144 the president's address. 



but simply to refer to an extremely narrow belt of glass ; so that, 

 to make my meaning clear, a lens should be considered as being 

 made up of a very great number of zones — like, in fact, a light- 

 house lens is made — only two of which for the present purpose 

 are being considered. The angle that the ray I makes with the 

 axis AA' on the left hand of the diagram we call a h that on the 

 right side being designated /?i ; whilst the angles for ray II are 

 called ao and /3. 2 respectively for each side. Now the sine-law is 

 this : that the ratio the sine of the angle ai bears to the sine 

 of the angle fi\ shall be the same as a 2 bears to /3 2 . If, 

 then, these ratios be equally proportionate, we speak of the 

 •• -ine-condition," or the "sine-law" as being fulfilled. I think 

 it will make my meaning more clear if I resort to an illus- 

 tration. Let us, for example, say we find the angle ay to 

 measure 13° 54', the sine of which we ascertain by the tables is 

 •240 ; whilst the sine of pi, estimated at 6° 55', we note as -120. 

 Here it is evident the ratio is as 2 to 1. Extending our examina- 

 tion to the angles a 2 and /? 2 , let us further suppose they are 

 22° 58' and 11° 15', the sines of which are respectively "390 and 

 •195 — just the same ratio as before, viz. as 2 is to 1. This is 

 what is called a " fulfilment of the sine-law." I have already 

 pointed out that coma is a defect confined to rays coming 

 from points of the image lying outside the axis of the lens, but it 

 remains for me now to further say that the beauty of the sine-law 

 is this : that if the sine-condition is fulfilled with regard to the 

 strictly axial points of the object, as I have previously explained 

 it causes a distinct and good image of the portions of the object 

 lying outside the optical axis, such as we might say lies at L 1# 

 Let us proceed, then, to see what happens if this sine-relation be 

 neglected, and how such non-fulfilment causes the defect (what- 

 ever it may be) we call coma. To begin with, I ought perhaps 

 to state that the ratio between the sines, whatever it may be, 

 is really the magnification of the object with the lens in question 

 under the circumstances, so that this particular lens we have 

 been dealing with would magnify the object twice. To be more 

 .iccurate, I should say that the zone Oj — that narrow strip of the 

 Lens containing the ray I — magnifies twice, and that the zone 2 , 

 containing ray II, does likewise. If, however, the sine-law be 

 not observed by the computer of the lens, the effect is th«it these 

 zones do not magnify the same, and hence that the rays coming 



