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III. — So77ie Bemarks on the Apertometer. 

 By Professor E. Abbe, Hon. F.E.M.S.* 



{Read litJi January, 1880.) 



Several papers have recently been published by Professor 

 Hamilton L. Smith, Dr. Woodward, Mr. Wenham, and Mr. E. 

 Hitchcock,! relating to the measurement of apertures, which 

 touch from different points of view the use and performance of the 

 apertometer. In order to remove certain difficulties which have 

 been met with in the application of my method, and some objections 

 which have been made to it, I beg to give here some further 

 explanations as to the arrangement of the apparatus and the 

 principles on which it is based. From the discussions, I infer that 

 some essential points in my method of measurement have not 

 received due attention, owing perhaps to the very brief — though 

 exhaustive — explanation in Mr. Zeiss' description of the instru- 



ment-t 



In measuring the apertures of an objective by observing the 

 limits of its telescopic field of vision, " the real area of field in the 

 microscopic action of the lens, or the central part of this area, must 

 be made to act as the area of aperture in telescopic vision." Or, the 

 same condition expressed in another way : the diaphragm, through 

 which in this telescopic observation the image-forming pencils 

 have access to the eye of the observer, must be in such a position 

 as to be conjugate to the same focus in front of the objective, 

 from which the rays start in microscopic observation. 



With the view of rendering clear the meaning of this condition 

 as well as its necessity, I may refer to a general proposition which, 

 though derived from the A B C of optics, applies to many important 

 questions in the theory of optical instruments. 



Let L be any system of lenses which takes in and transmits 

 rays from different objects, and and 0' two limited areas in 

 planes perpendicular to the axis, which in position and figure are 

 in the relation of an object to its image in respect to L, i. e. which 

 are situated at conjugate points of the axis and are conjugate one 

 to another as to their linear extension, then all the rays entering 

 the system L through the area will leave the system through 

 the area 0' ; and no single ray can emerge from L through the 

 area 0' which has not entered L through the area 0, from what- 

 ever objects the rays considered may start, or towards whatever 

 points they may proceed. (It is the same thing, whether is 

 considered to be the object and 0' the image or vice versa.) 



* The original paper is written by Professor Abbe in English. 

 t 'Am. Quart. Micr. Journ.,' 1. (1879) pp. 194, 272, 280, 284. 

 X This Journal, i. (1878) p. 19. 



