December 31, 1891] 



NATURE 



205 



the size of the first dark square is given by the formula 

 2XF 

 A ■ 

 Some interesting facts given by Messrs. Cooke show 

 the remarkable agreement between the theoretical and 

 observed values of these diameters. " A 6-inch objective, 

 of 91 inches focal length, was directed to a bright star, 

 and the objective cut down, in the first place, to a square 

 aperture, 15 inches diameter. The mean of four mea- 

 surements gave the diameter of the first dark ring (in this 

 case square in shape) as 0027 inch, while the formula 

 '^Yh. (where X = 1/45600 inch) gives -00266 as the theore- 

 tical value. A circular aperture, diameter r22 inches, 

 was then placed in front of the objective, when the mean 

 of four measurements gave a diameter of •0039 for the 



iF X I'22A 



first dark ring, while the formula 



gives a value 



of -0040" (p. 31). "The diameter of the first dark ring, 

 as depicted with the whole aperture of 6 inches in use, 

 was also measured as nearly as its minute size would 

 allow, the measurement obtained ranging about "0008 

 (subject to an error of perhaps 10 per cent.), while the 



value given by the formula is -00081 " (p. 32). 



As the spurious disk fades away into the first dark ring, 

 its apparent diameter will depend on the intrinsic bright- 

 ness of the star observed, and also to some extent on 

 irradiation. Hence the necessity for measuring the rings, 

 and not the " disks " themselves. 



An important fact follows from the appHcation of these 

 considerations, for on the apparent diameter of the 

 spurious disk depends the dividing power of the ob- 

 jective. If the diameter of the star disk— which may, 

 on the average, be taken as half that of the first dark 

 ring— be greater than the distance between the com- 

 ponents of a double star, the telescope must obviously 

 fail to divide it, no matter what may be the power of the 

 eye-piece employed. " In all objectives having their 

 focal lengths equal to fifteen times the aperture, the 

 linear diameter of the spurious disk may be said to 

 average "0004 inch, or about 1/2500 inch. With 6 

 inches aperture this corresponds to an angular dia- 

 meter of 09 second, and in a 12-inch aperture to 

 0-45 second. So these respectively represent the divid- 

 ing powers of such apertures upon double stars of 

 average brightness" (p. 31). For similar apertures, the 

 values given by Dawes for stars in which both compo- 

 nents are of the sixth magnitude are o"76 and o"-38 

 respectively. To reduce the star disks to the extent 

 necessary for the separation of the components of the 

 spectroscopic binary /3 Aurigiu (the angular distance being 

 about o"-oo5), an object-glass no less than 80 feet in 

 diameter would be required. 



The images of a star with the diffraction rings as 

 yielded by a sensibly perfect objective are shown in Fig. 

 i.^ Fig. I, a, represents the focused disk and ring system 

 seen under a high magnifying power ; i, b, and i, c, are 

 sections of the cone of rays taken very near to and on 

 opposite sides of the focus, also seen with a high power ; 

 and I , </, is a section taken about \ of an inch on either side 

 of the focus, and viewed with a moderate power. 



Before this perfection of image can be realized, we 

 gather that the objective must satisfy the following con- 

 ditions : — (i) The optic axes of the flint and crown glass 

 lenses should be coincident. (2) This common axis 

 should pass through the centre of the eye-piece. (3) The 

 dispersions of the flint and crown should neutralize each 

 other for the most visible rays of the spectrum. (4) There 

 should be no spherical or zonal aberration. (5) The 

 lenses should be free from astigmatism. 



' The diagram* are reproduced with the permission of Messrs. Cooke. 



NO. I 157, VOL. 45] 



The second of these adjustments is practically the only 

 one over which the observer himself has any control, and 

 he must remain contented with the means of ascertaining 



Fig. I. — Diagrams showing spurious disk and diffraction rings seen with 

 a perfect objective. 



how far his objective satisfies the remaining conditions 

 enumerated. 



The process of testing an objective is considerably 

 complicated by the imperfections of the eye as an optical 

 instrument. Its want of achromatism when the full 

 aperture of the pupil is used may frequently lead the 

 observer astray in making observations in which colour 

 effects are to be noticed. This defect is demonstrated, 

 as pointed out on p. 14, by the fact that coloured fringes 

 are observed to surround the image of a star seen in the 

 open field of a reflector, of the perfect achromatism of 

 which there can be no question. A sound practical hint 

 accompanies this statement. The use of a power from 

 50 to 70 times the aperture in inches is recommended for 

 purposes of testing, in order that the pencil of rays entering 

 the pupil may be reduced ; for if the power be equal to 

 or less than the quotient of the diameter of the objective 

 and the diameter of the pupil, the full aperture of the 

 pupil is utilized, and the defect is consequently at its 

 maximum. 



Colour-blindness, of which no mention is made by 

 Messrs. Cooke, is also common, and it is obvious that no 

 colour-blind eye is competent to make tests depending 

 on colour phenomena. 



Astigmatism, too, is not an uncommon defect, the rays 

 falling along one diameter of the lenses of the eye being 

 refracted in a greater or less degree than those falling 

 along the direction at right angles. Oculists combat this 

 by supplying compensating astigmatic lenses as spectacles ; 

 and unless such compensation be perfect, an astigmatic 

 eye must clearly be disqualified from making some of the 

 test observations. 



Another complication arises on account of atmospheric 

 dispersion (p. 18). This, of course, is at its maximum 

 for stars on the horizon, and the image of such a star 

 would appear to have a red fringe on the upper and a 

 green or blue fringe on the lower side, even in the most 

 perfect telescope, unless a compensating eye-piece be 

 used. Hence the importance of selecting stars of con- 

 siderable altitude for purposes of adjustment and testing. 



Further, the Huyghenian and Ramsden eye-pieces, 

 which are almost universally used, are not achromatic in 

 the strict sense of the term, and the eye-piece used for 

 testing should therefore not be selected at random (p. 13). 



Bearing these facts in mind, one may proceed, to test 

 the adjustments referred to. 



(i) Any difference in the position of the axes of the 

 component parts of the objective will cause the combina- 

 tion to act somewhat in the manner of an object-glass 

 prism, such as is used in photographing stellar spectra, 

 and the image of a star seen under such maladjustment 

 will appear as a spectrum. The red end of the spectrum 

 will obviously lie on the side towards which the flint is 

 displaced with regard to the crown lens, an effect which 

 is most noticeable when the eye-piece is racked within 

 the focus (p. 17). 



