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HISTORY OF SCIENCE. 



imagination, for only the centre rays of three pencils from the points 

 of the object A o B are shown. An inverted image is formed at A' B', 

 and is viewed through the second lens as if it were an object. The 

 diagram here does not show the whole course of the rays ; in reality, 

 j-the rays originally emergent from B, for instance, come to a focus at 

 /B', and passing on, enter the second lens, by which they are so refracted 

 that their course after leaving the lens is the same as as //"they diverged 

 from the point B". Similarly of rays from the points A and o. Thus, 

 an eye placed behind the second lens is affected in the same way as if 

 the object itself coincided with A" o" B". 



FIG. 64. 



In the account of the lens just given we have assumed something 

 as true absolutely which is true only approximately. The rays from 

 the point , Fig. 61, do not all meet together, after passing through 

 the lens, exactly at one point. They do so approximately if the lenses 

 are formed of only small segments of spherical surfaces; but when 

 the curvature is considerable, the aberration is very great. Descartes 

 entered into an investigation of the nature of the curved surface which 

 must be given to the glass in order that parallel rays falling upon it 

 may meet precisely in one point. He found that the section of the 

 required surfaces would be peculiar oval curves, instead of circles as in 

 ordinary lenses, and that in certain cases these ovals became hyper- 

 bolas or ellipses. Descartes contrived machines by the aid of which 

 he hoped to grind lenses into the required forms. The practical dif- 

 ficulties were, however, found insurmountable, and although other 

 eminent mathematicians have proposed different arrangements, hyper- 

 bolic lenses have never yet been shaped for any useful purpose. This 

 failure is the less to be regretted, as the hyperbolic lens could only 

 be applicable in certain cases, leaving the advantage in others to the 

 spherical form ; and the subsequent discovery of the achromatic prin- 

 ciple so far removed a more serious defect of the spherical lens, that 

 the greatest obstacle to distinct definition of the images was overcome. 

 The fabrication of the ordinary lens (a spectacle lens, for example) is 

 a comparatively simple operation. It consists in grinding a disc of 

 glass on a revolving piece of iron of a spherical form. Fig. 65 shows 

 a workman engaged in this operation. With his left hand he turns a 

 handle which by means of an endless band gives a very rapid rotatory 



