290 EDWARD M. NELSON ON 



different curves to the 1/2 in., from there to the 4/lOth it is very 

 flat, here its designer seems afraid that he has run away too far 

 from Prof. Abbe, so he has made two quarter-inches, one with only 

 a little more aperture than the Professor's, and one with a good 

 deal more ; but notice that this higher aperture l/ith has a steeper 

 slope than their other higher powers ; the line from the l/4th to 

 the l/5th, for example, inclines more to the horizontal, showing 

 that it has a wider relative aperture, when, of course, it should 

 incline the other way. This bears out the previous statement, 

 that this curve is based upon no plan. 



The Germans, as is well known, keep to their catalogue values 

 fairly closely, so it will be unnecessary to draw two curves, one 

 for the catalogue values and one for actual values, as the 

 curves would be very similar. A curve drawn from 17 measured 

 German objectives is not a smooth curve ; there is a kick about 

 the 4/lOth, from there to the l/3rd it is nearly horizontal, and 

 thence it slopes up pretty steeply. It shows that a lens of 

 power 25, viz. a 4/lOth, has an aperture of N.A. 0-4, whereas 

 the R.M.S. shows N.A. 0-57 and Prof. Abbe's one of N.A. 0-32. 

 After the 4/1 0th the curve is smooth, and not very unlike that of 

 the R.M.S. plan. 



Now we come to English measured objectives. To draw a 

 curve from a catalogue would be useless, as the difierence between 

 catalogue and measured values is so great. A catalogue 1/2-in. of 

 N.A. 0-65 (optical index 32-5), when measured, would probably 

 be a 4/lOth of N.A. 0-55 (optical index 22-0), and a l/4th of 

 N.A. 0-7 (optical index 17-5) is very likely a l/5th of N.A. 0-67 

 (optical index 13-6). The measurements of English lenses always 

 show a decrease of optical index from what the catalogue would 

 lead you to expect. 



The English curve is one of high relative apertures, for it tends 

 to flatness ; there is the usual kick about the 1/2 in., and a worse 

 one between the 1/5 and 1/6. It was drawn from the measure- 

 ments of 26 objectives by various makers. 



We now come to my own curve (fig. 3), which I ask you kindly 

 to take into your consideration. You will notice at once that it 

 is a smooth curve, therefore it has been drawn upon a plan ; there 

 is no kick at the 1/2 in., nor anywhere else. The optical index 

 is gradually diminished as the powers increase. The low powers 

 up to the 4/lOth have an optical index of about 20, so that part 



