ON THE GENERAL LAWS OF OPTICAL INSTRUMENTS. 285 



of the structure of the crystalline lens in fish, and was published in one of 

 the problem-papers of the Cambridge and Dublin Mathematical Journal. My 

 own method of treating that problem is to be found in that Journal, for 

 February, 1854. The case is that of a medium whose index of refraction varies 

 with the distance from a centre, so that if //, be its value at the centre, a 

 a given line, and r the distance of any point where the index is /A, then 



a 2 



The path of every ray within this medium is a circle in a plane passing through 

 the centre of the medium. 



Every ray from a point in the medium, distant &/ from the centre, will 



2 

 converge to a point on the opposite side of the centre and distant from it j- . 



It will be observed that both the object and the image are included in 

 the variable medium, otherwise the images would not be perfect. This case 

 therefore forms no exception to the result of Prop. IX., in which the object and 

 image are supposed to be outside the instrument. 



Aberdeen, 12th Jan., 185& 



