464 



Transactions of the Society. 



Conversely we can obtain the aperture a, which is sufficient for 

 the utilization of a given power of N diameters, provided a visual 

 angle v' is required for the least detail within the reach of that 

 aperture. This is given by the formula 



- N I 



a ~ 264-5 ' v' 



Table II. shows the values of a corresponding to different 

 amplifications under the supposition of a visual angle v = 2' ; it 

 exhibits, therefore, the maximum aperture which can be admitted 

 as useful for any given power under the above assumptions. 

 The assumption of any other visual angle as necessary for 

 distinct vision of the least detail, would change a in the inverse pro- 

 portion of v, so that for v = V we should have twice the figures 

 of a given in the second column of the table, and for v = 4' 

 one-half 



Table II. 



Though these figures cannot of course pretend to be more than 

 an approximation to the actual requirements under various given 

 conditions, yet they will indicate with sufficient accuracy the 

 limits of useful power; in that the delineating power of any 

 given aperture cannot be fully utilized when the number of 

 diameters (obtained with a really good quality of the image) is much 

 below the minimum figures of the table ; and that, on the other 



