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SUMMARY OF CURRENT RESEARCHES RELATING TO 
considers that a focal length of 1/12 for the English tube, and 1/18 for 
the short tube ought not to be exceeded. With these combined with 
strong eye-pieces, magnifications of 3000 times can be attained. As 
good examples of such objectives, he cites the No. 9 of Nachet, No. 10 
of Verick, the 1/12 and 1/16 homogeneous immersion of Zeiss, and the 
1/12 1*30 homogeneous of Leitz. 
The power of an objective, then, depends only upon its aperture, 
which is measured by the product 
n sin m, 
where n is the index of refraction and 2 m the angle under which the 
extreme rays from the object penetrate into the objective. The power 
of the objective is represented by the square of its numerical aperture. 
In a good objective it ought to be possible to utilize 1/3 of the total 
aperture. This condition is fulfilled when the central luminous circle 
seen on looking into the body-tube, has a diameter equal to 1/3 of the 
total diameter of the aperture. Now the ordinary mirror applied to 
Microscopes throws upon the object a luminous cone of about 30° 
angular aperture, which corresponds to a numerical aperture of 0*25. 
With such a mirror therefore an objective having an aperture three 
times as great, viz. 0*75, can be used. Beyond this, it is necessary to 
have recourse to special condensing apparatus, furnishing wider illumi- 
nating cones. 
Taking into account the nature of the light employed, the more 
correct expression for the power of an objective is 
n sin u > 
where \ is the wave-length. 
Thus p can be augmented by diminishing X, as well as by increasing 
n and u. The power of an objective expressed as 1 in white light will 
be 1 • 08 in blue and 1 • 32 for the extra- violet rays. It is not surprising 
therefore that photographs may be obtained of details with objectives 
which do not resolve them to the eye. 
The author gives the following practical directions for the use of 
high-power objectives : — 
(1) To always give to the body-tube of the Microscope the length 
for which the objectives are corrected, 0*160 m. for the short tube, and 
0 * 250 m. for the English tube. 
(2) To employ dry and immersion objectives which are mounted for 
correction, starting with a numerical aperture 0*75 (about 100° in air). 
If the graduation of the correction is not given in thickness of cover- 
glass, to find out the relation between them from the maker. 
(3) With homogeneous objectives, whenever it is required to utilize 
marginal pencils, to optically unite the upper lens of the condenser to 
the preparation by means of a liquid with index of refraction at least 
equal to that of the immersion medium, and to only use preparations 
mounted in a medium of this index. 
(4) With these objectives to always use a condenser. 
The subject of the illumination of the Microscope receives very com- 
plete treatment at the hands of the author. 
