XXX VI 



THK PROGRESS OF 



ating such superficies by revolution have always 

 two given points from whidi, if .straight lines be 

 drawn to any point in the curve, tin- one of these, 

 plus or minus that which has a given ratio to the 

 other, is equal to a given line. When the given 

 ratio is one of equality, the curve is a conic sec- 

 tion, and the two points its foci. The curves in 

 general are of the 4th or 2nd order, and have 

 been distinguished by the name of the ovals of 

 Descartes. 



I Jut no practical advantage has resulted from 

 this investigation. The mechanical difficulties 

 of working a surface into any figure but a spheri- 

 cal one, are so great that they have never been 

 overcome. 



The next improver of optics was James Gre- 

 gory, whose Optica Promota appeared in 1663. 

 It contained an account of his reflecting tele- 

 scope. The imperfection of the images formed 

 by spherical lenses led him to substitute reflec- 

 tion for refraction in the construction of the 

 telescope. Gregory thought it necessary that 

 the specula should have a parabolic figure ; and 

 the execution proved so difficult, that the instru- 

 ment, during his lifetime, was never brought to 

 any perfection. After his death, the specula were 

 constructed of the ordinary spherical form, and 

 the Gregorian telescope, till the time of Her- 

 schell, was more in use than the Newtonian. It 

 is curious, that though the optics of Descartes had 

 been published twenty-five years, Gregory was 

 ignorant of the law of refraction, and found it out 

 by his own unassisted exertions. 



Barrow's lectures on optics, delivered at Cam- 

 bridge in 1668, treated of all the more difficult 

 questions which had occurred in the then state of 

 the science, with the acuteness and depth which 

 are found in all his writings. 



About this time the Jesuit Grimaldi made 

 known some optical phenomena, which had 

 hitherto escaped detection. Having stretched a 

 hair across a sun-beam, admitted through a hole 

 in the window shutter of a dark chamber, he was 

 surprised to find the shadow much larger than 

 the natural divergence of the rays could have led 

 him to expect. Other facts of the same kind 

 made known the general law of the diffraction or 

 inflexion of light, and showed that the rays are 

 acted on by bodies, and turned out of their 

 rectilinear course, even when not in contact, but 

 at a measurable distance from the surfaces or 

 edges of such bodies. Grimaldi gave an account 

 of these facts in a treatise printed at Bologna in 

 1665. 



The dioptrics of Huygens, though a posthu- 

 mous work, was the production of his early youth, 

 and is said to have been a favourite book with 

 Newton himself. It contains a full development 

 of every thing relating to the construction of 



telescopes, particularly in that which concerns 

 the indistinctness arising from the imperfect foci 

 into which rays are united by spherical lenses. 

 Hules are deduced for constructing telescopes, 

 \\liich, though of different si/rs, >liall have the 

 same degree of distinctness, &c. Huygens wa 

 a practical optician; he constructed telescopes 

 with his own hands, and some of his object 

 glasses were of the enormous focal distance of 

 130 feet. 



His theory of light was communicated to the 

 Academy of Sciences of Paris in 167H, and af- 

 terwards published with enlargements in 1690. 

 Light, according to him, consist* of certain un- 

 dulations, communicated by luminous bodies to 

 the etherial fluid which fills all space. This fluid 

 is composed of the meet subtile matter, is highly 

 elastic, and the undulations are propagated 

 through it with great velocity in spherical super- 

 ficies, proceeding from a centre. The ingenuity 

 of the theory appears most conspicuous in the 

 explanation which it aflbrds of the constant ratio 

 which subsists between the sines of the angles of 

 incidence and refraction in the same medium. 

 But the happiest application of all, is to the ex- 

 planation of the double refraction of Iceland 

 crystal, or transparent calcareous spar. This 

 crystal has not only the property of refracting 

 light in the common manner of glass, water, and 

 other transparent bodies; but it has also an- 

 other power of refraction, by which even the rays 

 falling perpendicularly on the surface of the 

 crystal are turned out of their course, so that a 

 double image is formed of all objects seen through 

 these crystals. This property is not confined to 

 calcareous spar ; but belongs, in a greater or less 

 degree, to all substances which are both crystal- 

 lized and transparent. 



The common refraction is explained by 

 Huygens, on the supposition that the undulations 

 in the luminous fluid are propagated in the ibriu 

 of spherical waves. The double refraction is 

 explained on the supposition that the undulations 

 of light, in passing through the calcareous spar, 

 assume a spheroidal form ; and this hypothesis, 

 though it does apply with the same simplicity as 

 the former, yet admits of such precision, that a 

 proportion of the axes of the spheroids may be 

 assigned, which will account for the precise 

 quantity of the extraordinary refraction, and for 

 all the phenomena dependent on it, which 

 Huygens had studied with great care, and had 

 reduced to a small number of general facts. 



To render the theory of Huygens quite satis- 

 factory, a reason ought to be assigned why the 

 undulations of the luminous fluid are spheroidal 

 in the case of crystals, and spherical in all other 

 cases. This would render the generalization 

 complete. But till a connexion is clearly esta- 



