470 The Astronomer Royal on the Equations 



by showing that mechanical laws may be able to explain effects 

 never before ascribed to mechanical laws. As regards the 

 progress of intellect, it has been very important to show that 

 variation of velocities, as depending on the period of the oscil- 

 lations, is mechanically possible; it has been very important 

 to show that transversal vibrations are mechanically possible ; 

 it has been very important to show that crystalline separation 

 of differently polarized rays is mechanically possible. It is 

 not that I believe completely in any one of the mechanical 

 explanations which have been given, but that a priori difficul- 

 ties have been removed, and that it may now be considered 

 that there is a fair chance of reducing the whole to mechani- 

 cal explanation. 



In some cases the mechanical theory has stopped at the 

 first step, as for instance in the very remarkable equations in- 

 dicated by Prof. MacCullagh as competent to represent some 

 of the characteristic phaenomena of quartz. It was here an 

 important matter to show that there was opened even a possi- 

 bility of reducing these anomalous facts to mechanical laws. 



The suggestion, which it is the object of this paper to lay 

 before you, is of the same kind as that made by Professor 

 MacCullagh. 



In order to reduce the rotation of the plane of polarization 

 to laws, I shall follow the example of Fresnel in assuming 

 that plane-polarized light may be considered as compounded 

 of two beams of circularly-polarized light, one right-handed 

 and the other left-handed, and that the rotation of the plane 

 is produced by a difference of the velocities of the two circu- 

 larly-polarized beams. And this, I take this opportunity to 

 observe, is actually the simplest way of conceiving the change, 

 at least in instances like that of quartz, &c, and like that be- 

 fore us, when the same change is produced whatever be the 

 position of the plane of polarization (a fact which, at my re- 

 quest, Dr. Faraday has very carefully verified). Although 

 the conception of a plane vibration is easier where the plane 

 of vibration has immediate reference to the plane of reflexion, 

 &c, yet the conception of two circular vibrations is easier 

 where the plane of the compound vibration has no reference 

 to any plane in the apparatus, and is in fact perfectly arbi- 

 trary. 



Now let x x be measured in the direction in which the light 

 is supposed to travel in the first experiment; .r 2 in the oppo- 

 site direction, or in the direction in which the light will travel 

 when, the magnetic adjustments remaining the same, the re- 

 lative positions of the polariser and analyser are reversed ; 

 suppose these to be horizontal: let y x be measured horizon- 



