318 THE PRINCIPLES OF SCIENCE. 



so that the resultant is nothing at all, and acts at an infi 

 nite distance, which is practically the same as to say that 

 there is no possible single resultant. Two such forces 

 constitute what is known in mechanical science as a couple, 

 which occasions rotatory instead of rectilineal motion, and 

 can only be neutralized by an equal and opposite couple 

 or pair of forces. 



The most beautiful instances of singular exceptions are 

 furnished by the science of optics. It is a general law, 

 for instance, that in passing through transparent media 

 the plane of vibration of polarized light remains un 

 changed. But in certain cases, to which reference has 

 already been frequently made, namely, certain liquids, 

 some peculiar crystals of quartz, and transparent solid 

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

 periment (vol ii. pp. 234, 287), the plane of polarization 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 f , it arises from 

 the composition 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 dimen 

 sions of the circles or the rapidity of the motions. In 

 one case where the two circles are exactly equal, 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 arises. Among other sin 

 gular exceptions in optics may be placed the conical refrac 

 tion of light, already noticed (vol. ii. p. 1 75), connected 

 with the peculiar form assumed by a wave of light when 

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



