i6o 



NA TURE 



[December 17, 1891 



the elongation, the former, below Pole, later. In this way the 

 right ascension of Polaris plays a small part in its azimuth of 

 elongation, which is dependent solely on the declination and 

 latitude. Assuming the present declinations of the two stars 

 mentioned, with probable errors of < ± o"-2 and ± o"'3 re- 

 spectively, he finds that the right ascension would probably be 

 in error by ± o-oo2s. and ± o*oo4S. In fact, the probable 

 errors "dependent upon anything but the transit of the star to 

 be determined will be much less if the present method is used 

 (with an equal instrument), than if stars in the same declination, 

 but opposite Polaris in right ascension, were observed by direct 

 comparisons in the meridian." By applying this method to 

 other stars of different right ascensions and "gradually increas- 

 ing declinations," as the R.A. of Polaris or its opposite is 

 approached, numerous co-ordinates thoroughly independent can 

 be obtained, and will "provide aero points for the proposed 

 number of photographic plates 2° square, and consequently help 

 lo settle the places of all stars in that region." 



MEASUREMENT OF JUPITER'S SA TELLITES 



B V INTERFERENCE. 

 T T has long been known that even in a telescope which is 

 -'- theoretically perfect, the image of a luminous point is com- 

 posed of a series of concentric circles with a bright patch of 

 light at the common centre. This system of circles can easily 

 be observed by examining any bright star with a telescope pro- 

 vided with a circular diaphragm which diminishes the effective 

 aperture. The appearance of the image is shown in Fig. i, a. 

 In the case of an object of finite angular magnitude the image 

 could be constructed by drawing a system of such rings about 

 every point in the geometrical image. The result for a small 

 disk (corresponding to the appearance of one of the satellites of 

 Jupiter as seen with a 12-inch telescope whose effective aperture 



has been reduced to six inches) is given in Fig. i, d ; the chief 

 points of difference between this and Fig, i, a, being the greater 

 size of the bright central disk, and the lesser clearness of the sur- 

 rounding rings. The larger the disk the more nearly will the ap- 

 pearance of the image correspond to that of the object ; and the 

 smaller the object the more nearly does it correspond with 

 Fig. I, a, and the more difficult will be the measurement of its 

 actual size. Thus, in the case just cited, the actual angular 

 diameter is about one second of arc, and the uncertainty may 

 amount to half this value or even more. 



The relative uncertainty, other things being equal, will be less 

 in proportion to the increas-; in the aperture, so that with the 

 36-inch telescope the measurement of the diameters of Jupiter's 

 satellites should be accurate to within ten per cent, under favour- 

 able conditions. 



It is important to note that in all such measurements the image 

 observed is a diffraction phenomenon — the rings being inter- 

 ference fringes, and the >ettings being made on the position of 

 that part of a fringe which is most easily identified. But such 

 measurements must vary with the atmospheric conditions and 

 especially with the observer— for no two observers will agree 

 upon the exact part of the fringe to be measured, and the un- 

 certainties are exaggerated when the fringes are disturbed by 

 atmospheric tremors. 



If, now, it be possible to find a relation between the size of 

 the object and the clearness of the interference fringes, an inde- 

 pendent method of measuring such minute objects will be fur- 

 nished ; and it is the purpose of this paper to show that such a 

 method is not only feasible, but in all probability gives results 

 far more accurate than micrometric measurements of the image. 



In a paper on the " Application of Interference Methods to 

 Astronomical Measurements" ' an arrangement was described 



' Philosophical Magazine, }v\y xZtjo. 



NO. I 155, VOL. 45] 



for producing tuch fringes, by providing the cap of the objective 

 with two parallel slits, adjustable in width and distance apart. 

 If such a combination be tocussed on a star, then, instead of the 

 concentric rings before mentioned, there will be a series of 

 straight equidistant bands whose length is parallel with the 

 slits, the central one being brightest,^ Fig. i, c. 



The general theory of these fringes may be found in the 

 Philosophical Magazine iox 'Ma.rch i%g\. The general equation 

 showing the relation between the visibility of the fringes and the 

 distance between the slits is; 



V2 = 



/ <p{x) cos /^x</jr J -f / <p{x) sin kx dx 

 [ J^ (^) ^x]' 



(I) 



(2) 



which reduces to the simpler form 



/ <p {x) cos kx dx 

 V = J . . . . . 



j <f> {x) dx 



when the object viewed is symmetrical. 



A number of applications of this formula are discussed in the 

 former paper, but for the present purpose attention will be 

 confined to the case in which the object viewed (or rather its 

 projection) is a circular disk, uniformly illuminated. 



In this case equation (2) becomes 



v=jV 



(3) 



in which o is the angular diameter of the object, and Oj, is the 

 smallest angle resolvable by an equivalent aperture ; that is, the 

 ratio of a light-wave to the distance between the slits. 



Th.e curve expressing this relation is given in Fig. 2, in which 

 the ordinates are values of the visibility of the fringes, and the 

 abscissae are the corresponding values of the a/oo. 



From this it will appear that the fringes disappear at recurring 

 intervals, and in a laboratory experiment as many as four such 

 disappearances were noted, and the average error in the resulting 

 value of a, the angular magnitude of the disk, was found to be 

 less than two per cent. 



From the curve it is evident that the first disappearance is 

 most readily and accurately observed, and for this we have 



a 



-= I '22; 



«o 

 whence, putting s for the distance between the centres of the 

 slits, and taking for the wave-length of the brightest part of the 

 spectrum 0*0005 mm.,^ and dividing by the value of a second 

 in radians we have 



•38 



(4) 



In consequence of the kind invitation extended by Prof, 

 Holden, it was decided to make a practical test of the usefulness 

 of the proposed method at Mount Hamilton, 



' These will be superposed on another set of fringes due to diffraction from 

 the edges of the slits ; but the latter are too faint and broad to cause any 

 confusion. 



" 1 he wave-length will, c f course, vary somewhat with the object observed, 

 but may be made constant by interposing a red glass. 



