ON TKE THEOKY OF THE MICROSCOPE. 255 



are almost too fine for an angalar aperture of 100°. Fragments 

 of fine scales of Hipparchia Janeira, the cross striag of which are 

 equal to angular aperture of from 80*^ to 90°, are also serviceable. 

 According to my experience, a \evy safe estimate of the quality of 

 an objective may be formed after a little practice with the method 

 here recommended. At all events, the amount of optical capacity, 

 in regard to those functions which are independent of mere 

 angular aperture, may be more correctly estimated than is possible 

 with trials of ''defining and "resolving" power worked out 

 separately. 



What, however, this method does not give — namely, the 

 absolute limit of physical discriminating power, may be as readily 

 obtained by direct calculations from measurements of angular 

 aperture as by direct observation of test objects. 



XXIY. In conclusion, certain general deductions respecting 

 the construction of the microscope which follow necessarily from 

 the doctrines and facts above given may be stated. 



The optical capacity of the microscope depends, according to 

 our theory, upon two factors, which have their origin in two 

 different elements of construction. The first is the geometrical 

 accuracy of the course of rays; it determines, through the magnitude 

 of dippeision circles on the image, the size of the smallest details 

 which can, geometrically taken, find expression therein. The 

 second factor is indicated in the capacity of the objective to fulfil 

 certain physical conditions with which the repetition of these 

 details is at all events connected, namely, the integration of the 

 pencils of light split up by diffraction, without which the image 

 remains bare of contents. As on geometrical principles detail is 

 not imaged when its magnitude is less than that which expresses 

 the diameter of the dispersion circles (reduced to the linear 

 dimensions of the object), so on physical grounds detail is not 

 imaged when the angular dispersion of the diffraction pencil is 

 so large as to render their re-union impossible (even of two 

 pencils only), l^ow the condition for both functions are alike, 

 as has b3jn already shewn, roDted ia the objeotive alone, but they 



