516 



Transactions of the Society. 



the eye-piece scale and its length read off in the usual way. Fig. 54 

 shows a diagrammatic plan of the apparatus together with the ray 

 diagram necessary for demonstrating the optical principle of the 

 method. 



The scale division h, in the principal focal plane of the collimat- 

 ing lens of focal length / , is projected into the principal focal 

 plane of the lens L being tested as a length hj ; this again is 

 projected by the objective of the auxiliary Microscope on to the 

 scale in the eye-piece as a length h 2 . Let the focal length of the 



Collimator 



A uxiliary Microscope 



Fig. 54. — Diagram of substage focometer system. 



lens L which it is desired to find be /, and the initial magnification 

 of the auxiliary Microscope be M. Then 



^=1 and ^1=1 

 h f c h 2 M 



K _/ or f== fjh 



Mh 



MA / 



whence 



f 



But =^- is a constant for the instrument, k say, thus 

 M h 



f = k h 2 



For convenience in use it is very desirable to make k equal to 

 some simple number, as 10. 



To do this when h is a millimetre it is clear that the focal 

 length of the collimator (/ c ) in millimetres must be made equal 

 to ten times the initial magnification (M) of the auxiliary Micro- 

 scope, then 



/= 10 hi. 



If with these dimensions of the optical elements the eye-piece 

 scale is a centimetre divided into a hundred parts, each division of 

 it will correspond to a millimetre of focal length. Should, for 



