B 



A POPULAR ACCOUNT 



rings ; the exterior ring, or that which 

 is most distant from the centre of the 

 lens, will be collected by refraction into 

 a focus, at a point on the axis of the lens 

 at a certain distance from the surface. 

 The next ring of light within the last 

 will be also collected into a point, but at 

 a greater distance from the surface ; and 

 so on, each ring of light is collected into 

 a focus, the distance of which from the 

 surface increases, as the distance of the 

 ring from the centre of the lens dimi- 

 nishes. To illustrate this, let L L be a 

 section of the lens at right angles to its 

 axis; and suppose its surface divided 

 into rings as repre- Fig. 3. 



sented in fig. 3, and 

 let the order of the 

 rings be reckoned 

 from the edge of 

 the lens towards the 

 centre, calling the 

 external ring the 

 first ring, the next 

 within that the se- 

 cond ring, and so 

 on. Let L L,fig.4, be a section of 

 the lens by a plane through its axis; 



Fig. 4. 



and suppose that the whole lens, ex- 

 cept the first ring, be covered by an 

 opaque circular cover, and light be inci- 

 dent on its surface, this light will be re- 

 fracted to a certain point f t in the axis ; 

 and this point will, therefore, be the 

 focus of ihe first ring. Again, removing 

 the cover from the lens, let another be 

 substituted, which will leave the second 

 ring alone exposed to the light. The 

 rays will now be collected in the point 

 f s . The same process being continued, 

 and the third, fourth, and other rings 

 being successively exposed to the light, 

 their foci will be found at the points / 3 , 

 ,/j, &c. the rings nearest to the centre of 

 the lens having their foci most distant 

 from its surface. It was easily deduced 

 from the law of refraction, that, the foci 

 of the rings near the centre of the lens 

 were much closer together than those 

 near its surface. 



Since the images of objects were 



known to be formed by collecting the 

 rays emerging from them into the focus 

 of the lens, it followed from these con- 

 siderations that each of the rings, into 

 which we have supposed the surface of 

 the lens to be divided, must produce a 

 separate image ; and thus an indefinite 

 number of images of the same object 

 would be found at different distances 

 from the lens, and arranged in regular 

 succession along the axis. This effect, 

 called spherical aberration, caused a con- 

 fusion in the appearance of the image, 

 which confusion was increased with the 

 magnitude and curvature of the lens. 



Seeing that this defect was essential 

 to the very nature of spherical lenses, 

 Descartes proposed to investigate the 

 figure of a lens which should be free 

 from this defect; and such that each 

 ring, into which its surface would be 

 divided, might collect the rays to a focus 

 at the same distance from the lens. 

 The high analytical acquirements of this 

 mathematician, united with the know- 

 ledge of Snellius's law, rendered the so- 

 lution of this problem a matter of no 

 great difficulty. He accordingly found 

 a class of curves, since called the Car- 

 tesian ovals, which possessed the re- 

 quired property. When the densities of 

 the medium of incidence and the me- 

 dium of refraction are given, the figure 

 of the surface, which will collect into an 

 exact focus rays emerging from any 

 given point, will always.be determined 

 by one of these ovals. When the incident 

 rays are parallel, the oval becomes a 

 conic section *. 



Ignorant of the cause of the principal 

 defect of lenses, which was subsequently 

 discovered by Newton, Descartes ex- 

 pected much greater results from this 

 discovery than it was capable of pro- 

 ducing. He invented machines, and en- 

 gaged skilful artists to grind spheroidal 

 lenses, according to the figures sug- 

 gested by his theory. After the expen- 

 diture of much labour and ingenuity, no 

 adequate advantage was obtained, and 

 at this day, when practical science has 

 attained such an extraordinary degree of 

 perfection, the spherical lenses are still 

 universally used. 



(12.) In unfolding the theory of the 

 rainbow Descartes has been singularly 

 happy, and certainly has brought the 

 explanation of this phenomenon as near 

 to perfection as could be done by one 

 who was ignorant of the different re- 



* For an account of these curves, see Lardner's 

 Algebraic Geometry, p. 452- 



