134 POLARISED LIGHT AND THE MICROSCOPE. 



beginning. This happens every time the quicker of the two 

 motions has gained one whole oscillation on the slower, and then 

 the complete cycle of changes of Fig. 5 has taken place in the 

 series of curves traced out by the weight. 



For example, suppose the pendulum vibrates in the plane of 

 the strings once every second and in the perpendicular direction 

 once in lo^n seconds. Then, in 21 seconds, it performs 21' of 

 the quicker oscillations or 20 of the slower, so that the former 

 gain one oscillation over the latter. If, then, the weight be 

 pulled aside in a diagonal direction, its motion will undergo the 

 complete cycle of changes of Fig. 5, and again swing in the 

 same diagonal after 21 seconds. In half this interval (or loj 

 seconds) it will vibrate in the opposite diagonal to that in which 

 it started, as at (e). 



Reverting to polarised light, we have seen that the doubly- 

 refracting section is capable of transmitting rays of light polarised 

 along either optic axes without altering their character. There are 

 two such rays — i.e.^ those which we have called the ordinary, and 

 the extraordinary rays — and they travel through the substance at 

 somewhat different rates. Hence, as they penetrate further and 

 further into the substance, one of them gains slightly on the other, 

 just as one oscillation gained on the other in the pendulum. Hence, 

 remembering that the rays really consist in vibrations transmitted 

 from point to point through the ether, we see that the circum- 

 stances of the case are exactly analogous to those of the pendulum 

 experiment. It necessarily follows from this analogy that the 

 changes in type of the light at different depths, when the ray enters 

 the section polarised at an angle of 45° with the optic axes, 

 exactly reproduce the changes of type in the pendulum oscilla- 

 tions at different times, when it is started swinging diagonally. 



Another consequence of the analogy is that in the polariscopic 

 section the complete cycle of cha?iges takes place when the light-vibra- 

 tions in one of the rays have gained a whole oscillation over those in 

 the other. When the gain is half an oscillatiofi, half a complete 

 cycle has taken place, and the polariscopic appeara?ices are then most 

 marked. 



