OOTOBEE 26, 1900.] 



SCIENCE. 



621 



hypothesis, of a kind which in the sequel 

 may be modified to meet the true case. I 

 shall proceed, therefore, to trace what may 

 be temporarily called the effective planes of 

 shadow in diffuse light. In other words, 

 planes are to be passed between the two 

 gratings through their consecutive wires 



etc. , are the successive positions of the focal 

 plane or screen. Grating spaces and image 

 spaces are denoted by a, h, and s, respec- 

 tively. Reference planes designated by 

 Greek letters will be presently referred to. 

 Wherever lines mass in a single point, there 

 one may look for a deficiency of light coming 



and the loci of intersection determined. If 

 the wires are vertical the result may be 

 mapped out by drawing the traces of the 

 two planes in question on a horizontal 

 plane, and the object would be gained by 

 solving a few straightforward problems in 

 the modern geometry of pencils of rays. It 

 will greatly facilitate inspection, however, if 



to an observer behind both gratings. Cor- 

 responding groups of intersections thus de- 

 termine a focal plane. 



To begin with Fig. 3, in which a = & or the 

 two paralleled wire gratings are identical, 

 the diagram is seen at once to reproduce the 

 results of Table 1 . At relatively remote dis- 

 tances the diverging planes tend to pass out 



some of the chief cases which have been 

 considered are drawn out in plan. This 

 has been done in Figs. 3-8, which will be 

 found additionally useful in the physical 

 questions of the next section. A and B 

 show the positions of the gratings and S, S', 



of the field, and the images must therefore 

 weaken for this reason alone. Table 3 de- 

 scribes the images a and 5, the latter colored ; 

 the focal plane a' with s = |^ is also sharp. 

 Following S, the planes *S', S", etc., did not 

 appear distinctly enough to be recorded. 



