SOLUTIONS OF PROBLEMS. 79 



Since CP touches the circle, we have 



CP*=CA.CB, 



= (CO-OA)(CO+OB); 



but OA = -Q ; 



therefore CP 2 = CO 1 + CO I OB - ^) - a 2 , 



\ / 



an equation whence OB may be found, B being the point in the medium 

 through which all rays from C pass. 



NOTE. The possibility of the existence of a medium of this kind possessing 

 remarkable optical properties, was suggested by the contemplation of the structure 

 of the crystalline lens in fish ; and the method of searching for these properties 

 was deduced by analogy from Newton's Principia, Lib. I. Prop. vn. 



It would require a more accurate investigation into the law of the refractive 

 index of the different coats of the lens to test its agreement with the supposed 

 medium, which is an optical instrument theoretically perfect for homogeneous 

 light, and might be made achromatic by proper adaptation of the dispersive 

 power of each coat. 



On the other hand, we find that the law of the index of refraction which 

 would give a minimum of aberration for a sphere of this kind placed in water, 

 gives results not discordant with facts, so far as they can be readily ascertained. 



