514 EECORD OF CURRENT RESEARCHES RELATING TO 



duced as right angles ; even the more distant curves of both systems 

 of hyperbolas whose branches do not intersect in the figure but 

 evidently diverge from each other (e. g. those for u = • 8), intersect 

 at right angles in the image, though their point of intersection — 

 corresponding to an imaginary point in mathematics — is at a distance 

 from the centre of the image which no rays of light emerging from 

 air can reach, outside the circle on the plane of the image which 

 corresponds with the boundary of a cone of rays of 180° in air. 



With objectives whose focal distance is not very short — down to 

 about 3 mm. — the appearance described may be seen with the naked 

 eye by removing the eye-piece from the tube of the Microscope and 

 looking down the open end, keeping the eye as much as possible in 

 the centre, and near the sj)ot where the real image would be formed 

 when the Microscope is used in the ordinary way, and viewing the 

 air-image floating above the objective. 



With objectives of very small focal distance, an auxiliary Micro- 

 scope of low power must be inserted in the tube, and a diaphragm 

 placed in a position conjugate to the aplanatic focus. 



This method converts the whole optical system into a telescope 

 with a terrestrial eye-piece through which the drawing which serves 

 as the object is viewed. The microscopic objective which is being 

 tested acts as a telescopic objective, its aperture angle gives the angle 

 of the field of view of the telescope, and what in the ordinary use of 

 the Microscope is the field of the object, the element of surface in its 

 aplanatic focus, acts as entrance aperture when thus used like a 

 telescope. 



Numerous trials have been made by Professor Abbe with 

 objectives of various construction and by difi'erent makers, and the 

 results have invariably confirmed the theory above laid down. 

 With the exception of the objectives manufactured by Zeiss, there 

 are probably none that have been constructed with this prin- 

 ci^de avowedly in view. If in spite of this the objectives of all 

 opticians on the Continent, in England, and America satisfy this 

 condition, the fact shows more convincingly than any theory could 

 do, that this peculiar convergence of the rays is undoubtedly an 

 essential constituent of aplanatism in a lens-system. 



The above experiment is instructive in many other respects. It 

 illustrates practically some theoretical deductions regarding the 

 ima^e produced by a cone of rays of large angle, as for examjile, 

 the influence of the angle of aperture on microscopic vision. The 

 portions of field between the hyperbolic curves which are so 

 extremely dissimilar, (the area of those on the outside being many 

 times the area of those in the interior,) appear as squares of equal 

 dimensions, and when the diagram is uniformly illuminated no 

 difierence in the brightness can be discerned, although in the 

 squares on the margin the rays are compressed which proceed from 

 an illuminating surftice many times larger than that corresponding to 

 the middle squares. This fact shows plainly the great inequality in 

 value of the different parts of the angular aperture with respect to 

 their share of the quantity of light which the system receives. 



