690 SUMMARY OF CURRENT RESEARCHES RELATING TO 



index is to bo measured is adjusted in the usual way and fixed on tho 

 graduated disc T (with vernier at n and n), which is free to 



turn. Tho prism is first placed 



Fig. 146. vfith. one face perpendicular to 



j^S7n- tho telescope, so that tho imago 



x$^*~^ : foK of tho slit reflected from tho faco 



&f p -*^ t" o * 8 seen * n ^ e ccn t re °f the field. 



g ty ja/r u ' i This is tho initial position. As 



Pi 7 ' K' : 'K'o^ L * '*— ^ tho prism is turned a spectrum 



V^ **\§/ appears in the upper half of the 



^^77^1— rr^^ neu l 5 cacn li ne °f th Q spectrum, 



ifflBj/»r as it is made to coincide with the 



slit, represents a ray which has 

 been refracted into the prism, reflected normally at the second 

 face, and refracted out by the same path ; henco the angle through 

 which tho prism has been turned is the angle of incidence i for that 

 ray, whilo tho angle of refraction is the angle of the prism. If 

 the prism be turned further until the second face is perpendicular 

 to the telescope, the difference of readings for the initial and final 

 positions gives the latter angle, which is therefore the angle of 



refraction r for each ray. Then a = — — • 

 J r sin r 



The spectrum will reappear before the final position is reached 

 at the point where the rays are refracted through the second, and 

 reflected internally at the first surface ; and the angle i is now the 

 difference between the corresponding reading and that of tho final 

 position ; this gives a second determination of the index. This method 

 dispenses entirely with the usual collimator ; it will be noticed, how- 

 ever, that the angle of the prism must be less than tho critical angle 

 of its substance. 



This method is practically identical with that adopted by Prof. 

 Abbe in his Eefractometer, and Prof. Lommel subsequently acknow- 

 ledged this,* not being aware of Prof. Abbe's paper. 



Optical method for the absolute measurement of small lengths.f 



— M. M. de Lepinay makes use of Talbot's fringes, which are produced 



w r hen a parallel-faced transparent plate is interposed in the path of a 



beam of light which has passed through a diffraction grating. If /x 



is tho index of the plate, t its thickness, n the order of the fringe, 



a - 1 

 then 2 —- — t = n. 



A 



The author measured by this means the thickness of a quartz 

 plate cut parallel to the axis, and about 4 mm. thick, using the third 

 spectrum produced by a grating of 400 lines to 1 mm. /a was taken 

 as the mean of the best known measurements, A as the mean of the 

 wave-lengths found by Mascart, Ditschreiner, and Van der Willigen. 

 Pays of different wave-lengths give a succession of values for t, of 

 which the mean is taken. The author claims greater accuracy for 



* Zeitschr. f. Instrumentenk., v. (1885) p. 200. 

 t Comptes Eendus, c. (1885) pp. 1377-9. 



