OF NEWTON'S OPTICS. 



over those used by Galileo and others. 

 Kepler was, however, aware of the me- 

 thod of correcting the position of the 

 image, by the use of additional eye- 

 glasses ; but probably considered that 

 the complexity of the instrument, and 

 the loss of light, would render it inferior 

 to the Galilean telescope. 



The optical discoveries of Kepler were 

 not confined to the telescope. He made 

 experiments on refraction by lenses, and 

 succeeded in establishing some of the 

 properties of their foci. He also ex- 

 plained the formation of the inverted 

 image on the retina. He attributed erect 

 vision from an inverted image to an 

 operation of the mind, by which it refers 

 the lower part of the image to the upper 

 side of the eye, but considered it beyond 

 our power to determine the manner in 

 which the mind perceives the images of 

 objects upon the retina. He investigated 

 the power of the eye to accommodate 

 itself to different distances, and attri- 

 buted it to the contracting power of the 

 ciliary processes. 



(10.) At the period to which we now 

 refer, the beginning of the seventeenth 

 century, the most important discovery 

 in the theory of refraction since the time 

 of Ptolemy, was made by Willebrord 

 Snellius, professor of mathematics at 

 Leyden. This philosopher, by a careful 

 comparison of numerous refractions at 

 different incidences, found that if a 

 sphere were described round the point of 

 incidence, and a cylinder circumscribed 

 this sphere, having its axis perpendicular 

 to the refracting surface, the parts of the 

 incident and refracted rays, between the 

 centre of the sphere and the cylinder, 

 were in a constant ratio, so long as the 

 refracting medium remained the same. 



To explain this important law more 

 fully, let I, Jig. 2, be the point of inci- 

 Fig. 2. 

 A 



dence, and S I S the refracting surface, 

 S B S being a vertical section of the re- 

 fracting medium, or rather a section 

 supposed_to pass through the incident 



ray, and perpendicular to the surface. 

 With I as centre, and any distance I S, 

 describe a circle in the plane of the sec- 

 tion, and draw tangents at S S, perpendi- 

 cular to the refracting surface. Let the 

 incident rays meet the upper tangent at 

 P', P", P'", &c. ; and let the correspond- 

 ing refracted ray meet the lower tangent 

 at p', p", p"' y &c. It was found by Snel- 



P'T P"I P''I 

 lius, that the ratios J_,_..__,g. 



were equal so long as the media S A S 

 and S B S remained the same. Taking 

 the radius I A or I B as the unit, the 

 lines P'l, P"I, P'"!, Sec. are the cosecants 

 of the angles of incidence ; and the lines 

 p'l, p"l, p'"l, &c. are the cosecants of 

 the angles of refraction. These quanti- 

 ties are, therefore, in a fixed proportion. 

 The cosecants of angles being the reci- 

 procals of their sines, it follows that 

 when the media on each side of the re- 

 fracting surface are given, the sine of the 

 angle of incidence bears to the sine of the 

 angle of refraction an invariable ratio. 



(11.) The discovery of the law of refrac- 

 tion has been sometimes erroneously as- 

 cribed to Descartes. With a degree of 

 disingenuousness and want of candour, 

 or rather of common justice, which not 

 unfrequently characterised the conduct of 

 that great philosopher, he has announced 

 in his Dioptrics, published eleven years 

 after the death of Snellius, the law of 

 refraction as the result of his own in- 

 quiries, without taking the slightest no- 

 tice of the previous discovery of Snel- 

 lius, although there is no doubt that he 

 was acquainted with it ; and there is even 

 strong reason to believe that Descartes 

 had the manuscripts of Snellius in his 

 hands, and availed himself of the full 

 and unrestricted use of them. 



About the time of the death of Snel- 

 lius, which happened in 1626, at the 

 early age of thirty, Descartes applied 

 himself to optical investigations ; and, in 

 1637, published his Treatise on Dioptrics. 

 Guided by the law of refraction, with the 

 recent discovery of which he was made 

 acquainted, he made some important ad- 

 ditions to, and improvements in, the 

 science. The fact that spherical lenses 

 were incapable of collecting rays of light 

 into an exact focus, had been known by 

 experience ; and the cause of this sphe- 

 rical aberration, as well as its quantity 

 and laws, were easily deduced from the 

 Snellian law. To comprehend the nature 

 of this defect of spherical lenses, let the 

 light incident upon them be conceived to 

 be divided into a number of concentrical 



