118 THE AMERICAN MONTHLY [Apr 



raatic object-glasses, such as No. 1, No. 2, &c, or sys- 

 tem A, etc., the English and American manufacturers, af- 

 fecting a higher degree of accuracy, have undertaken to 

 name\he objectives they construct by their real or sup- 

 posed agreement in magnifying power with single lenses 

 of specified focal lengths. At first sight nothing could 

 appear simpler or more exact than such a nomenclature ; 

 nevertheless, recent articles in the journals would seem 

 to indicate that the general plan is capable of considera- 

 ble modification in its practical application, and that 

 grave misunderstandings have hence arisen. Under these 

 circumstances, it appears desirable to give some account 

 of the principles involved and of positive difficulties to 

 be considered in their application, particularly as the 

 microscopical text-books contain little or no information 

 on the subject. In fact, the only scientific description of 

 the matter with which I am acquainted is the paper of 

 Mr. Charles R. Cross 'On the Focal Length of Micro- 

 scopical Objectives' {Journal of the Franklin Institute, 

 June, 1870, p. 401). This paper gives a reasonable for- 

 mula for the approximate computation of equivalent focal 

 lengths, and furnishes some other valuable information, 

 but does not discuss all the points at issue. 



We learn from the elementary treatise on optics that 

 when an object is placed in front of a single convex lens, 

 at a distance somewhat greater than its focus for par- 

 allel rays, a real image is formed on the other side of the 

 lens, which may be received on a screen. This image 

 will be larger, and formed at a point more distant from 

 the lens, the nearer the object approaches to the focus for 

 parallel rays ; and two equations are given which express 

 the relationship of the distances to each other, and to 



111 p' 



the magnifying power, viz.: = —-{-—, and - 



/' p p' p 



= m, in which /is the length of the focus for parallel 



