334 F. J. CHESHIRE ON SIMPLE METHODS OF 



in such a position that light passes through it in the opposite 

 direction to that in which it passes when in ordinary use, an 

 aerial image of the distant object will be formed at its lower* 

 principal focus. The microscope body should then be adjusted 

 to focus this image in exactly the same way as an ordinary 

 object is focussed. Then, having noted the position of the 

 body of the microscope, rack it down until the dust on the first 

 lens surface is in focus. The distance racked down, which is 

 best determined by means of a scale carried by the body, is 

 equal, of course, to the distance between the principal focus and 

 the first lens surface. The objective should now be reversed, so 

 that the light passes through it in the opposite direction, and 

 the experiment repeated to determine the position of the upper 

 principal focus with respect to the outer surface of the posterior 

 lens of the objective. In Huygenian eyepieces the lower, and 

 in high-power objectives in general the upper principal focus 

 is virtual, i.e., parallel incident rays do not converge to a point 

 outside the optical system, but they appear to diverge from a 

 point within it. Experimentally, however, the only difference 

 is that the microscope body must be racked up, and not down, 

 to focus the dust upon the lens surface after focussing the image 

 of the distant object. 



Having determined the positions of the focal points of an 

 objective, etc., of known focal length, the positions of the prin- 

 cipal points can be readily determined by setting off the focal 

 length along the axis, from each focal point in turn, in the 

 opposite direction to that in which light must pass through 

 the objective to produce an image at the focal point from 

 which the measurement is made. 



Optical Tube-length. — Instead of determining the positions of 

 the focal and principal planes with respect to the lens surfaces, 

 it is generally more convenient, in the case of objectives, to do so 

 with respect to the face of the flange which butts against the 

 nose of the microscope body. This can be done by focussing in 

 succession the picture in the upper focal plane and the face of the 

 flange, and measuring the necessary body displacement. The 



* Throughout this paper the two foci of condensers, objectives, and 

 eyepieces are distinguished by the words "upper" and "lower," which 

 have reference to the positions occupied by the foci in a microscope in 

 ordinary use. 



