Recent Progress in Theoretical Physics. 245 



two poles of the electro-magnet, bored through for the reception 

 of the substance and the passage of the light, and IST., is the anal- 

 yzer by which the position of the azimuth of the light reaching 

 it is determined. When Gr is a determinate length of " heavy 

 glass " (a silico-borate of lead), the analyzer requires a rotation of 

 6° on producing the electro-magnetism, in order to be placed in 

 the same relation to the azimuth of vibration of the light reaching 

 it, as it was in, before the circuit was closed. That is, if the posi- 

 tion of the analyzer is such before the electro-magnetic circuit is 

 closed, that the field is dark, on closing the circuit, and thus plac- 

 ing the glass in a strong field of magnetic force, the azimuth of 

 the polarized light is so changed that a perceptible amount gets 

 through, and the analyzer must be rotated 6° in order to again cut 

 it off and render the field dark as before. This an^le throusch 

 which the light is turned, is, however, in addition to the length of 

 the stratum of the medium through which it is compelled to pass, 

 directly proportional to the strength of the current producing the 

 magnetism (or rather to that resolved part of the magnetic force 

 produced by the current, which is in the direction of the ray). 

 The amount of the rotation also depends upon the refractive 

 energy of the medium subjected to the magnetic strain. The rela- 

 tion is sometimes stated thus : " The angular rotation of the plane 

 of polarization is numerically equal to the amount by which the 

 magnetic potential increases from the point at which the ray enters 

 the medium to that at which it leaves it, multiplied by a coefii- 

 cient, which, for diamagnetic media (like glass), is generally posi- 

 tive." — Maxwell. 



first and second kind. An elementary discussion of the principal features of 

 vortex motion, involving only the simplest Quarternion notions, is given in 

 Prof. Clifford's recently published " Elements of Dynamics — Part I," page 

 191, et seq. Sir Wm. Thompson has also published an extensive paper in the 

 Trans, of the Royal Soc, Edin. Vol. 8 for 1869, in which many new theories 

 are established and many illustrations of vortex motions in fluids are given, 

 by means of real or or ideal electro-magnets variously ai'ranged. A sum- 

 mary of several of these theories and analogies will be found in Thompson's 

 " Reprint of Papers on Electro-statics, and Magnetism." — London, 1873. An 

 earlier 'paper, suggesting the idea of vortex atoms, was published in Vol. 34, 

 p. 15, of the Phil. Mag., 1867. London, Dublin and Edinburgh. 



