338 



SCIENCE. 



[N. S. Vol. XXI. No. 531. 



in the first place to rediscuss the questions 

 at issue and point out more in detail than 

 heretofore how, according to elementary 

 theory, the velocities of plane and circu- 

 larly polarized rays in any optically or 

 magTietically active medium must be neces- 

 sarily related to each other, and how, ac- 

 cording- to elementary theory, it is impos- 

 sible that Professor Rowland's equations 

 can represent a twisted plane polarized 

 ray. 



In the second place, it will be shown 

 how these velocities in the magnetically 

 active field are related to the velocity in 

 zero field according to the several pro- 

 posed hypotheses. Were it possible to 

 make this comparison experimentally, we 

 should have a test as to the validity of 

 the proposed hypotheses, but such test is 

 as yet beyond reach by reason of the small- 

 ness of their differences. 



An attempt is made, in the third place, 

 to show that a moderate degree of absorp- 

 tion would exert a negligible influence in 

 modifying the results already developed 

 for perfectly transparent media. 



The conclusions arrived at in this paper 

 may be briefly stated as follows : 



1. The increase or decrease in the veloc- 

 ity of circularly polarized light observed 

 by Mr. Mills, and previously by Professor 

 Brace, are perfectly in accord with and a 

 necessary consequence of the elementary 

 trigonometrical equations expressing the 

 propagation of twisted plane polarized 

 light, and the phenomenon is independent 

 of any hypothesis, electromagnetic or other- 

 wise, as to the manner in which the twisting 

 is produced. 



2. The equations given by Professor 

 Rowland to express the propagation of 

 twisted plane polarized light are not suit- 

 able for that purpose, for they in fact ex- 

 press the propagation of a uniformly and 

 continuously rotated plane polarized ray, 



such as is at present unknown to experi- 

 mental physics. 



3. The velocity of a twisted piano polar- 

 ized ray is so related to the velocities of 

 the right and left circularly polarized rays 

 of which it is composed that its reciprocal 

 is the arithmetical means of the reciprocals 

 of its components ; and the velocity of Pro- 

 fessor Rowland's rotating plane ray is the 

 arithmetical mean of the velocities of its 

 right and left circularly polarized com- 

 ponents. 



4. The differential equation based on two 

 different electromagnetic hypotheses as to 

 the action of the medium in producing 

 rotation or twisting of plane polarized light 

 in a magnetic field involves an equation 

 expressing the relation of the velocity of 

 this kind of light at zero field to its velocity 

 in the given field. On the hypothesis of or- 

 bital motions of charged ions the differ- 

 ential equations show that the field would 

 cause a decrease in the velocity of plane 

 polarized light during the twisting ; while 

 on the hypothesis of charged ions having a 

 motion of translation across the field, the 

 differential equations show that the field 

 would cause an increase in the velocity by 

 an amount one-third as great as the de- 

 crease just mentioned. This increase or 

 decrease is of the second order of small 

 quantities, and is so minute as to be at 

 present beyond the range of observation, 

 varying as it does as the square of the 

 observed change produced by the field in 

 the velocity of circularly polarized rays. 



5. MacCulloch's differential equations 

 involve practically the same decrease of 

 velocity by the medium as those based on 

 orbital motions of charged ions. 



6. A moderate amount of absorption in 

 the medium would not practically modify 

 the conclusions true for perfectly trans- 

 parent media on either hypothesis. 



