The Helmholtz Theory of the Microscope. By J. W. Gordon. 383 



illustrate this point. Here, we have the path of a train of plane 

 wave-fronts indicated by thirteen sections denoting successive 

 phases of three complete undulations. The phases of rest are 

 denoted by the section lines t (trough) and c (crest) respectively. 



" ■ AA/V*" 



it tt t c e A 



t it 



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f)«il>»IUIA 



Fig. 76. 



The intermediate positions of most rapid motion upward and 

 downward are denoted by section lines shown with arrow-heads, 

 and a wavy curve at the top of the diagram indicates for a particular 

 instant of time the simultaneous displacement of a series of 

 particles forced by the wave motion away from their normal 

 position on the zero-line o . . . o. 



Now, suppose that by some refracting contrivance we force the 

 plane wave-fronts when they reach a certain plane A to assume a 

 spherical form with a radius of curvature equal to the distance 

 A F. Then F will become the focus of the beam of light, and if 

 we assume a single particle of tangible matter to be set in motion 

 at that point by the luminiferous oscillations, it is obvious that 

 the index particle will be kept in a state of rhythmic movement 

 as iong as the beam of light continues to flow, that is to say, as 

 long as the light shines through the aperture A A. And the 

 movement will not only be rhythmic, it will be violent in pro- 

 portion to the area of the wave-fronts that pass the aperture, for 

 since these wave-fronts condense upon the particle and impart the 

 whole of the energy which they individually carry in a single blow, 

 the amount of the energy so imparted must be exactly proportional 

 to the area of the wave-front which carries it. When the wave- 

 front and the aperture coincide, the disturbance of the particles 

 will be proportional to the area of the aperture itself. 



Now consider the case of the polyphasal surface drawn upon the 

 diagram from the top of section 9 to the foot of section 13. A train 

 of such polyphasal surfaces may be drawn, as is indicated in the dia- 

 gram, but the successive members of the series cannot of course be dis- 

 tinguished — like the wave-fronts — at any moment by their relative 

 phase values, for all phases may be found at every instant in every 

 one, excepting only the mutilated members of the series. It is 

 clear that these polyphasal surfaces or fronts will be propagated 

 forward in precisely the same way as if they were wave-fronts. 

 For every point in any one of these slanting surfaces is also a point 



2 o 2 



