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SCIENCE. 



[N. S. Vol. XII. No 304. 



slit sufficiently disposed of, the case of a 

 single wire and multiple slit is not far to 

 seek. There will be a series of light and 

 shade bands for each edge of the wire, and 

 the two series will eventually run through 

 each other. A single slit has within the 

 geometrical shadow the well known brown- 

 ish band, finely fluted and broad for a thick 

 wire, coarsely fluted and narrow for a thin 

 wire. With 2 slits there will be 2 shadow 

 bands with a maximum of light between 

 for a flue wire, or 3 bands with an intensely 

 dark one in the middle for a stout wire 

 (say 3 mm.). With 3 slits and a fine wire 

 3 shadow bands appear at long ranges 

 {ijfx = 1/3), more at short distances. With 

 a coarse wire 4 at long ranges with the two 

 internal bands intense, 5 or more at short 

 ranges, etc. It follows eventually that with 

 a multiple slit and wire the diffraction pat- 

 terns may be looked upon as compounds of 

 the light and shade bands of each edge. At 

 a; = 2, 2/ = .5 meters, a blur usually appears 

 for the thin wire, sharp fine lines edging a 

 broad central shadow for the thick wire. 

 This continues up to 2 meters in the latter 

 case ; but with the thin wire with y between 

 1 and 2 meters, there are apt to be colored 

 blue and red bands of a very complicated 

 pattern. Bej'ond two meters the figure is in 

 all cases again simply white and black, with 

 the former or the latter wider conformably 

 with the structure of grating A, supposed 

 to be at 2 meters from B. Size of rod is 

 without influence here. With the thick 

 wire the central ever-narrowing shadow 

 may be visible beyond 2 meters, and as 

 it apparently thrusts the bands apart the 

 figure is relatively broad. In so far as the 

 edge effect predominates and overlapping 

 is obscured in the middle, the bands appear 

 in focus at all distances. 



8. From these results to the actual case 

 of the grating is an easy step. Grating A 

 furnishes the multiple slits, about 5-10 of 

 which are effective for every wire of grat- 



ing B. Each of these has its own series 

 (about 8 in the above case) of shadow 

 bands, all identical in form. When for 

 any position on the axis the shadow bands 

 of all the wires of B coincide, there will be 

 a focal plane at that point and B will pro- 

 ject an image oi A. At other points there 

 will be no image, for patterns overlap irreg- 

 ularly, light falling on shade and produc- 

 ing more or less uniform illumination. 

 Figs. 3-8 show the conditions to be such 

 that many band series must overlap, and 

 hence the greater definition of focus. 



At close ranges, therefore, both the width 

 of the wire (in relation to the independent 

 shadow bands of each of its edges) and the 

 distance apart of the wires (in relation to 

 the above Figs. 3-8) must be of proper 

 value to produce coincident effects. At 

 long ranges coincidences depend more on 

 the diagrams. 



From another point of view we may con- 

 sider the band series of the right and left 

 hand edges of the wire of the grating in- 

 dependently. The former will be brought 

 to focus at those points of the axis where 

 the successive images of corresponding 

 edges overlap. The latter equally so. The 

 two images so formed, and corresponding re- 

 spectively to the two edges of all the wires 

 of -B, will not blend in a compound image, 

 unless the images coincide. If the sep- 

 arate edge images are apparently displaced 

 relatively to each other, i. e., if there is ap- 

 preciable non-coincidence of shadow bands, 

 there will be no focal plane even if the im- 

 ages of the separate edges are perfect. 

 Hence there is an adequate account given 

 of the absence of focal planes predicted by 

 the above constructions. Again, just as 

 there may be color effects for a single wire 

 at certain distances, so for the wires con- 

 jointly there will be color phenomena be- 

 tween the images of all corresponding 

 edges. Finally, an inkling is given as to 

 why focal planes which from diagrams 3-8 



