TRANSACTIONS OF THE SECTIONS. 371 



The incident converging cone was sometimes formed by a 

 lens of short focus, placed at the distance of its focal length 

 from the surface. In this case the lamp was removed to a con- 

 siderable distance, and the plate on the first surface dispensed 

 with. The same experiment was repeated with the sun's light, 

 instead of that of a lamp, and the emergent cone of i-ays thus 

 formed was of sufficient intensity to be reflected from a screen 

 at some distance. In this manner the section of the cone was 

 observed at various distances from its summit. 



When these phaenomena were examined in detail, and com- 

 pared with the results of theory, they appeared to differ in two 

 important particulars. In the first place, the observed cone 

 was very nearly a solid cone of rays, while that of theory was 

 but a conical surface. Secondly, the two cones differed widely 

 in magnitude, the angle of the experimental cone being nearly 

 double of that of the theoretical one. This discordance between 

 the results of experiment and those of theory, the author con- 

 ceived to ai'ise from the rays which were inclined to the optic 

 axis at small angles, and which were transmitted through the 

 aperture on the second surface in consequence of its sensible 

 magnitude. To examine this point he proceeded in the next 

 place to try the effects of apertures of various dimensions. 

 The effects of these variations in the resulting phaenomena cor- 

 responded exactly with his preconceived views. The rays 

 which in the first experiments filled the whole of the conical 

 space, parted in the centre, when the aperture was much di- 

 minished ; and the section of the cone, instead of a complete 

 luminous circle, was reduced to a luminous annulus, whose 

 breadth diminished with the aperture. Simple theoretical con- 

 siderations showed that the angle of the true cone in this case 

 must be, very nearly, half the sum of the angles of the observed 

 interior and exterior cones ; and when this correction was ap^ 

 plied to the measurements, the resulting angle agreed, as nearly 

 as could be expected, with that deduced from theory. 



A remarkable variation of the phaenomenon was obtained by 

 substituting a narrow linear aperture for the small circular one, 

 in the plate next the lamp in the first-mentioned mode of per- 

 forming the experiment; and by adjusting it so that the plane 

 passing through it and the aperture on the second surface 

 should coincide with the plane of the optic axes. In this case, 

 according to the received theory, all the rays transmitted 

 through the two apertures should be refracted doubly in the 

 plane of the optic axes, so that no part of the line should ap- 

 pear enlarged in breadth on looking through the aperturfe on 

 the second surface. But if Professor Hamilton's conclusion 



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