92 On the Manufacture and Theory of Diffraction-gratings. 



sets of equally distant and not too thin bars inclined at a small 

 angle. Where the opaque and tranparent parts severally overlap, 

 the obstruction of light is, on the average, less than the double of 

 that due to each set separately*, and consequently these places ap- 

 pear by comparison bright. The interval between the bars is 

 evidently half the long diagonal of the rhombus formed by two 

 pairs of consecutive lines, and is expressed by a cos \ 0-4-sin 0, 

 or approximately a-r-6, where a is the interval between the pri- 

 mary lines, and 6 the mutual inclination of the two sets. 



When parallelism is very closely approached, the bars become 

 irregular, in consequence of the imperfection of the ruling. This 

 phenomenon might perhaps be made useful as a test. 



If the planes of the films be not quite parallel, bars parallel 

 to the original lines may appear when the line of intersection of 

 the planes is in the same direction. This arises from a fore- 

 shortening of one of the sets, making it equivalent to a grating 

 of a somewhat higher degree of fineness. 



When examined under the microscope, the opaque bar on the 

 copy, which corresponds to the shadow of the groove of the ori- 

 ginal, is seen to be composite, being not unfrequently traversed 

 along its length by several fine lines of transparency. In one 

 case, where the copy was on common glass, this effect went so 

 far that at certain parts of the grating the periodicity was altered 

 by each line splitting into two, the first spectrum altogether dis- 

 appearing. In order to make this observation, the eye should 

 be placed at the point where the pure spectra are formed and be 

 focused on the grating. The places in question will then ap- 

 pear as irregular dark bands. 



The disappearance of the first spectrum is very unusual ; but 

 it is common for bands to appear when the eye is placed in the 

 place of the fourth and higher spectra. When the order is high, 

 the bands will not be black, but coloured with light belonging 

 to one of the other spectra. There is no difficulty in under- 

 standing how this occurs. In the process of copying, the groove 

 of the original is widened into a bar, whose width depends on 

 the closeness of contact, an element which necessarily varies at 

 different parts of the plate. The dark bands are the locus of 

 points at which the relation of the alternate parts is such as to 

 destroy the spectrum in question. 



I have not had an opportunity of trying the method of copy- 

 ing on lines closer than 6000 to the inch ; but I have no doubt 

 that the limit of fineness was not attained. I should expect to 

 find no difficulty with lines 10,000 or 12,000 to the inch; but 

 beyond that point it is possible that the method would fail, 



* The mathematical reader will easily prove this from the law of ab- 

 sorption. 



