252 



Proceedings of the Royal Irish Academy. 



of the visible image in the plane /' as coloured edges, as previously 

 mentioned. 



"We will now inves- 

 tigate the influence of 

 these images, direct and 

 diffracted, formed in the 

 upper focal plane of the 

 objective, upon the image 

 of the olject formed in the 

 focus of the eye lens of 

 the microscope, by the aid 

 of diagram (2), in which 

 B indicates the place of 

 the real image of the ob- 

 ject. Let a and a' be the 

 direct and one of the first 

 order of diffracted images 

 of the source of Kght. 

 The rays emitted from a 

 and a' will interfere at B, 

 and if the distances a B 

 and a' B differ by a whole 

 wave length a bright line 

 win be produced ; i£ the 

 difference be half a wave 

 length darkness will re- 

 sult. Prom centre a 

 strike two arcs, one 

 through B, the other 

 through a point distant 

 from ^ by a wave length. 

 From a' describe a third 

 arc through the point 

 within B. The crossing 

 point P of the two arcs 

 marks where the undula- 

 tions starting from a and 

 a' are found to differ by 

 a whole undulation, and 

 consequently where the 

 first bright diffraction 

 line is situated. The 



03 



Diagram (2). 



sides of the small triangle whose apex is ia P, though arcs of 

 circles, are so short that they may be considered straight Unes, and as 

 this triangle is similar to the triangle a' aB, we have the relation 



or 



BP:\ = aB: aa'; 

 BP=Ba.X^aa'. 



