OP ARTS AND SCIENCES. 307 



structing the curves with polar co-ordinates, taking the radius vector 

 equal to the focal length and its angle equal to the angle of incidence, 

 we obtain a line every point of which would be in focus at tlie same 

 time. This shows that in a photographic camera for lines passing 

 through the axis, corresponding to the vertical slit, the surface instead 

 of being a plane should have a radius of curvature of only .3 the focus. 

 For lines perpendicular to these, or circles concentric with the centre, 

 corresponding to the horizontal slit, the curvature should be .7 the 

 focus. We also see the importance of having telescope lenses care- 

 fully centred, and why the images of stars, if this adjustment is not 

 exact, are elliptical instead of circular. 



Since writing the above, a further application of these formulas has 

 been suggested in the case of the eye, that the imperfect vision at 

 a distance from the centre of vision may be due to the rays passing 

 obliquely through the lens. It will also be noticed that the curvature 

 of the retina corresponds nearly with that which would give the best 

 vision. As stated above, for radial lines the radius of curvature should 

 be about .3, and for concentric circles .7, its distance from the lens. 

 The actual curvature in the normal eye is about .5, or the mean of 

 these values. 



