2d 



Transactions of the Society. 



antipoints, placed so as to overlap one another, would yield total 

 amplitude curves very unlike those which we have been consider- 

 ing, so that all the results so tar reached must be considered 

 precarious if this new hypothesis be entertained. There are 

 also certain phenomena highly characteristic of this graduated 



antipoint of which the monophasal anti- 

 point affords no kind of explanation. To 

 these we may now proceed. 



It is necessary for this purpose to 

 investigate the law according to which a 

 polyphasal surface such as that of fig. 11 

 must be propagated, and for this purpose 

 we may provisionally* have recourse to 

 the well-known principle of Huyghens. 

 Let E. . .E of fig. 12 be such a surface, 

 and let the derived surface r...v be 

 drawn parallel to it and at a distance 

 = X from it. Then the surface r . . . r will 

 exactly reproduce the surface E . . . E as shown, the final phase in 

 every ray being equal to the initial phase + \. If we trace another 

 surface, r* . . .r i} midway between these two, we shall have a third 

 surface in which the phase on any given ray is intermediate between 

 the initial and the final phases. Similarly, if we select a fourth 

 plane, r { . . ,r y intermediate between the last named and E. . .E, w$ 



Fig. 11. 





<0- 



^Nsf^tfr 





i 



! "1* 



* 



Fig. 12. 



shall there find the phase value intermediate between the initial 

 and halfway phases. It will be clear without formal proof that 

 the lines <£ . . <£ . . <£ of the diagram indicate monophasal surfaces, the 

 existence of which in the position so delineated is implied by the 

 existence in the initial plane of a polyphasal surface, having the 

 postulated graduation of phase values in its various zones. 



We thus" see that a surface having this structure, itself the 



* "Provisionally," because the polyphasal surface cannot be propagated strictly 

 according to Huyghens' law, i.e. not with the velocity of light ; but for short 

 distances the assumption is allowable. \ 



