Tliti Presidenes Address. By H. C. Sorby, F.R.S., &c. 109 



adopted by Nobert, which is based on the supposition that the rays 

 of Hght used for illumination are parallel, and entirely ignores the 

 question of aperture. As Dr. Woodward has shown,* the limit 

 given by Nobert's formula is not at all borne out by observation, 

 since lines can be distinguished at a much smaller interval than 

 indicated by the manifestly incomplete theory. This remark will 

 not aj)ply in the case of Helmholtz's formula, which appears to be 

 fully substantiated by observation. 



Adopting, then, the most simple applications of Helmholtz's 

 formula as an illustration of the general question, I have calculated 

 what is the limit for the red and blue ends of the spectrum, and 

 for the mean rays, according to the following wave-lengths, given 

 for simplicity in fractions of an inch : 



Red end sttto 



Mean rays ^^^^ 



Blue end STjiro 



I have also calculated the limit for a few widely different angles 

 of divergence, giving double these in order to make the comparison 

 more simple with the angle of aperture as usually expressed, 

 assuming of course that the angle of divergence of the light from 

 the condenser is equally great. 



60', which gives the wave-length as the limit. 

 97°, which gives three-fourths of the wave-length as limit. 

 120°. 

 150°. 



180°, or an angle so great that its sine is near unity, whether practicably 

 possible or not. This gives for the limit half the wave-length of the 

 light. 



The results are expressed in the following table, in which I 

 give the nearest round numbers : 



All these limits are calculated for dry lenses. For immersion 

 lenses of equal aperture the limits would in all cases be about 

 three-fourths of the various magnitudes here given. In order to 

 see such minute intervals, of course a high magnifying power is 

 necessary, but when the interval is less an increased power would 

 magnify the defects and the object equally. 



* ' Monthly Microscopical Journal,' vol. ii., 1869, p. 289. 



