from it in the latter. stancy of the ratio between the sine of incidence and the sine of refraction, it may happen, that refraction will be converted into reflection, and the contrary. For example, a ray of light passing from air into water, and almost skimming it's surface, or making the angle of incidence almost a right angle, is refracted at an angle of about 48° 50′: if therefore the ray returned from the water into the air, it would be refracted at an angle of 90° nearly, or would just skim the surface of the water; and if the angle of return were more than 48° 50′, the ray in the water would be reflected.

Hence, and from the con

The refrangibility and reflexibility of rays depend both on the same cause. Those which are the least refrangible are likewise the least reflexible. For instance, the red ray requires a greater angle of incidence than the rest for it's refraction to be changed into reflection.

Newton explains at large all these phenomena of light. His Treatise on Optics constitutes an era in this science, as his Principia in that of physical astronomy. Some of his experiments were at first disputed, because they were repeated unskilfully; but in the multitude of his facts, observations, and reasonings, he fell only into a few slight mistakes, which do not in the least affect the substance of his work.

Other celebrated geometricians, treading in the steps of Newton, applied themselves to investigate the laws of the refraction and reflection of light, and to subject them to calculation, according to the prin ciples of attraction. On this subject Clairaut's paper

in the Memoirs of the Academy of Paris for 1739 deserves particular notice.

The refraction of light sensibly affects astronomical observations; and to divest them of this source of illusion, which tends to make the stars appear in places different from what they really are, is indispensable. Our globe is surrounded by a spherical body or envelope of air several miles in height, the strata of which diminish in density as they are farther from the surface of the Earth. If a star be in the zenith of the observer, the ray of light, which conveys it's image to him, entering perpendicularly into the upper and extreme stratum of the atmosphere, does not change it's direction; it is only weakened, and the star is seen in it's true place. But in all other cases, the ray, entering obliquely into the atmosphere, is refracted, and changes it's path from one stratum to another, as the densities of the strata are different: it describes therefore a curve, the last element of which, that which terminates at the observer's eye, occasions the star to appear higher, than it really is. Owing to this refraction, the light of the Sun begins or ceases to be perceptible to us, when that luminary is 18° below the horizon, before it's rising, or after it's setting; which is the occasion of the morning and evening twilight. The duration of the shortest twilight for a place of a given latitude is determined by the method of maxima and minima, as I have already observed.

Here we find refraction acts in an opposite manner to parallax this tends to place the star lower; that, higher. If therefore we knew exactly the quantity of refraction

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refraction for all the angular distances, at which a star might be found with respect to the zenith, the effect resulting from parallax and from refraction might be determined by the same calculation, by taking the difference between them. But the refractions are very inconstant; they vary according to the changes, that take place in the state of the atmosphere; diminishing when the air is clear, as on lofty mountains, or when it is rarefied by heat, as in the vicinity of the equator; and increasing when the air is loaded with dense vapours. The ancients knew the effects of refraction in the gross, but we do not find, that they took any notice of them in astronomical calculations. Tycho Brahe was the first, by whom they were subjected to general laws, which, though sufficiently imperfect, at least drew the attention of astronomers to this important object. Bouguer, in a piece which obtained the prize of the Academy of Sciences at Paris in 1729, determined the curve described by a particle of light passing obliquely through the atmosphere; and in consequence he constructed a table of astronomical refractions for every degree of the altitude of a star above the horizon but this table, the theory of which is a little hypothetical, has not all the accuracy, that could be wished. Bradley, some time before his death, presented astronomers with a very simple and commodious formula for the calculation of refractions.

All the writers on optics, down to Newton, and his immediate successors inclusively, considered only the general laws of the motion of light, it's propagation in a right line through the same medium, it's reflection

reflection on meeting with any obstacle, it's refraction on passing from one medium to another, &c. It's force, or intensity, still remained to be measured; as, for example, how much more powerful the light of the meridian Sun is at the summer than at the winter solstice; how much the light of the Sun exceeds that of the Moon, at equal altitudes above the horizon; &c. Huygens had given some hints respecting this new branch of optics; he had pointed out a method for estimating the quantity of light, which Jupiter and Saturn receive from the Sun, and for comparing the light of the Sun with that of the stars. But this method was founded on some vague and doubtful hypotheses; and besides, the question required to be elucidated by a series of accurate and numerous experiments, from which the means of measuring the degrees of light in all cases might easily be drawn.

Bouguer undertook this delicate task, and carried it to a considerable length; by which he appropriated to himself a subject curious in it's own nature, and of frequent application in physics. His first researches he published in 1729, in a little tract, entitled An Optical Essay on the Gradation of Light. This was greatly enlarged, and republished in 1760, after the author's death, with the substitution of the word Treatise instead of Essay in the title page. This treatise contains a number of experiments and observations, of philosophical and mathematical disquisitions, and of interesting applications to the different problems, which the subject admits. In it we are taught how to compare the light transmitted by different bodies, as the Sun, the Moon, the planets,

the stars, &c.; to find the quantity of light reflected by rough or polished surfaces, and what is lost by the absorption or dispersion of the rays; to estimate the different degrees of transparency in bodies; &c. I can only point out these subjects, on which the reader may consult the work itself.

The utility of the science of optics is conspicuous chiefly in the construction of instruments for assisting the sight. Before Newton made his experiments, philosophers supposed, that the imperfection of dioptric glasses arose from the sphericity of the figure, which was commonly given to object glasses; for the rays of light falling on a spherical surface of any extent do not reunite in one point after having traversed it, as each linear ray has it's particular focus, and the greater the number of these foci, the less distinct will vision be. This is what is called the aberration of sphericity. To obtain a vivid and clear image, the aperture for the object glass was made small, while the spherical figure was retained. Des Cartes, and some other geometricians, however, proposed to relinquish this shape, and adopt curves taken from the conic sections, which possess the property of uniting the rays in one point. But, not to mention, that it would be next to impossible to fabricate such object glasses with sufficient nicety, they would have remedied only a part of the defect; for they would not remove the aberration of refrangibility, that is to say, the dispersion of the rays arising from their unequal refractions. Accordingly it was found necessary, to return to the sphe rical form for the object glass, to which, by adding