M. V. von Lang on a Horizontal Goniometer. 137 



The chief requisites of such an instrument are two concentric 

 axes — the inner one carrying the vernier and the prism-table, 

 the outer movement carrying the telescope and the graduated 

 circle. A collimator with slit is ; of course, fixed to the tripod 

 of the instrument. 



The two axes are not put into one another, as is done in 

 geodetical instruments, for the sake of repeating the angles ; 

 but here the tripod (G-) is terminated in a strong cone that 

 forms the axis on which the circle (C) turns, whereas a hole 

 in the centre of the cone supports the axis (A) of the vernier 

 (n). Fig. 7 shows this arrangement in a sectional drawing. 



Both axes may be clamped by the screws L L', and micro - 

 metrically moved by the screws M W. Suppose we clamp 

 the inner axis with the prism, of which the angles of deviation 

 (D) and of incidence (i) are to be measured. Let S be the 

 reading of the vernier by direct observation of the slit, R the 

 reading by observation of the slit after reflection from the 

 first plane of the prism, and T the reading by observation of 

 the spectrum. Then we have 



D = T-S, ;=90°-i(S-R); 



and the index of refraction in the direction given by the angle 

 r is found from the known formulas 



ta„(,-^) = ta4ta„(;-^)cot^, 



A being the angle of the prism. 



As long as the relative position of the prism and the vernier 

 is not altered, we have 



S + R = C= constant. 



For if we turn the prism (with the vernier of course) through 

 an angle + %, all readings will increase in the same ratio ; but 

 the reflected image of the slit turns at the same time through 

 an angle — 2%, so that the sum S + H will indeed remain con- 

 stant. We find by the quantity C, 



and this formula allows us to find the angle i from the read- 

 ing S. In this way it is possible to determine the angle of 

 incidence even when it is very small ; in which case it cannot 

 be observed directly, as telescope and collimator cannot be 

 brought so near to each other. 



If we put the telescope to the slit and then turn the inner 



C 

 axis till the vernier gives 90° + -~- 3 then the light will fall per- 



_ sini 



