On the '■ Lag " in Microscopic Vision. By E. M. Nelson. 415 



Take another objective, which with a power of 140 just resolves 

 35,000 lines to the inch; then 140 divided by 350,000 = 0-0004, 

 which multiplied by a million = m = 400. The " lag " is now 

 400 — 444 or — 44, the negative sign indicating that the Microscope 

 is doing relatively more than the unassisted eye. The objectives in 

 the following table were tested with a wide-angled solid cone of axial 

 illumination, the condenser was kept accurately centred, and the 

 edge of the lamp flame strictly focussed upon the object. This is an 

 important point, because if the condenser is racked so that the flame 

 image is a little out of focus, a hollow annular cone would be substituted 

 for a solid axial one, and the character of the illumination would be 

 changed into one which would partake somewhat of the nature of 

 oblique light with a slot ; and the resolving power of the objective 

 would consequently be increased. The column marked O.I. shows the 

 optical index of the lens ; it is found by dividing one thousand times 

 the N.A. of the objective by its initial magnifying power. Example : — 

 a 4/10 of N.A. 0*62 has an initial power of 33, its O.I. is therefore 



- -—- = 18*8. The eye-pieces distinguished by numerals arecompen- 

 33 



sating ; those by letters Huyghenian ; that by XII is a twelve-power of 

 my own construction. The column P contains the combined magnify- 

 ing power of the objective and eye-piece. This, together with the N.A. 

 and initial powers of the objectives, was measured in every instance, 

 and was not derived from the values given in catalogues. The column 

 t shows the number of thousands of lines per inch resolved. With 

 regard to m, a simpler way of finding this quantity is to multiply P by 



12900 

 100 and divide by t. Example in the seventh line: — = 516. 



Ad 



The column marked " Lag " is, as we have seen above, m — v, and 

 as v = 437 throughout this table, it therefore is m — 437. 



A number obtained empirically is placed in the last column, which 

 shows the order of merit of each objective's performance in resolving 

 a certain number of thousands of lines to the inch with a certain mag- 

 nifying power, and on account of its general utility may be preferred 

 by some to the column marked " Lag." The number is obtained by 

 dividing 10 v by m — t — O.I. It will be conceded that if two 

 objectives having precisely the same initial powers but different aper- 

 tures resolve the same band with a low-power eye-piece, the preference 

 ought to lie with the wider angled lens ; by subtracting the O.I. from 

 the denominator compensation is to a certain extent effected. Again, 

 if two objectives of different powers have the same optical index, some 

 allowance will have to be made for the objective which resolves the 

 higher band ; thus a 1 inch of • 26 N.A. and a 1/4 of • 95 N.A. have 

 both an O.I. of 23 • 5 ; it would be very much more difficult for the 1/4 

 to resolve 60,000 lines to the inch than it would be for the 1 inch to 

 resolve 15,000 ; compensation for this is effected by subtracting the 

 number of thousand lines to the inch resolved from the denominator. 



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