FOCOMETRY AND APERTOMETRY. 333 



draw-tube, from which the eyepiece has been withdrawn, and 

 then focussing and measuring the image of a stage micrometer 

 scale upon it. It may also be done with an ordinary negative 

 micrometer eyepiece, provided the field lens of it be first removed. 

 The best method, however, is to have a hand-magnifier, such as 

 Zeiss' ( X 10), mounted as an eyepiece, with the usual eyepiece 

 scale in its focal plane. The magnification having been deter- 

 mined for the short tube by one of these methods, the draw-tube 

 is then pulled out to its full extent, and the magnification again 

 found. Let the short-tube magnification equal M, and the long- 

 tube magnification equal Mj, and let 8 equal the distance in 

 millimetres (or inches) through which the draw-tube has been 

 pulled out, then the focal length /, from what has been already 

 shown, is obtained from equation (3) above. 



It should be noted that this result is independent of any 

 interval which may occur between the piincipal points of the 

 objective, and also of the distance through which the objective is 

 moved to focus the image in the second plane. In the case of an 

 immersion lens, as is evident from the diagram, it is the back or 

 upper focal length that is determined, not the lower. 



The method may be employed for finding the focal length of an 

 ordinary Huygenian eyepiece by fitting the nose of the microscope 

 with a short tube, or adapter, in which the eyepiece can be 

 pushed to be used as an objective, with the eye-lens directed to 

 the micrometer on the stage. A condenser may in a similar way 

 be fitted to the microscope, and have its focal length determined. 

 It is advisable to stop down eyepieces and condensers before 

 making these measurements, in order to get a well-defined image 

 of the divisions of the stage micrometer scale. 



Determination of the Focal and Principal Points of Objectives, 

 Eye^neces, etc. — Fit the body of the microscope with an eyepiece 

 and low-power objective in the usual way, and then, after 

 removing the optical part of the sub-stage condenser, screw the 

 objective under examination into an adapter-ring fitting the 

 stop-ring of the condenser ; or let it rest approximately in the 

 axis of the instrument on a 3x1 slip on the stage of the 

 microscope. The plane mirror should then be manipulated to 

 direct light from a distant object (brickwork, say, on the 

 opposite side of the road) along the axis of the microscope. 

 If the objective is placed with its anterior lens uppermost, i.e.y 



JouRN. Q. M. C, Series II.— No. 51. 22 



