528 Transactions of the Society. 



place therefore of the full aperture &> the angular aperture fixed by 

 the diaphragm opening (we will call it 8) must be substituted, and 



then the formula becomes v =( — | ; that is to say, with the 



same illumination, the brightness of field will vary in inverse pro- 

 portion of the square of the linear amplification. For example, 

 make h = 30° (magnitude of illuminating cone), and use amplifica- 

 tions of 240, 300, 360, 420, &c., and we get for brightness of 

 field in the several cases yV» ^z, -st, 4V respectively. Raising, 

 however, the value of 8 to 60° or 90"^ by increasing diaphragm 

 aperture or employing a lens, the brightness will reach from four 

 to nine times the intensity in the respective cases, provided always 

 that the objective aperture admit cones of such angular incidence. 



The above rough calculation is corrected in greater detail by the 

 authors, with the final conclusion that the sectional areas of the 

 corresponding light-cones (those, namely, of the final Microscope 

 image, and of the incident light on the objective) are to each other 

 as the squares of the numbers representing their respective magni- 

 tude. When, then, the light emerging from the ocular (at eye- 

 point) just fills the area of the pupillary opening, the corresponding 

 cone of light entering the objective is therewith determined. For 

 if the latter exceed the dimensions calculated on the above-stated 

 relation of proportion, the excess of light could not be utilized. 

 And, as the sectional area of a cone is always somewhat lar^^er 

 than the interior area of its " calotte," * we arrive at the conclusion 

 that a luminous surface seen through the Microscope can under 

 no circumstances possess greater intensity than when seen with 

 the naked eye. 



Since this paper was written the author has been enabled, by the courtesy of 

 Mr. Crisp, to examine a simple Microscope made by Dolloud (date ?) on the 

 plan of Wollaston's instrument. The optical conditions are, however, changed 

 by removal of the diaphragm, and by giving a sliding vertical motion to the " condenser." 

 The distance of mirror from condenser when the lens is raised so as to bring its 

 focus to the level of the object, is 4 inches : the distance between surface of 

 lens and plane of object being then "9 inch. The lens is worked to radius of 

 •5 inch, and has a front surface of -5 inch. The diameter of mirror is -7 inch, 

 and being distant 4 inches from the lens, allows, when inclined at 45°, the reflec- 

 tion of a parallel beam of light to fall upon the surface of the condenser, occupy- 

 ing its full diameter. In this position, therefore, the light-cone thrown on the 

 plane of the object has a radiant base of • 5 inch, its apex being distant about 

 •9 inch, and the outer rays have consequently considerable inclination to the 

 axis. When the lens is moved down towards the mirror as far as the meclianical 

 arrangement permits, the distance from object to lens is 1'4 inch, and from 



* Because the light-intensity of the respective cones does not exactly bear tlie 

 ratio of the squares of their respective angular magnitudes, but of the respective 

 portions of interiors of spheres conceived to be described round the apex of each 

 cone, on diameters drawn at equal distance from their apices {calotten-fliiche). 

 See pp. 76, 77, second edition of Professors Niigeli and Schwendener's Hand- 

 book, 1877. 



