PROPAGATION OF LIGHT. 15 



if A denote the length of the wave, T the time of vibration, 

 and v the velocity of wave-propagation, 



X = VT. 



(17) In the foregoing illustration we have assumed the 

 vibratory motion of the molecules of the ether, to take place 

 in a direction perpendicular to that in which it is propagated. 

 The grounds of this assumption will be explained hereafter. 

 But, in the meantime it is important to consider, in more 

 detail, other properties of the movement. 



Let us suppose, then, that each molecule performs its 

 vibrations in a right line,* passing through its position of 

 rest, and that these vibrations are all completed in the same 

 time. Let us further suppose, that the two halves of the 

 complete oscillation are perfectly similar, the deviation of the 

 molecule from its position of rest on the two sides being 

 equal at the corresponding times of the two half-oscillations. 

 These conditions will be satisfied by an equation of the 

 form 



y-irin |f (*-,), 



in which t is the actual time, t Q the time of the commence- 

 ment of the vibration, and T the time of the vibration itself, f 

 The displacement, ?/, vanishes when t - t Q is any multiple of 

 \ T ; and its values are equal, with opposite signs, for any 

 two values of t-t which differ by JT. The displacement 

 increases from t - t = 0, to t - t = J T, when it reaches its 

 maximum ; and it decreases from - t = J T, to t t = -J- T, 



* More complex forms of vibration will be considered hereafter. 



f The same conditions would be satisfied by the more complicated function 



. ZTT . 4ir . 6?r 



y = ! sin t + 02 sin t + a 3 sm t + &c. 



and there are certain phenomena connected with the dispersion of light which 

 seem to require the more complete expression of the periodical function. 



