2 Transactions of the Society. 



fronts, the form of the antipoint is a circular disc surrounded by- 

 rings, the disc having a radius estimated by Sir George Airy at 



2^ (Ail ' V ' r ' 5) ' 



IV. In the case of a circular antipoint the light amplitudes 

 vary in successive zones according to a numerical law illustrated 

 by fig. 2, on p. 6 (Airy, p. 6). 



V. The law of diffraction from spherical wave-fronts is such 

 that, if F be the radius of curvature of the wave-front where it 

 passes the aperture, and 6 be the angle to the axis of collimation 

 of the axis along which a beam of parallel light passing the same 

 aperture would be diffracted, the diffracted cone will come to focus 

 in the focal plane at a point distant by sin 0.F from the axis of 

 collimation (Helmholtz, p. 10). 



VI. The dimensions of the antipoint depend only upon the 

 divergence angle of the focussed beam, and are in no way deter- 

 mined by the magnitude of the aperture causing diffraction (Helm- 

 holtz, p. 11). 



VII. If any optical system yields a correct — that is to say, a 

 flat and aplanatic — image of a plane object, the law of magnification 

 in that system will be that the conjugate images will be propor- 

 tioned to one another inversely in the ratio of the sines of the 

 divergence angles of the beams by which they are severally formed. 

 Thus the law of relative magnitudes is the same for conjugate images 

 as for conjugate antipoints (Helmholtz, p. 12), and, therefore, 



VIII. The state of resolution of a correct image cannot be 

 either improved or impaired by mere change of scale brought about 

 by eye-piece magnification or otherwise, but depends only upon 

 the angle under which incident light is received from the object 

 (Helmholtz, p. 12). 



IX. If two beams of light, although originating in independent 

 light sources, follow very closely adjacent and nearly parallel paths, 

 so that they interpenetrate one another, they will modify one 

 another where they interpenetrate, and may thereby become attuned 

 to one another almost as if they had had a common origin, and so 

 as to be capable of exhibiting all the phenomena of interference 

 (Eayleigh, p. 16). 



X. The limit of resolving power is not simply a question of 

 the propinquity of luminous objects, but depends in a material 

 degree upon the phase relations of the light by which they are 

 severally rendered visible (Eayleigh, p. 17). 



XI. A dark bar on a bright field may theoretically be visible 

 as a boundary between adjacent luminous areas if it has a breadth 

 of -^ X and, under favourable conditions of illumination, even if 

 its breadth be less than this (Eayleigh, p. 18). 



XII. Is the antipoint itself polyphasal ? The black and white 

 dot phenomena discussed in the light of this hypothesis (p. 19). 



