826 SUMMARY OF CURRENT RESEARCHES RELATING TO 



theoretically one single lens defined in position on the same axis by four 

 points, viz. the two focal points and the two principal points. If one of 

 these pairs of points has been determined, a knowledge of the dioptric 

 power gives the other pair. 



Two methods are given for the experimental determination of the 

 focal points of a centered dioptric system. 



(1) The first process depends on the formula of magnification 



G = /. 



If p denote the distance of the object from the nearest face of the 

 diopter, py the distance of the first focal j)oint from the first face of the 

 diopter, we have 



q=P -JOy. 



Then 



G = 



/ 



I> -P/ 

 and 



/ 

 Pf = P-^' 



Thus, in order to know pj, it is necessary, during the determination 

 of the magnification, to measure the distance p of the object from the first 

 face of the diopter. 



The determination of the second focal point is made in the same 

 manner by reversing the system. 



(2) The second method depends on the formula, 



G = q'¥ 



in which q' = p — p'j-, 



p' being the distance of the image from the nearest face. 



The practical operation consists in the employment of a sufficiently 

 powerful Microscope. The image and refracting surface are brought 

 successively into focus for that Microscope ; the displacement, measured 

 by a micrometer-screw, gives the absolute position p' of the image, and 

 thus the second focal point is obtained. The first is found in the same 

 manner by reversing the apparatus. 



The position of the focal points being known, that of the principal 

 points is obtained by measuring off the focal length from these points. 

 Finally, the principal space (distance between the principal points) is 

 obtained by measuring the thickness of the system i. e. the distance 

 between the summits of the extreme refracting surfaces. These pro- 

 cesses for determining the optical constants have the advantage over 

 those of M. Cornu, who uses the formula of conjugate foci, in that the 

 apparatus under examination can be kept in a constant position. 



When great precision is not required, the following simple method 

 may be used : — An object strongly illuminated at the side of the observer 

 throws its rays on a small plane mirror at a distance of about 5 metres. 

 The beam reflected nearly normally traverses the Microscope under 

 experiment, and gives a very small image of the object, as if the latter 

 were disposed at a distance of 10 metres. The image is situated so near 

 to the principal focus that the diftercnce is negligible. 



