318 MAURICE A. AIXSLIE ON THE MEASUREMENT OF 



focal lengths of the objectives is 39'4/12'6, or 3'125 ; but the 

 magnifications, in the case of the Holos " 10" eye-piece, are in 

 the ratio of 4'08 to 1, and in the case of the Zeiss eye-piece, 4'33 

 and 4*20 to 1, according as the focus was readjusted by the 

 coarse adjustment or the draw- tube. 



(2) That the magnifying power is not proportional to the power 

 of the eye-piece, imless the optical tube-length is unaltered by 

 change of eye-piece ; the numbers given in columns one and three 

 for the magnifying power are proportional to the powers of the 

 eye-pieces, while those in columns one and two are not. The 

 substitution of the Zeiss eye- piece for the Holos, without alteration 

 of tube-length, increases the power 9*3 per cent, in the case of the 

 Leitz No. 1, and 13 per cent, in the case of the Zeiss 12-mm., the 

 ratios being r093 and 1*13 to 1 respectively. Neither of these 

 equals the ratio of the powers of the eye-pieces, which is 1*255 to 1. 

 Thus if the magnifying power were merely computed as pro- 

 portional to the powers of the eye-pieces, an error would be 

 introduced which would be greater in the case of the low- power 

 objective than in that of the high. 



(3) The percentage difference between the magnifying powers 

 in columns two and three is greater in the case of the low-power 

 objective : 14*6 as against 10*8 in the case of the 12-mm. 



It is therefore obvious that it is unsafe to attempt to compute 

 the magnifying power of one combination from that of another, 

 unless the positions (relative to the ends of the tube) of the 

 various focal planes are known ; in the absence of such know- 

 ledge, the power of every combination must be separately de- 

 termined. It is only fair, however, to say that the case here 

 taken is rather extreme, though by no means so extreme as it 

 might be ; if objectives (say a \ and an \) or eye-pieces of the 

 same type are compared, the errors in the result are as a rule 

 considerably smaller. 



The error pointed out by Mr. Bale, due to the increase of 

 linear magnification at the edge of the field, undoubtedly exists ; 

 but I am not sure that it admits of quite such simple treatment 

 as he has indicated. Apart from the geometrical distortion which 

 he has dealt with, there exists in almost all eye-pieces a certain 

 amount of optical distortion of the image, towards the edge of 

 the field, and this optical distortion might very easily aflect the 

 results obtained ; sind it varies very considerably with the type 



