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Transactions of the Society. 



vicinal slits meet almost as soon as they have left the point where 

 they originated, and get into interference with each other, just as 

 similar portions of a plane wave would do, and the outcome must 

 be the same, viz. one portion of the diffracted waves joins up with- 

 out difference of phase and proceeds in the direction of the original 

 wave from C, forming the direct light; but other portions join 

 with differences from slit to slit of one or several wave-lengths, 

 and unite to form diffracted waves of corresponding order. The 

 mathematical treatment is extremely laborious in this case, but 

 we can easily arrive at an approximate solution graphically. 



Describe a circle 1) E over C as centre ; this obviously corre- 

 sponds to the direct light joined ^^p in its original phase after 

 passing the grating. To find the first diffracted wave, we have 



to introduce a difference of phase of one wave-length between 

 adjoining slits. To do this we may describe a circle (representing 

 an elementary diffracted wave) from 4 with length 4 — D4, as 

 radius ; from 3 we describe a circle with 3 — D 3 plus one wave- 

 length (represented by a suitable length) ; from 2 a circle with 

 2 — D 2 plus two wave-lengths, from 1 with 1 — D 1 plus three 

 wave-lengths ; on the other hand, from 5 we take a radius of 

 5 — D 5 minus one wave-length, and so on throughout. A wave 

 tangent to all these elementary ones will be the diffracted wave we 

 are seeking ; trial shows that a circle struck from C as centre 

 closely fulfils this condition. It should also be clear that, con- 

 sidering any one slit, the angles between the direct and the 

 diffracted "rays" must be precisely the same as with plane waves, 

 and also that the elementary wavelets from different portions of 

 any one slit must be subject to the same interferences amongst 



