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A Note on the Determination of the Foci of Microscope 

 Objectives and Screen Distances by Simple Arithmetic. 



By Edward M. Nelson, F.R.M.S. 



{Bead March 16th, 1894.) 



From time to time various articles have appeared in text-books 

 and in periodicals with regard to the determination both of the 

 foci of microscope objectives, lantern and camera lenses, as well 

 as of the distance a screen should be placed from a lantern to 

 obtain, with a projection lens of a given focus, a disc of a given 

 size. 



As both these questions are involved in the same discussion, 

 they may be taken together. The usual argument, found in text- 

 books and periodicals treating of the lantern and camera, can 

 hardly be called an optical one, for it merely consists of the 

 solution of an elementary geometrical problem, involving a rule-of- 

 three sum, but which, at the same time, wholly ignores the first 

 principles of optics. The formula in question is found under 

 many forms, the following is an example :— 



T^. , disc X focus ,. . 



Distance = -, .. (i.) 



mask 



We will first examine the method by which this formula is ob- 

 tained. It might aptly be termed the pinhole method, for it con- 

 sists in drawing two lines across one another, as in the Fig., which 

 is neither more nor less than an illustration of a pinhole camera. 



Instead of adhering to the usual nomenclature, it will be pre- 

 ferable to call the disc the image (^), and the mask the object (o), 



