86 Problems on the Diffraction of Light. 



conclusions in a very simple manner. I think, therefore, that 

 the expression Fresnel zones or Fresnel strips would be more 

 appropriate. 



Fresnel himself did not fall into the pitfall which is pointed 

 out in this paper. All his statements are well guarded and 

 correct. Lame, in his Text-Book on Physics (1840), con- 

 siderably extended Fresnel's reasoning, and drew further 

 conclusions from the division of a plane wave into strips, but 

 he also avoided the algebraic addition of the effects of different 

 strips which have not the same phase. 



Verdet was less careful, and through the following passage 

 (Lecons d'Optique physique, vol. i. p. 181) is responsible for 

 the idea that the successive strips divided in Fresnel's manner 

 give rise to vibrations of opposite phases irrespective of their 

 distance from the central point : — 



" II est facile de voir que deux arcs elementaires consecutifs 

 envoient au point P des vitesses de signes contraires ; car a 

 chaque point pris sur Fun de ces arcs correspond un point 

 situe sur Fare precedent et dont la distance au point P est 

 inferieure d'une demi longueur d'ondulation a celle du 

 premier point au meme point P, d'ou il resulte que ces deux 

 points envoient a P des vitesses de signes contraires." 



The reasoning here is obviously wrong. Consider two 

 successive elements sending vibrations to P which range in 

 phase from to ir and from tt to 2-7T respectively. It does 

 not follow that the resultant of one element should have a 

 phase opposite to that of the other element, quite irrespective 

 of the law of distribution of the individual vibrations sent out 

 from different parts of each element. If the vibrations are 

 evenly distributed, Verdet's conclusions would be justified, 

 hut the radius vector having a minimum length at the central 

 spot, alters very little near that point. The vibrations from 

 the first element combine at the point P therefore to a 

 resultant having a difference of phase considerably smaller 

 than that calculated from the supposition of an uniform 

 distribution. 



I cannot help thinking that writers on Physical Optics 

 have followed too blindly the footsteps of Verdet, whose argu- 

 ments do not seem to me to be always so conclusive as they 

 are commonly supposed to be. 



I have avoided in this paper speaking of a " linear wave," 

 as I believe more harm is done by the introduction of such 

 an idea than can be counterbalanced by the slight simplifica- 

 tion of expression. Students who are taught to live only in 

 a two-dimensional space will not be able to make much use of 

 their science in after life. 



