Cambridge Philosophical Society. 421 



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

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

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

 for greater accuracy. 



Let R, II' 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; m 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, 

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

 by the following formulse, which happen to be extremely convenient 

 for numerical calculation ; — 



I=1(R' + R)j '^^:^' 2=i(r' + r)P;^':" - 



2^ '' ''croon i •; 2 rlmirln >o; 



n sin(r'—- r) tan (r'—r) 



cos 2z«r== -^ :— : coso= ^^ —. 



sin(R'-R)' ^ tan(R'-R) 



The author stated that he liad already observed with this instru- 

 ment, and after a little practice had found that it worked in a very 

 satisfactory manner. When the light of the clouds was reflected 

 horizontally by a mirror, and modified so as to produce ellipti- 

 cally-polarized light in which the ratio of the axes was about 3 to 1, 

 it was found that the mean error of single observations amounted 

 to about a quarter of a degree in the determination of the azimuth of 

 the major axis, about three or four thousandths in the determination 

 of the ratio of the minor to the major axis, and little more than 

 the thousandth part of an undulation in the determination of p. 



Since the magnitude of p depends upon the length of wave, or, 

 what comes to the same, the refrangibihty of the light, it follows 

 that a knowledge of the former leads to a knowledge of the latter. 

 It may thus be said that the instrument determines the azimuth and 

 excentricity of the ellipse described, and the refrangibility of the 

 light. An error of the thousandth part of an undulation in the de- 

 termination of p would correspond to an error in the place in the 

 spectrum assigned to the light operated on amounting to less than 

 the twentieth part of the interval between the fixed lines D and E. 

 Now by the use of observing media it is possible, without too much 

 reducing the intensity of the light employed, to alter greatly its mean 

 refrangibility ; and yet for each medium the refrangibility may be 

 determined very accurately by means of the value of p. Accord- 

 ingly, the instrument is specially adapted for investigations relating 

 to the dispersion of metals, and for other similar researches, f'' 'f^f^S 



^, , .. . J 07/;? 3-iB 



ijc* bli/o/r tgooi U to .bsiigfj.fgnriiro ei irJgii ori^r rloirfvv nl 



