1878.] of determining the Ratio of Dispersions. 



491 



give equal deviations, the angles of incidence and emergence are simply 

 interchanged. Hence when the prism is turned from one to the other 

 of two azimuths for which the, image of the fiducial edge is on the wire 

 of the viewing telescope, the angle moved through is equal to the 

 difference between the angles of incidence and emergence in either 

 position. Both azimuths, and therefore their difference, can be deter- 

 mined with accuracy, provided the azimuths be sufficiently remote from 

 that of minimum deviation. 



The process of observation, then, is this. Set the prism a good way, 

 such as 10° or 15°, from the azimuth of minimum deviation, and read 

 the graduation. Turn the viewing telescope till the fiducial edge is on 

 its wire. Taking care to keep the telescope fixed, turn the prism 

 through the position of minimum deviation till the edge is again on 

 the wire, and read again. 



Let 0, be the angles of incidence and emergence or emergence and 

 incidence, of which let be the greater. Let 2 a, be the angle, i, of the 

 prism, 2 /? the sum of 2 a and the minimum deviation, 2 7 the mea- 

 sured angle through which the prism has been turned, or0-^. Since 

 the sum of the internal angles =2 a, we may represent them by a + x 

 and a— x. Let + "^ be denoted by 2 y. Then we shall have — 



sin (y + 7) sin (ij— 7) sin (5 

 sin (a-f-^) - sin (a — x)~ sin a 



Eliminating x from these two equations, we find — 



2 cos 2 acos (8 — 7) cos (/3 + 7) /-i \ 

 cos 2 y= yr u / I\ • • • C 1 )' 



COS (a — 7) COS (a + 7) 



which gives y, and then y + 7, i.e., or yjr, is known. The angle of in- 

 cidence for a known reading of the graduated circle being known, we 

 have only to apply the difference between this reading and that for 

 achromatism to that angle of incidence in order to get the angle of 

 incidence for the azimuth of achromatism. 



Second Method. — In this a little telescope is used, which is attached 

 to the stand of the prism, so as to move with the verniers of the circle. 

 The telescope need not be achromatic, but has cross wires in its prin- 

 cipal focus. 



After determining the azimuth of achromatism, the slit is illumi- 

 nated by a soda flame, and the prism with the verniers turned till the 

 fiducial edge is on the wires of the measuring telescope, when the circle 

 is read. The prism is then removed, and the measuring telescope 

 turned till the fiducial edge is seen directly, and the circle is read 

 again. Half the supplement of the difference of the readings gives 

 the angle of incidence when the reflected image was on the cross 

 wires ; and by applying the difference of readings for reflection and for 



2 k 2 



