20 Transactions of the Society. 



II. — On the Mode of Vision with Objectives of Wide Aperture* 

 By Prof. E. Abbe, Hon. F.E.M.S. 



( Read 12th April, 1882.) 



The idea of " all-round vision " as a peculiar capacity of wide- 

 angled lenses has been put forward with opposite aims. The object 

 of one side has been to indicate an advantage of wide aperture- 

 angles in the vision of solid objects, depending on the angles 

 qua angles and the admission of rays from all sides of the object 

 at the same time. The other opinion claims that this must be a 

 disadvantage, constituting an unnatural mode of vision, causing 

 particles to look spherical (when sufficiently minute) even if in 

 reality cubes, and giving rise to a confusion of dissimilar images. 



The tacit supposition of both views is, that the optical conditions 

 of microscopical observation are essentially the same, even with the 

 minutest objects, as those of naked-eye vision — that a solid object 

 is depicted through the Microscope in the same perspective, in 

 which it would appear to the eye in ordinary vision, if it were 

 looked at in the direction of the delineating pencils. 



They assume, for example, that a minute die at c d (fig. 1) 

 if depicted by means of oblique pencils r (such as are admitted 

 through the marginal zone of a wide-angled objective) will appear 

 in the microscopic image with the perspective in which it would 

 be seen by an eye in the direction of r. It would thus appear 

 as the projection of the die on a plane P perpendicular to the 

 direction r, or, which is the same thing, as if it were placed in an 

 inclined position on the stage under axial illumination (fig. 2). 



Fig. 1. Fig. 2. 



In fact it is supposed that obliquity of the delineating pencils 

 to the axis of the Microscope is equivalent to and produces the 

 same effect, i]i regard to the manner of projection of the image, 

 as an oblique position of the object under perpendicular (axial) 



* The paper (received 3rd March 1882) is written by Prof. Abbe in English. 

 Its publication has been delayed pending the completion of Prof. Abbe's paper 

 in the last volume. 



