512 



RECORD OF CURRENT RESEARCHES RELATING TO 



Fig. 35 



form to be described later on), 

 with the same centre and con- 

 jugate axis but witb different trans- 

 verse axes, will be reproduced in 

 the image as a system of parallel 

 straight lines. It is here assumed 

 that the pencils of rays which form 

 the image, cross on entering the 

 lens-system in the aplanatic point 

 which is situate on the side next 

 the object, and for the sake of sim- 

 plicity the angle of convergence of 

 the rays in the conjugate aplanatic 

 point on the side next the image is 

 assumed to be so small that sine and 

 tangent may be regarded as equal. 



These conditions are fulfilled 

 if with an objective of large aper- 

 ture, the pupil of the observer's 

 eye — or whatever opening admits 

 the rays to the eye — is brought to 

 the axis of the system, and at the 

 spot where the conjugate aplanatic 

 focus on the side next the image 

 is ; because in this case no ray can 

 reach the eye which has not passed, 

 on its entrance into the system, 

 through that element in the object 

 which is on the axis conjugate to the 

 pupil or other opening. The as- 

 sumption as to the angle of con- 

 vergence in the aplanatic point next 

 the image is evidently satisfied suffi- 

 ciently in microscopic objectives. 



The hyperbolas above referred 

 to are constructed from the equa- 

 tion 



y = — /\/ x^ — a}, 

 a 



where A (the common conjugate 



axis for both sets of hyperbolas) 



represents the distance of the plane 



p of the object from the correspond- 



[L is a eystem of lenses which is aplanatic for the conjugate points O and O* ; 

 the condition of convergence being fulfilled, 

 - si 11 W 

 " —. — =^ = const, for any two conjugate rays through O and O* . 



P Pis a plane perpendicular to the axis, at a distance A below the aplanatic 

 focus O ; P* P* is the image of this plane, depicted by pencils whose principal 

 rays cross at O and 0* — under these conditions the image P* P* shows the dis- 

 tortion described aLovc. The thicker lines indicate the principal rays.] 



