226 Transactions of the Society. 



The three sets of equidistant lines from which the hexagonal 

 headings of the scale result, correspond in direction and distance 

 of lines, to the various pairs, which may be formed with consecu- 

 tive pencils — as is indicated in the figure. Each set of lines can 

 be produced alone by any pair in which the connecting line is at 

 right angles to the direction of the lines, for instance the set (1) 

 by the pairs a and c a and /, h and g, d and e — in bright field or 

 in dark field. The seven pencils interfering together, give the 

 common image with the hexagonal markings, which I have calcu- 

 lated in all its detail as a pure interference -phenomenon, which is 

 quite independent of the real (quite unknown) structure of the 

 scale, only depending on the distance and position of the spectra 

 in relation to the axis. The calculated image is as follows 

 (fig. 10) : bright spots, representing the maxima of light, and 

 hexagonal figures around those representing the lines, in which 

 the interference produces minimum of light. A similar image, 

 with a somewhat different distribution of light, is, theoretically, 

 the result of the interference of say three pencils forming a triangle 

 (as a, b, c — or a, d, e)— as are effective in observing Pleurosiyma 

 with a dry lens in oblique light — quite in accordance with the 

 well-known aspect. 



Now from the theory above follows that there must be visiljle 

 in dark field three new sets of lines, bisecting the angles between 

 the common lines — corresponding to the combinations of the 

 spectra — 



g, c or f, d 



i, f „ c, ^ 



b, d „ g, e 



the distance of which must be narrower in the ratio of 1 : a^S : 

 and three sets of lines coinciding with the common sets — but 

 narrower in the ratio 1 : 2 — corresponding to the combinations — 



b, e 



c, f 

 d, g 



The interference of three pencils as 



g, c, c or I, d, f 



lastly produces a new image with hexagonal markings, the hexagons 

 with their sides normal ( _L ) to the axis of the scale (not parallel 

 as in the common image) and smaller in the ratio 1 : \/S — both 

 combinations the same (dark field, of course). 



All those phenomena you may observe in accordance with the 

 theoretical anticipation — hj stopping off the pencils which are to 

 be excluded. Most easily you will get the lines which bisect the 



