THE PRESIDENT'S ADDRESS. 143 



m 



of the radial one ceases to be good. In microscopical objectives 

 this defect is sometimes — though rarely, I admit — to be detected 

 when using an Abbe test-plate (which consists of parallel lines 

 drawn through a surface of finely deposited silver). At one focus 

 all lines appear focussed, it is true, but only in concentric circles ; 

 whereas another plane of focus shows them sharply defined, but 

 only in narrow bands radiating from the centre of the field as 

 the spokes of a carriage wheel. It is not possible to focus both 

 directions at one and the same time. Plates 9 and 10 are 

 photomicrographs taken with a lens affected with this fault, and 

 as it is rare I thought it worth while to show it to you. 



Coma is a defect confined entirely to rays coming from points 

 of the image lying outside the axis of the lens, and one not 

 easy to explain for the simple reason that several who use the 

 expression place upon it a meaning of their own. Although in 



l' Sine- law 



A R,ATI0 MAINTAINED WITH RE&ARD TJ STRICTLY, f XIAL POI NTS or OBJECT 



Fig. 5. 



what follows I shall use the expression in a somewhat restricted 

 sense, still, even then, the nature of the fault is such that it is not 

 easy to explain in a few words. To make what follows more 

 intelligible, I think it will be best to define it first, declaring it 

 to be a peculiar defect due to the " non-fulfilment of the sine- 

 law," because by so doing this will lead me at once to explain 

 what this sine-law is, which will then enable me afterwards to 

 show how its neglect causes coma. 



In Fig. 5 the axis of the lens is shown at AA', and L, a 

 point of the object, is seen lying upon it. I is a ray proceeding 

 from L to the lens O, meeting it at a point Oi, from which it 

 passes to focus at F. Another ray following the course of II 

 strikes the lens at 2 , focussing at the same point F. It is to be 

 further understood, when in the future the zone Oi is spoken of, 

 it is not meant to include a piece of the lens from to Oi, nor 

 when talking of zone 2 . the portion included between and 2 , 



