spherical Wave of Light. 6i 



An application of Huyghens' Principle to a spherical 

 wave of light. By R. F. Gwyther, M.A. 



This is an attempt to form a theory of diffraction on 

 geometrical principles only. To make such an attempt 

 does not appear to me unreasonable, since, with our present 

 knowledge, one might prefer to look upon the breaking 

 up of a wave as a geometrical artifice rather than as a 

 geometrical representation of some physical phenomena. 



Introduction. 



We can easily express in terms of co-ordinates the dis- 

 placements resolved along axes in a hypothetical spherical 

 wave, and for our purposes we need not at first consider 

 any difficulty there may be in understanding how such a 

 wave could originate ; our equations will express the nature 

 of its progress when once originated. 



As we consider light to consist of displacements, and to 

 be propagated by strains in an ether in which the velocity 

 of normal vibrations is incomparably greater than that of 

 transverse vibrations, and as the principle of the independent 

 co-existence of small motions is essential to the whole 

 theory of light, it is no further hypothesis to assume that 

 at any moment we may regard each element of a disturbed 

 spherical surface to be itself an origin of an elemental wave 

 the resultant of all such elemental waves reproducing for 

 future time the actual wave motion which we were originally 

 considering. It is my object to determine the form of the 

 displacement in the secondary waves, in order that the 

 resultant displacements may be everywhere equivalent to 

 those of the original wave. 



In the first place, I show that if an elemental wave is to 

 represent a plane polarised ray of which the displacement 

 E 



