The Hclmholtz Theory of the Microscope. By J. W. Gordon. 441 



aspects. We thus arrive at an upright cone, of which the base measures A 

 and the height is proportional to the amplitude of the undulation. The 

 cone, therefore, may be formed with any angle, and in fig. Ill it is 

 shown with an inclination equal to the mean slope of the curve in 

 fig. 109, the corresponding points being denoted by the same letters in 

 both diagrams. 



Such being the light-intensity ^>of the antipoint, suppose that it is 

 moved along the path denoted in fig. 112, thus producing an optical 

 line. It is plain that the line will be fringed by a pair of diffraction 



Fig. 112. 



bands each ^ X in breadth, and in which the light-intensity at any point 

 will be proportioned to the area of those sections of the cone which 

 have passed over the point. We thus obtain a new light-intensity curve 

 as shown in fig. 113, of which the ordinates are proportional to the hyper- 

 bolas that can be cut from the antipoint cone by planes parallel to the 

 axis. Here then we have a .new form of light-intensity curve, and 

 leaving out of account the terminals of the line, we observe that the 



Fig. 113. 



form shown is not now a solid of revolution but a moulded volume 

 bilaterally symmetrical about the vertical plane in which the line lies. 

 Having thus obtained our image-line, we may proceed to develop 

 an image-surface from it by causing it to move parallel to itself over 

 the area to be depicted. The result is, of course, an accumulation of 

 light on every point in the surface proportional to the area of the 

 section of the fringe-curve which has passed over that point, and we 

 thus obtain a final curve as shown in fig. 114, where the ordinates of the 

 new curve are proportional to the areas of the curve in fig. 113. To save 

 space this curve is drawn to a reduced scale — one-half the scale of fig. 113. 



