466 Prof. Challis's Explanations of Phenomena of Light 



It will be seen from this expression that if the phases c and d be 



the same, or differ by an even multiple of -, the two sets of un- 



dulations are in exact accordance, and the resulting value of the 

 maximum velocity is the sum of m and ?n' ; but if the difference 



of phase be an odd multiple of -, that the undulations are in 



complete discordance, and the resulting maximum velocity is the 

 difference of m and m'. In the latter case, if m = m r , the velocity 

 vanishes at all points of the axis. Also the general values of V, 

 w y and or show that in the same case the direct and transverse 

 velocities and the condensation vanish at all distances from the 

 axis. Consequently the combination of the undulations under 

 these circumstances would have no effect in producing light. 

 Not only has this theoretical result been verified experimentally 

 in the combination of rays of light, but, as is known, experiment 

 has also indicated the same interference of undulations of the 

 air under like circumstances, at least so far as regards direct 

 vibrations. This fact is confirmatory of the hypothesis that the 

 sether is constituted like the air. 



Hitherto we have had under consideration only undulations of 

 that form which, as being independent of arbitrary conditions, 

 they take initially whatever be the mode of their generation, 

 and which for that reason I have called the primitive form. The 

 characteristic of such undulations is the symmetrical arrange- 

 ment of the direct and transverse velocities and of the conden- 

 sation about their axes, which is at once explanatory of the term 

 non-polarized applied by experimentalists to rays of the form in 

 which they are originally generated. But this symmetry may 

 be disturbed by arbitrary conditions, as is proved by the analy- 

 tical circumstance that the value of the factor /is determined 

 generally by the integration of the partial differential equation 



g|+ g+4^0 (art. 36). 



In art. 28 I have'obtained a particular solution of this equation, 

 which indicates that the transverse motion is wholly perpendi- 

 cular to a plane the position of which depends on an arbitrary 

 angle 9 contained in the integral. Consequently to produce 

 such transverse motion, it is only required to impress on a pri- 

 mitive ray a disturbance symmetrical with respect to a plane, 

 but in other respects not restricted. Accordingly it is found by 

 experiment that rays submitted to such disturbances are polarized, 

 and the plane of symmetry of the disturbance is the plane of 

 polarization. It is also shown (arts. 40 and 41), in conformity 

 with experience, that when a primitive ray is so modified, equal 



