112 



employed for the purpose, the author proceeded to describe a new 

 instrument which he had invented, and which he exhibited to the 

 meeting. In the construction of this instrument he had aimed at 

 being independent of the instrument- maker in all important points 

 except the graduation. The construction is as follows : — 



A brass rim or annulus is mounted so as to stand with its plane 

 vertical when placed on a table. Within this rim turns a brass gra- 

 duated disc ; and the angle through which it turns is read off by 

 means of verniers engraved on the face of the rim, and reading to 

 tenths of a degree. This disc is pierced at the centre, and carries 

 on the side turned towards the incident light a retarding plate of 

 selenite, of such a thickness as to give a difference of retardation in 

 the oppositely polarized pencils amounting to about a quarter of an 

 undulation. In front it carries a hollow cylinder, turned on the 

 lathe along with the disc itself. Round this cylinder there turns a 

 collar containing a Nicol's prism, and carrying a pair of bevel-edged 

 verniers, by which the angle may be read off through which the 

 prism has been turned. Thus the retarding plate moves in azimuth 

 carrying the prism along with it, and the prism has likewise an in- 

 dependent motion in azimuth. 



In observing, the light is extinguished by a combination of the 

 two movements, in which case the elliptically-polarized light is con- 

 verted by the retarding plate into plane polarized, which is then ex- 

 tinguished by the Nicol's prism. On account of chromatic varia- 

 tions, the light is not, strictly speaking, extinguished, unless homo- 

 geneous light be employed, but only reduced to a minimum. There 

 are two principal positions of the retarding plate and Nicol's prism 

 in which the light is extinguished, or at least would be extinguished 

 if the incident light were homogeneous ; and for each principal 

 position there are four subordinate positions, since either the retard- 

 ing plate or the Nicol's prism may be reversed by turning it through 

 180°. The mean of the four subordinate positions may be taken 

 for greater accuracy. 



Let R, R' be the readings of the fixed, r, r' those of the moveable 

 verniers in the two principal positions ; I the index error of the fixed 

 verniers, that is, the azimuth of the major axis of the ellipse de- 

 scribed, measured from a plane fixed in the disc ; i the index error 

 of the moveable verniers, that is, the azimuth of the principal plane 

 of the prism, measured from a fixed plane in the disc ; w the angle 

 whose tangent is equal to the ratio of the axes of the ellipse de- 

 scribed ; p the difference of retardation of the oppositely polarized 

 pencils transmitted through the plate, measured as an angle, at the 

 rate of 360° to one undulation. Then the unknown quantities I, i, 

 •ux, and p are given in terms of the known quantities R, R', r, and r' 

 by the following formulae, which happen to be extremely convenient 

 for numerical calculation : — 



I=1(R' + R); ,= .l(r' + r); 



n sin (r' — r) tan (/—>•) 



cos 2zsr= - — : cosp= - — 



sin(R'-R) P tan(R'-R). 



