W. LeConte Stevens — Microscope Magnification. 55 



DT 

 U= w . . : (6) 



It remains now to be seen what modifications need to be im- 

 posed upon formula (6), since formula (1), from which it is 

 developed, is confessedly only approximate. Its second mem- 

 ber should, be equal to the product of the magnifying powers, 

 m and m', of objective and eyepiece respectively, as deter- 

 mined by experiment. 



Assuming that the eye-piece has been constructed in accord- 

 ance with the conditions implied in the formula, F is to be 

 determined from/' 7 , which in turn can be measured with but 

 little error by use of the camera lucida. Let an eyepiece mi- 

 crometer be placed at the diaphragm and properly illuminated, 

 the microscope body being so tilted that the optical center of 

 the eye lens shall be 25o mm above the white paper on the table. 

 With the camera lucida the divisions of the micrometer are 

 projected on the paper, and the magnification, m\ is directly 

 determined. To find f ; , since the image is virtual, the value 

 of rnf is substituted in the formula, 



m' = 5+l . . . -. (7) 



This method may be checked by detaching the eye lens and 

 testing it independently by Cross's formula, to be presently 

 given. 



The value of f\ the focal length of the objective, cannot be 

 determined by ordinary methods because the microscope ob- 

 jective usually consists of two or more systems of lenses, each 

 made up of a crown and a flint ; and the error involved in 

 measuring the thickness of each of these separately and also 

 their distance apart is so considerable as to make the final 

 result very uncertain. The best formula to apply is that 

 deduced some years ago by Prof. C. B. Cross.* This formula 

 is of such importance that its deduction and application are 

 best given in this connection. 



Let the field lens of the eye- piece be removed, and two 

 micrometer scales be employed, one of which, divided into 

 lOths of a millimeter, is placed on the stage as an object, while 

 the other, divided into millimeters, is placed at the diaphragm 

 in the focal plane of the eye lens. The image of the stage 

 micrometer is focused upon the eye-piece micrometer, and the 

 comparison of these images gives the magnifying power, ?n, of 

 the objective at the distance selected. Assuming provisionally 

 an optical center for the objective under the given conditions, 



* Journal of the Franklin Institute, vol. lix, p. 401. 



