ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 815 



will illustrate this. Both arc taken across tlic nodule, and while No. 1 

 starts straight from the median line and slopes down towards each edge, 

 No. 2 starts straight from the edge and slojjes down towards the median 

 line. Now, if these two curves are placed opposite each other, there 

 will be a considerable space between them, and we are driven to this 

 conclusion, that either each side represents a different layer of structure, 

 or we have one very thick plate of silex — a sui^position quite at variance 

 with what we know of diatom structure generally. 



I have said that the same appearance is always identical with the 

 same curve of the valve— No. 1 showing white, and No. 2 black inter- 

 spaces ; but this only on condition that the largest cone of light j)ossible 

 is poured into the objective. With a narrow cone of illumination the 

 two sides j)resent the same image, but by using the largest aperture of 

 the achromatic condenser, and placiug the bull's-eye condenser between 

 it and the mirror, the valves become at once differentiated in a manner 

 unmistakable. 



I may state here incidentally that it is not possible to develope the 

 structure such a glass is capable of showing ; with only the edge of the 

 flame and dry achromatic condenser the bull's-eye added between is 

 necessary, and with this the use and expense of an oil-immersion con- 

 denser is quite unnecessary. Of course I am aware that the aperture is 

 measured by the back lens of the objective. I know that the back lens 

 of an oil-immersion of 1*4: N.A. can only be filled with the use of an 

 oil-immersion condenser on an object mounted in the same refractive 

 index ; but I also know that the objective has not yet been made which 

 will allow the back lens to be so filled with light without utterly 

 breaking up the image. The full aperture of such a lens, then, can never 

 be utilized, and the use of the bull's-eye condenser will allow as much of 

 it to be used as is practicable. 



I am aware that my prints of Pleurosigma angulatum do not agree 

 with the celebrated print by Dr. E. Zeiss, exhibited here at the meeting 

 held on April 11th of last year, and which received the highest praise 

 at that time from some of our leading microscopists as being the greatest 

 advance yet made in the delineation of that diatom. I admit it to be a 

 very striking picture, that photographically it is deserving of all praise ; 

 but the conditions of its production are in violation of every principle 

 laid down by Dr. Abbe himself in his different papers on the theory of 

 microscopic vision. First it is a most flagrant example of what Dr. Abbe 

 calls empty magnifying power ; and secondly, 'the image is false, for the ^' 

 reason mentioned in his paper on the Relation of Aperture to Power, 

 wherein he shows that where the magnifying power of an objective is 

 pushed up much beyond the number of diameters necessary to show the 

 details resolved by the aperture, all details under such circumstances, 

 whether square, triangular, or lozenge shape, acquire the same appear- 

 ance of being round or oval. What then has happened in this particular 

 instance ? The aperture of the objective by which the photograph of 

 Dr. Zeiss was produced has been narrowed down by insufficient illumi- 

 nation from 1"3 N.A. to 0*70; the power has been forced up to 4900 

 diameters, and the result is circles where there should be squares or 

 hexagons. 4900 diameters is more than 40 times the initial power of 

 the objective used, even if all the aj)erture had been utilized ; what then 

 can be the value of such an image as a truthful interpretation of 

 structure when produced with little more than half that aperture ? In 



