256 ON THE THEORY OF THE MICROSCOPE. 



are rooted in entirely different elements of its construction. The 

 dioptric limit of resolution caused by inevitable defects of focal 

 union of the rays of light, finds its measure in the serviceable amount 

 of magnifi/ing power of the objective, and is inversely propor- 

 tional to its focal length. The physical limit of resolution, on the 

 other hand, depends wliolly on angular aperture^ and is proportional 

 to the sine of half the angular aperture. jS^evertheless, both 

 functions conduce toward one and the same end, namely, the 

 rendering visible particles of matter which fill infinitely small 

 space, and both are equally necessary for this end. Hence it 

 follows that a rational construction of the microscope must aim at 

 a due balance of powers in order that the limits of each may 

 approximate harmoniously; for it is obviously just as useless to 

 carry out the physical conditions of ''resolving" power, to 

 an amount greatly in excess of that which can be utilised by any 

 attainable (and still serviceable) amplification, as it would be, on 

 the other hand, to increase the magnifying power beyond that 

 which the amount of *' resolution '* demands. In the first case, 

 w^here the angular aperture is in excess of the serviceable ampli- 

 fying power pertaining to the focal length of the objective, there 

 is a latent power of resolution whicli is lost to every eye ; in the 

 second case, when the magnifying power of the objective exceeds 

 the dioptric limits of resolution greatly beyond that which the 

 detail accessible to the aperture of the objective requires, an 

 empty amplification (that is to say, one in which proportionate 

 detail is absent) is the consequence^. 



XXY. The considerations here adduced lead to certain rules 

 respecting the right proportion between focal distance and angular 

 aperture, which are opposed in many points to the hitherto preva- 

 lent practice. The remarks which follow are supplementary to 

 what has been stated in paragraph ix., and may be of general 

 interest as tending to shew the extent and the limit of 

 microscopic observation. 



Since theory demands a limitation of angular aperture of 110 

 degrees for all dry combination^^, the calculation of minutest detail 



