on the Aj>jH'((r<(nn' of a Di[j'ractlon-Gratin(j. 501 



band was reduced so as to give the distance of the band from 

 the commencement of the period. It was then not difficult 

 to pick out the binds that recurred from period to period, 

 discardino- occasional accidental errors. In this way the 

 ])()sition of the correction necessary to eliminate such periodic 

 errors was found. The nuignitiide of the correction was 

 subsequently determined by a process of trial and error. 



The illustrations accompanying this paper are reproduced 

 from photographs of gratings taken by the methods described. 

 They have been enlarged from the original negatives by 

 about eight diameters, so as to make the reproductions of the 

 same breadth as the ruled surface of the grating. Figs. 2 

 and 3 (PL XXIV.) are photographs of a strip cut on a Hat 

 speculum by Lord Blythswood's dividing-engine before any 

 correction had been applied. This strip was selected for 

 purposes of illustration, as the bands are more pronounced in 

 consequence of the greater errors in ruling. The rate of 

 ruHng is about 14,400 lines per inch. The photographs 

 were taken by the light from the blue line of helium (wave- 

 length 4471*5) in an order to the left of the central image. 



Fig. 2 was obtained by placing the photographic plate in 

 a position such as Ps.'"W'b"\ the slit 8^82 being removed. 

 In this case dark bands on the photograph correspond to 

 ])laces where the rate of ruling is diminishing in passing 

 from left to right over the grating (right to left over the 

 reproduction). 



Fig. 3 was obtained by the method described in the pre- 

 sent paper, the photographic plate being in the position A^B^C^ 

 (in this case so arranged as to be perpendicular to the axis of 

 the telescope) and the slit being displaced towards Si. Here 

 dark bands correspond to places where the ruling is narrower 

 than the average. 



In a sense, then, we may regard fig. 2 as a pictorial 

 representation of the first diiferential of the ruling represented 

 by Hg. 3. 



A Curious Case of Interference, 



In the previous paper [loc. cit.) it was pointed out that the 

 poinls Fj, Fo, regarded as tw^o sources of light might produce 

 interference-effects as in Fresnel's experiments ; but in 

 general the effect could be disregarded. 



I have, however, met with one interesting case in which 

 interference-bands are produced by a grating. This is a 

 grating ruled on a speculum-metal plate with Eutherfurd's 

 •dividing-engine, July 10, 1880. It is marked as containing 

 15,840 spaces at the rate of 17,296 per inch. Each line of the 

 spectrum given by the grating is accompanied by a pair of 



