436 Mr EARNSHAW, ON THE DIFFRACTION OF AN 



The Interpretation of the Formula for the Brightness. 



It will be found upon trial that the value of Z is not altered when 

 — is written for + ; and hence it follows that the light is symmetrically 

 arranged with regard to the axis of x. 



It will likewise be found that the value of Z is not affected when any 

 one of these values, e + 60°, 9 + 120", 6 + 180°, + 240", 9 + 300", is 

 substituted for ; and hence it follows that if from the origin of co- 

 ordinates, or centre of the screen, six lines be drawn upon it making 

 respectively the angles 0", 60", 120°, 180", 240°, 300" with the axis of x. 

 or, which is the same, inclined at angles of 60" to each other, the light 

 upon the screen is similarly and symmetrically arranged with regard to 

 every one of them. 



Wherefore, the light being symmetrically arranged about these six 

 lines, it will only be necessary to examine our formula for Z between 

 the values 0=0 and Q = 30". 



It will at once be seen from an inspection of the equation preceding 

 the one marked {B), that the value of Z depends upon the three terms 



sin^ {m sin 6) sin^ jwesin (60' -k- Q)] sin^ \msm{Q(y-9)\ 

 sin^9 ' sin^(6O" + 0) ' smM60" - 0) 



each of which is precisely similar to the principal term in the expression 

 for the intensity of light in the experiment of Fraunhofer's gratings ; 

 and at first sight it might be deemed sufficient to examine each of these 

 terms separately, and thence judge of their united effect: but it will be 

 found upon trial that the multiphers by which they are connected toge- 

 ther exercise such an important influence upon their values, as to render 

 this method utterly inapplicable in the present instance. Thus, if 6 be 

 very small, the second and third terms are very nearly equal, and having 

 different signs their sum is very small ; but being afterwards divided by 

 sin Q, the quotient is large ; and their united effect is as great as that 

 of the first term. 



