xxix.} EXCEPTIONAL PHENOMENA. 653 



straight line, they do not balance each other. Examining 

 the formula for the point of application of the resultant, we 

 find that it gives an infinitely great magnitude, so that the 

 resultant is nothing at all, and acts at an infinite distance, 

 which is practically the same as to say that there is no 

 resultant. Two such forces constitute what is known in 

 mechanical science as a couple, which occasions rotatory 

 instead of rectilinear motion, and can only be neutralised 

 by an equal and opposite couple of forces. 



The best instances of singular exceptions are furnished 

 by the science of optics. It is a general law that in passing 

 through transparent media the plane of vibration of pola- 

 rised light remains unchanged. But in certain liquids, 

 some peculiar crystals of quartz, and transparent solid 

 media subjected to a magnetic strain, as in Faraday's ex- 

 periment (pp. 588, 630), the plane of polarisation is rotated 

 in a screw-like manner. This effect is so entirely sui 

 generis, so unlike any other phenomena in nature, as to 

 appear truly exceptional ; yet mathematical analysis shows 

 it to be only a single case of much more general laws. As 

 stated by Thomson and Tait, 1 it arises from the com- 

 position of two uniform circular motions. If while a point 

 is moving round a circle, the centre of that circle move 

 upon another circle, a great variety of curious curves will 

 be produced according as we vary the dimensions of the 

 circles, the rapidity or the direction of the motions. When 

 the two circles are exactly equal, the rapidities nearly so, 

 and the directions opposite, the point will be found to' 

 move gradually round the centre of the stationary circle, 

 and describe a curious star-like figure connected with the 

 molecular motions out of which the rotational power of the 

 media rises. Among other singular exceptions in optics 

 may be placed the conical refraction of light, already 

 noticed (p. 540), arising from the peculiar form assumed 

 by a wave of light when passing through certain double- 

 refracting crystals. The laws obeyed by the wave are 

 exact] y the same as in other cases, yet the results are 

 entirely sui generis. So far are such cases from contra- 

 dicting the law of ordinary cases, that they afford the best 

 opportunities for verification. 



1 Treatise on Natural Philosophy, vol. i. p. 50. 



