584 • KEPORT — 1894. 



All these appearances belong to the same class as the spurious disk of a star 

 with its attendant diffraction rings when viewed through a telesco^ie, and as the 

 images which very minute objects present when examined by the microscope. In 

 all these cases the image, as was long ago pointed out by Fraunhofer, is not a 

 reproduction of the object. In fact, when the object is so small or so remote 

 that the rays of light that reach the coUimating lens from different parts of it 

 differ only by a part of a wave-length or by a few wave-lengths, the diffraction 

 phenomena which are always present become of large size. These, in the cases 

 we have to deal with, fake the form of a direct beam of light spread out, with 

 coloured fringes extending like a fan to the right and left. If the telescope with 

 which the object is viewed can take in the whole of these we get a true de- 

 lineation of the object. But if it can only take in some of them, thtn the image 

 we see is not a representation of the object, but the image of another object, viz. of 

 that object which would emit the same central beam and those only of the fringes 

 which the instrument can grasp, but not any of the others. In all cases this apparent 

 object differs from the real object, and in some cases is wholly unlike it. 



If, for example, after removing the eye-piece, we look directly at the light 

 transmitted by the coUimating lens, and make the adjustments such that the in- 

 strument takes in only the central beam and the first diffraction spectrum on either 

 side, then on replacing the eye-piece we sliall see a double line instead of a coiTect 

 image of the slit. This, with some very thin appendages which can on'y be seen 

 when the light is sufficiently briglit, is, in fact, the kind of object which would emit 

 a central beam and a first diffraction spectrum, and these only, of those breadths, 

 in those phases, and with that ratio of the brightness of the central beam to 

 the first diffraction spectrum which prevail between those parts of the light as 

 actually received by the coUimating lens. 



The image that presents itself might conceivably be calculated by dividing the 

 wave front as it passes the coUimating lens into pairs of strips, and integrating tl?e 

 illumination these produce on the focal plane. This is the method employed in 

 the case of tbe spurious disks of stars. Jiut even if this method were practicable 

 it would be inferior to a tentative geometrical treatment of the problem which, 

 though it does not furnish the exact result, is more instructive. The geometrical 

 method makes clear, which the integrations would not, why the thin appendage 

 lines present themselves in addition to tlie main double line. 



It was obviously desirable to attack the problem in its simplest form, which 

 occurs when the incident light reaches the slit of the collimator normally. It is 

 possible from general considerations, based on the theory of diffraction gratings, 

 to conclude that then the main part of tbe light of the image as seen must be con- 

 centrated into tico parallel strips constituting a so-called double line. The next 

 step is to assume a distribution of light in two such strips which would produce, 

 and which therefore would be the image formed by, a central beam and diffraction 

 spectra of which those of even orders, the 2nd, 4lh, &c., are of zero illumination. 

 This can be done in various ways, producing different distributions of the light 

 between the central beam and the spectra of odd orders. The next step is to 

 select among these one which gives nearly tbe same ratio of brightness of the first 

 spectrum to the central beam as prevails iu the light which actually reaches the 

 collimator from the slit. This was effected by making the strips broad, brighter 

 in the middle, and with an interval between them about one-seventh of their 

 width. The next step is to modify this distribution of light, so as to secure zero- 

 illumination in the third spectrum, while retaining the e.xtinction of the spectra of 

 even orders. This was efiected by removing one-eighth of the light from each of 

 the two strips ; transferring half of this eighth to a certain part of the other strip, 

 and with the other half forming an appendage line outside the strip, at a distance 

 from it of nearly half its width, and only one-seventh as broad. The distribution 

 of light, when modified in this way, on both the constituents of the double line 

 would present the appearance of a somewhat coarse double line, with a narrow 

 interval between them, and accompanied by two hair-like appendage lines, one to 

 the right and the other to the left of the main double line; and this resembles 

 the image as it actually presents itself in the telescope of the instrument. 



We thus see that part of the light must appear in the form of faint appendages 



