1898.] MICROSCOPICAL JOURNAL. • 103 



much greater aperture tlian 1-0, with a single-notched 

 stop, through which sun rays were sent by a hiliostat. 

 The beam through the notch being- first so oblique as to 

 be outside or excluded by the 1-0 dry aperture of the 

 objective, a strong green spectrum alone appeared at 

 one side of that aperture, at back of the lens. 

 The notch was then gradually deepened until a very 

 small direct or dioptric pencil was just seen on the 

 opposite side of the aperture — replacing the eye-piece. 

 The strisB were just seen. The diatom was proba- 

 bly something less than 95,000 per inch, and any dry 

 lens must be some little less than 1-0 in N". A. Here 

 then, with very mtense plane-wave illumination — in fact 

 nearly " uniform plane waves " — we have also as nearly 

 as possible the theoretical limit attained, or closely 

 approached, with a circular aperture. 



Turning now to the more average kind of microscopic 

 image, the extreme closeness with which Lord Rayleigh's 

 10 per cent reduction of efficiency in circular apertures 

 represents the facts of observation as found by the most 

 competent observers, will forcibly strike everyone who 

 has studied microscopy for any length of time. But Dr. 

 Mercer, has recently tested the question photographically. 

 It is comparatively easy to prepare circular and square 

 apertures of equal dimensions. He also ruled upon the 

 same glass plate six sets of lines at intervals of 0-42, 

 0-46, and 0.5 mm. and their doubled intervals of 0-84, 

 0-92, and 1-0 mm. apart. The apertures were 5-0, 5*5, 

 and (5-0 mm. diameter. It will he seen that both lines 

 and apertures give excesses of about 10 and 20 per cent, 

 representing those calculated by Lord Rayleigh and Airy 

 respectively. An serial image of these lines focussed by 

 the condenser, was used as the object, and successive 

 pihotographs taken with all the square and circular aper- 

 tures. Then only similarity of resolution had to be com- 

 pared, which can be done within very small limits of 



