October 26, 1900.] 



SCIENCE. 



625 



case A may be moved quite up to the ob- 

 ject glass or drawn on it. Knowing the 

 position of the images, it is possible that 

 such an arrangement might be used in 

 measuring distances, A being for this pur- 

 pose taken suitably greater than B. 



Here I may revert to the observations 

 with and without spectacles instanced 

 above. If the eye is so circumstanced as to 

 focusing power as to be able to see grating 

 A in the distance through grating B dis- 

 tinctly, then the shadow bands will be out 

 of focus and faint. If, however, a near- 

 sighted eye or one made abnormal by convex 

 or in a second case by concave lenses, grating 

 A is quite out of the range of vision. The 

 eye will then find and fix upon one of the 

 focal planes, virtual or real, due to the pro- 

 jection of A by B. If there be not too 

 much stray light, the shadow bands in such 

 a case are painfully obtrusive. 



LONG SHADOWS CAST BY THIN WIRES IN NON- 

 PARALLEL LIGHT. 



6. It is finally necessary to explain the 

 long lines of shadow assumed tentatively 

 in the above hypothesis. Even in sunlight 

 a filamentary wire will not cast an effective 

 shadow further than 5 or 10 inches; the 

 shadows here encountered may be 100 feet 

 in length. 



Clearly the phenomenon is one of diffrac- 

 tion, and it will be expedient to recall the 

 fundamental case of a single slit and a 

 single edge. The pattern is well known, 

 consisting outside of the geometrical shadow 

 of a very bright and then very dark band, 

 followed by colored alternations of light 

 and shade more cramped and much less 

 distinct and intense. Within the shadow 

 the light sinks gradually into darkness. 



Suppose the slit to be displaced laterally 

 to the left a small distance ; the whole dif- 

 fraction pattern will then move toward the 

 right over the same distance \{ x = y, and 

 for other distance ratios, proportionally. 



Now suppose that both slit actions occur 

 simultaneously. The feature of the diagram 

 will be the two maxima of light enclosing 

 between them a shadow band without 

 color, which is a compound of the darkness 

 within the geometrical shadow for the first 

 slit, now limited on the right side also by 

 the maximum of the second slit and its ex- 

 ternal dark band. The effect therefore is the 

 same as if the bar betioeen the two slits were pro- 

 jected. For X ^y the distance between the 

 light maxima will be the same as the dis- 

 tance between the slits otherwise in pro- 

 portion to relative distance. If the slits 

 are finer the phenomenon is darker and 

 sharper; if coarser, brighter and more 

 vague. If the slits move closer together 

 the bands move closer proportionally. Color 

 is rarely apparent. 



It follows from the preceding that with 

 3 slits and an edge, 3 maxima of light 

 and 2 dark bands without color will ap- 

 pear; with 4 slits, 4 maxima and 3 shadows, 

 etc. The whole phenomenon may be 

 regarded as crowded into the geometrical 

 shadow of the first slit. Hence if the 

 slits increase in number the number of 

 bands will soon reach a limit as more 

 and more light falls inside the edge of the 

 shadow in question. With a coarse grat- 

 ing (rods and spaces say .2 cm.) but 5 

 shadow bands may appear for an indefinite 

 number of spaces. In general the diifrac- 

 tion pattern covers a certain area ; if the 

 slits move closer together there will be 

 more and finer bands visible ; if they move 

 farther apart, fewer. With an edge just in 

 front of a telescope or on the objective and 

 light nearly screened off, an indefinite num- 

 ber of lines may be seen on looking at a 

 distant white surface through grating A. 

 From the distance of A from the objective 

 (.1 to several meters) and the size of 

 image and object the magnification of the 

 telescope may be inferred. 



7. With the case of an edge and multiple 



