583 



XI. — On the " Lag " in Microscopic Vision — (continued). 

 By Edward M. Nelson. 



{Bead June llth, 1903.) 



This continuation of my former paper,* is mainly of antiquarian- 

 interest, as it deals with early non-achromatic and achromatic objec- 

 tives. For the benefit of those who have not that paper before them r 

 it may be as well to recapitulate, very briefly, the meaning and the 

 method of estimating both the " Lag " and the " Order of Merit " 

 in an object-glass. 



First, it was explained, that as the measure of the limit of 

 ordinary unaided vision was the tangent of the visual angle for a 

 minimum visible, so the measure of the limit of either microscopic 

 or telescopic vision was the tangent of the similar microscopic or 

 telescopic angle. For example : if an interval of 1 in. can just 

 be seen by unaided vision at a distance of 10 yards, then with a 

 perfect telescope, having a power of 10, the same interval ought 

 to be seen at a distance of 100 yards, in which case there would 

 obviously be no " lag " ; because the optical instrument was doing 

 precisely what it ought to do, and what might reasonably be 

 expected of it. Therefore if tan v represents the tangent of the 

 visual angle, and tan m that of the telescopic angle, then, in the 

 example above, the " lag " or 



tan m — tan v = 0, 



thus indicating that the optical instrument, when its amplifying 

 power is taken into account, in no way lags behind unaided vision. 

 But it was pointed out, that with telescopes, and those no 1 : 

 particularly good ones, it had been observed that sometimes they 

 performed better than might be expected of them, and in the 

 example just given, the distance at which the 1 in. interval 

 might be separated with a power of 10 was found, for some unex- 

 plained reason, to be increased to 110 or 120 yards, in which cases 

 the " lag " became a negative quantity, 



or tan m — tan v — — a. 



But when the power was increased, owing no doubt to the super- 

 amplification of optical imperfections, the " lag " sometimes became 

 a positive quantity, thus, if a power of 100 were employed, the 



* Journ. R.M.S., 1900, p. 413. 



