November i6, 1893] 



NA TURE 



57 



rays \so p a c a po' for one of the pencils, and opbdbpo' 

 for the other. 



From considerations quite analogous to those em- 

 ployed in the former case, it can be shown that the 



, M#?#MM#« ] 



limit of accuracy attainable in the estimations of angles 

 involves an error of about one-fifth of the angle subtended 

 by a light wave at a distance equal to the diameter of 

 the objective. This is halved by the fact that the angular 

 motion of the beam is twice that of the mirror ; so that 



with a telescope of locm. aperture the limit of accuracy 

 may be estimated at ogfjj-ff.jjj, or say o.\". But taking 

 o.oi fr. as the smallest perceptible displacement of the 

 mirrors c d, the corresponding angle of rotation of the 



NO. T255, VOT.. 49] 



line c d (lo cm. long) would be only ougJouoij, or say 

 0.0 1 ".^ 



It is not at first evident that there is any relation be- 

 tween the refractometer and the spectroscope. A com- 

 parison of Fig. 6 and Fig. 7 shows, however, that there 

 is a strict analogy. Fig. 6 represents a disposition some- 

 times adopted to observe the spectrum by means of a 

 concave grating, and Fig. 7, with unimportant modifica- 

 tions, is the arrangement actually employed in the 

 analysis of radiations by means of their " visibility 

 curves," as will be explained below. 



Exactly as in the case of mirrors and lenses, we may 

 here, too, sacrifice "resolution" and "definition" by 

 using only the extreme portions of the surface, with an 

 actual gain in "accuracy." To compare numbers, it 

 appears that the average error in the comparison of 



Fig. 6. 



wave-lengths by a gratine with 250,000 lines is about one 

 part in half-a-million. With this number of waves in the 

 difference of path of two interfering pencils, the corre- 

 sponding error in the refractometer observations are of 

 the order of one twenty-millionth. 



The name "interferential refractometer" seems rather 

 inappropriate to an instrument which has so many im- 

 portant applications beside the measurement of indices 

 of refraction ; but as it has been sanctioned by long 

 usage it will be retained. 



Among the many forms of the apparatus which have 

 been rendered classic by the works of Arago, Fresnel, 

 Fizeau, Jamin, and Mascait, and which are so admirably 

 adapted to the work for which they were designed, there 

 are none which aie not open to serious objections when 

 applied to the solution of such problems as the measure- 



FiG. 7- 



ment of lengths and angles, for the analysis of the con- 

 stitution of the light of spectral lines, and especially for 

 the determination of wave-lengths in absolute measure. 

 For these, the form of instrument shown in Fig. 8 has 

 many important advantages, among which the following 

 may be mentioned : — It is simple in construction, and is 

 easily adjusted ; it may be used with a broad luminous 



1 In the use of the revolving mirroras in galvanometers, gravity and torsion 

 balances, &c., the accuracy can be increased by enlarging the surface of the 

 mirror ; but the moment of inertia is thereby increased, and in greater pro- 

 pirtion. But in the refractometer the mirrors c d may be made insig- 

 nificantly fmall, and yet, with the same distance between the outer edges, 

 the accuracy may be increased at least tenfold. It is important tonoie that 

 any linear motion of the line joining the mirrors, or even a rotation about 

 ihislme, has no effect on the fringes. It seems probable that this form of 

 instrument may be of service in such problems as the measurement of the 

 mjon's attraction, constant of gravitation, variations of the vertical, &c. 



