432 Mr EARNSHAW, ON THE DIFFRACTION OF AN 



selected for this purpose, the diffraction of light at the object-glass of 

 a telescope with a triangular aperture, for two reasons, — because the 

 phaenomenon is very singular and very beautiful; — and because Sir 

 J. Herschel has declared that "to represent analytically the intensity 

 of the light in one of the discontinuous rays, will call for the use of 

 functions of a very singular nature and delicate management." His 

 description of the phtenomenon is as follows. {Encydop. Metroj). 

 Light. Art. 772.) 



" When the object-glass of the telescope was limited by a dia- 

 ])hragm so that the aperture was in form of an equilateral triangle, 

 the pliEenomenon seen by viewing a star through the telescope was 

 extremely beautiful : it consisted of a perfectly regular, brilliant, six- 

 rayed star, surrounding a well-defined circular disc of great brightness. 

 The rays do not unite to the disc, but are separated from it by a 

 black ring. They are very narrow and perfectly straight ; and appear 

 particularly distinct in consequence of the total destruction of all 

 the diffused light, which fills the field when no diaphragm is used : 

 a remarkable effect, and much more so than the mere proportion of 

 the light stopped." 



Let us suppose the aperture of the telescope an isosceles triangle, one 

 of whose equal sides = a ; the perpendicular from the vertical angle upon 

 the base = 3f, and the inclination of either side to the base = a. 

 Let the image of the star be received upon a screen passing through 

 the focus of the object-glass ; and take the projection of the centre of 

 gravity of the triangular aperture upon the screen for the origin of co- 

 ordinates ; the axes of x and y upon the screen being respectively per- 

 pendicular and parallel to the projection of tlie base of the triangular 

 opening, and the axis of % coinciding with the axis of the telescope, and 

 passing through the centre of gravity of the aperture. Suppose b = focal 

 length of the object-glass, and let x, y, % be co-ordinates of any point P 

 in the wave surface, which emerges from the object-glass, and tends to 

 the origin of co-ordinates as its focus; 



,-. x^ + y'^ + %^ = b\ and 3c = a sin a. 



