TRAXSACTIONS OF SECTION A. 569 



slit of the collimator. The object of the paper is to explain the mode of formation 

 of these bands. 



In an absolutely perfect grating all the light going to form the spectral line 

 of any particular order is brought to a single focus by the objective of the telescope, 

 and the emergent cone of light is bounded by the image of the grating formed by 

 the objective (the distance between tbe grating and the objective being greater 

 than the focal length). In the case of a grating containing two rulings differing 

 by a small amount the light from each portion will be brought to its own 

 appropriate focus, and the two emergent cones of light will be bounded by the 

 corresponding parts of the image of the grating. A screen placed in the position 

 of this image would be uniformly illuminated, but if it were moved nearer to the 

 lens the boundary between the two rulings would receive light from 6oM the cones 

 or from neither of them, according to the relative positions of the foci. If the 

 screen were moved further from the lens the effect would be exactly reversed, sq 

 that a light band iu one case becomes a dark band in the other. 



The theoretical results, which have been verified by observation, may be 

 summarised as follows : — 



Orders on the right of the central image (the observer is supposed to be facing 

 the grating). — Case 1. In passing from a wide to a narrow ruling in going from 

 left to right. Focus in, light band. Focus out, dark band , 



Case 2. In passing from a narrow to a wide ruling in going from left to right, 

 Focus in, dark band. Focus out, light band. 



Orders on the left of the central I'ma^e.— .-The results just given must be 

 reversed. 



The bands disappear when the telescope is focussed exactly on the grating. 



5. On a new Electromagnet and an Echelon Spectroscope for Magneto-optic 

 Observations. By Professor A. Gray, F.R.S., and Dr. W. Stewart. 



6. On Resolving Power in the MicroscojJe and Telescope. 

 By Professor J. D. Everett, F.R.S. 



The author maintains, in opposition to the view put forward in standard books 

 on the microscope, that resolving power, whether in the microscope or the tele- 

 scope, depends simply on keeping down the size of the disc which, owing to 

 difiraction, is the image formed by the objective of a luminous point of the object. 

 The illumination of the disc diminishes from the centre outwards according to a 

 well-known law, first worked out by Airy, becoming zero at a definite distance ; 

 but for a considerable distance within this limit the illumination is too faint to be 

 appreciable, and the visible size of the disc therefore increases with the brightness 

 of the luminous point which is imaged. The radius of the disc, reckoned up to 

 the theoretical limit of zero illumination, is directly as the wave-length of the 

 light employed, and inversely as the sine of the semivertical angle of the cone of 

 rays which emerges from the objective. The effect of large aperture in the tele- 

 scope, or of large N.A. in the microscope, is to increase the sine of this angle, and 

 in the same proportion to increase tbe fineness of representation. 



Dawes' results for the closeness of double stars which can be just separated by 

 a given objective lead to the conclusion that the two discs, corresponding to the 

 two nearly equal components of the star, can be just recognised as two when the 

 illumination due to one at the centre of the other is about -^ of the central 

 illumination ; and Abbe's determinations of the resolving powers of microscopical 

 objectives, as dependent on N.A., lead to exactly the same conclusion for the 

 microscope, an agreement which seems to have hitherto escaped attention. 



Abbe s own view, as stated in the concluding sentence of his Paper to the 

 Royal Microscopical Society (vol. i. 1881, p. 42.3), is: — 



' The very first step of every understanding of the microscope is to abandoi^ 



