PENETRATION IN OBJECTIVES. 175 
to see the whole of one of them under one focussing. This 
amount cannot be obtained from a 1% inch objective of 16° air- 
angle, even allowing the 230 micras, which the accommodation of 
the eye affords, and if we wish to photograph such an object as 
the above, the four inch of 8° air-angle will not be found possessing 
sufficient focal depth. 
The Foraminifer Ovbulina universa, a beautiful spherical body 
with fine surface markings, is now before us. It possesses a 
diameter of 600 micras, and consequently 300 micras of penetra- 
tion are necessary to see the whole under one focussing. ‘The 
1% objective and A ocular magnifying together 30 diameters will 
just suit this, provided it does not possess an angle of over 20° in 
air, but if we wish to photograph this spherical body a much lower 
power than the 1% inch must be employed, as the focal depth of 
this objective is not higher than 86 micras. Ovrbulina universa 
affords us good proof of the accuracy of Professor Abbe’s figures. 
Under the 1% inch objective of 16° and the A ocular the spheres 
are splendidly seen, and the same may be said of the 2 inch of 16° 
and B ocular, but when the picture is thrown upon a ground glass 
screen the want of penetration is soon apparent, for it is only 
when the amplification of the picture has been reduced to rather 
less than ro diameters that a satisfactory result is obtained. 
Similar illustrations may be offered of the higher power objectives, 
the difficulty of photographing depth in polycistina is $hown by the 
photographs A and D in our September number of last year. The 
larger species of Polycistina require a depth of 75 micras to show 
them distinctly, whereas a half-inch objective of 40° in air when 
used with the A ocular to produce 1oo diameters of amplification 
possesses but 10°6 micras. 
A one-sixth objective, magnifying 300 diameters, loses exactly 
one » in depth between 74° air-angle and 1°2 Numerical aperture, 
so that while the spores of Penicillium glaucum (diameter of spores 
3 ») could be photographed with the former, it would be impossible 
to obtain perfect sharpness with the latter. 
The figures in Table I. for the one-twelfth and one-twentieth 
objectives are equally confirmed by the results obtained in practice. 
The short diameter of Bacterium termo may be taken as ‘8 p requir- 
ing a penetration of ‘4 » to yield a clear picture, and this is 
obtainable by using a homogeneous one-twelfth of 110 N. A. to 
produce an amplification of 600 diameters. © A one-twentieth 
objective, magnifying 1,000 diameters, although producing a fairly 
sharp picture to the observer's eye, cannot produce an equally 
sharp image on a prepared plate, as the focal depth of such an 
objective will only approximate to ‘37 p, and this statement is 
borne out by the photographs published by Dr. Sternberg in his 
translation of Magnin’s treatise on the Bacteria, wherein those 
