Mr. J. Bridge on the Diffraction of Light. 323 



case the positioiis of maximum and minimum displacements will 

 be unaltered. 



(4) If any focal line (line through focus) be drawn, the inten- 

 sities in it at equal distances from the focus are equal. This is 

 seen immediately in the formulae, for a change of sign of a does 

 not affect A^ + B^. Or thus : the displacement at any time t in 



X 

 the one case is equal to the displacement at the time ^ — t m 



the other case, so that the maximum displacements being the 

 same, the intensities are also the same in both cases. 



(5) Similar apertures give similar figures of diffraction with 

 dimensions inversely as their own. 



For if X and y are multiplied, and at the same time a. divided 

 by a constant, A and B will also be multiplied by the same 

 constant. 



Otherwise ; in a small right-angled triangle one side is con- 

 stant if the hypothenuse and opposite angle vary inversely. 

 From this it appears that the displacements in two given planes 

 making angles with the apertures inversely as their dimensions 

 are the same. 



(6) If the apertures have the values of y equally distributed 

 on opposite sides of the axis of a?, B = 0, and A is double what it 

 would be on one side. 



(7) If the aperture be moved to any parallel position, so that 

 every x is increased by |, A and B become 



and 



, 27ra| , ^ . 27r«? 

 A cos ^ -t-Bsm— r— , 



^ 27r«| . . 27r«? 

 B cos ^ —A sm — r — . 



(8) The figures formed by a series of equal similarly situated 

 apertures may be found from that produced by one aperture and 

 that produced by a series of points having the same arrangement 

 as the apertures. The intensity at any point will be the product 

 of the intensities from the two figures. 



For the disturbance arising from each point of one aperture, 

 combined with that from corresponding points of the others, 

 becomes multiplied in a certain proportion depending on the 

 arrangement; therefore the disturbance from one aperture be- 

 comes multiplied by the ratio of that from a series of points to 

 that from one point ; so that the intensity is the product of the 

 intensities in the two cases. Darkness will therefore exist from 

 the series of apertures wherever it would exist from one aperture 

 and from the series of points. 



Y2 



