INTERFERENCE OF LIGHT. 79 



that the distance of the body from the vertical, measured in 

 either of these planes, is the same at any instant as if the 

 other vibration did not exist ; so that each vibration subsists 

 independently of the other, and the result will be a compound 

 elliptical vibration. We have here supposed the coexisting 

 vibrations to take place in separate planes, in order that 

 their independence may be more distinctly recognised. When 

 the two vibrations are in the same plane? it is obvious that 

 the resulting vibration will be also in that plane ; and that 

 its amplitude will be the sum of the amplitudes of the com- 

 ponent vibrations when their directions conspire, and their 

 difference when they are opposed. 



(99) Let us transfer this to the case of Light : Let us 

 suppose that two sets of waves start at the same time from two 

 near luminous origins (which, for simplicity, we shall assume 

 to be of equal intensity), and that a distant particle of ether 

 is thrown into vibration by both at the same time. Then, 

 supposing that these two vibrations are performed in the 

 same plane, it follows from what has been said, that, when 

 their directions conspire, they will be added together, and 

 the resulting space of vibration will be double of either ; and 

 that, on the contrary, they will counteract one another, and 

 the resulting vibration will be reduced to nothing, when their 

 directions are opposed. 



It is evident, further, that the directions of the vibrations 

 will conspire, and therefore 

 the space of vibration be AV^N 

 doubled, when the two waves 

 arrive in the same phase ; A f "^Vj 

 and that, on the contrary, 

 their directions will be op- A v __ / 



posed, and the resulting vi- 



bration reduced to nothing, when they arrive in opposite 



