Application of Undulatory Theory. By A. E. Conrady. 409 



placement peculiar to the diffracted waves, or, briefly, the magnitude 

 of their elongation, and by the relative phase, which latter is ex- 

 pressed either by the value of the phase angle, or else by the sign 

 of the computed amplitude ; the angle t, or a in my previous 

 communications, merely expresses the undulatory nature of the 

 phenomena, but does not affect either the intensity or the relative 

 phase of the light. The idea that its presence in a formula must 

 cause embarrassment could only occur to one totally devoid of 

 mathematical instinct. 



But the application of the graphical method to this problem 

 may be of considerable interest 

 to those who cannot or will not 

 study a mathematical proof. 



The principal result of the 

 mathematical investigation re- 

 ferred to was that diffraction- 

 spectra from plane gratings have 

 either the same or else the op- 

 posite phase of that simulta- 

 neously existing in the direct 

 light, and this can be shown gra- 

 phically in the following manner. 



It is desired to determine the 

 amplitude and phase of the light 

 reaching Q 1 from a slit S (fig. 77) 

 lighted from a distant point P, 

 the amplitude to be compared 

 with that which would obtain at 

 point Q at the same distance 

 from the slit as Q 1 , but in a direct 

 line with P, and the phase to be 

 referred to that which light from 

 the centre of the slit would pro- 

 duce at Q 1 . 



Both P and Q, being at a distance which is assumed to be great, 

 as compared with the width of the slit, all the light will reach Q 

 in the same phase, and we shall, therefore, get a resulting ampli- 

 tude at Q, which is the simple sum of all the disturbances proceeding 

 from the slit. But otherwise at Q 1 . For here we have obvious 

 differences of the paths, by which light from P through the different 

 portions of the slit, reaches Q 1 ; hence there will be more or less 

 weakening of the light at Q 1 through interference. If we now 

 divide our slit into a number of equal parts so narrow that the 

 light from any one part may be assumed to reach Q 1 in the same 

 phase, we shall be able to combine the light from these parts 

 in pairs by the simple process shown in fig. 75. Such a pair close 

 to the centre will have an inappreciable difference of phase, and 



Fig. 77. 



