicated with Huyghens, among whom we find Wren and Wallis taking a conspicuous part.

In the theory of motion, another important principle seems to have been first brought to light by the researches of Huyghens; the discovery of the centre of oscillation: an enquiry of a singularly refined and beautiful character, and which has become connected with the most extended speculations in analytical mechanics. The nature of this enquiry will be readily understood, when we merely consider for a moment, that in a pendulum consisting of a large mass of matter, every particle, if suspended separately, would vibrate in a different time, according to its distance from the point of suspension when, therefore, these particles are all connected together, they must affect each other's motions; but upon the whole there will be some one of them whose times of vibration, when independent, are the *, equal; xeovos, time.