364 Definition of Intensity in the Theories of Light and Sound. 



Admitting, after some hesitation, "that two vibrations may 

 be superposed with coincident phase/'' he proceeds as follows : — 



"In these cases we must not treat each vibration as a cause 

 in itself, invariable under all conditions. If we regard the two 

 vibrations as unaltered by the superposition, we shall in general 

 be wrong." 



This line of defence cuts away the ground upon which rest 

 the undulatory theories of light and sound. Those theories 

 alike assume the application of the principle of the superposi- 

 tion of small motions in all cases with which they undertake to 

 deal. The theory of interference assumes that the motion in a 

 wave may be represented by the ordinate of a particle — and that 

 where two waves are superposed in which the vibration is in the 

 same plane, their joint effect is represented by the algebraical 

 sum of the expressions for the ordinates corresponding to each 

 wave taken separately. 



This implies that the superposition of two equal waves in the 

 same phase will produce, as regards any particle at a given time, 

 twice the force acting upon it, twice the velocity impressed upon 

 it, twice the space described by it, which would occur if either 

 wave were destroyed. 



What Mr. Bosanquet has to do is to reconcile this state of 

 things with the production, under the same circumstances, of a 

 quadruple amount of illumination or loudness. 



The received theory in effect states that where two equal waves 

 in the same phase act together, the effect of each in producing, 

 at a distant point of the air or aether at a given time, effective 

 force, velocity, and displacement will be precisely the same as 

 either would have produced under the same circumstances if it 

 had acted separately — and that if we have three or more such 

 waves superposed, no alteration will occur in the separate action, 

 so estimated, of each. 



The received definition of intensity, on the other hand, im- 

 plies that, coexisting with the state of things just described, 

 we shall have, where two waves operate together, each wave pro- 

 ducing twice the effect estimated by the amount of sound result- 

 ing from it which either would produce separately; where three 

 waves act together, each will produce three times the effect, so 

 estimated, which it would have produced separately ; and so on. 



To what purpose, I would ask, are we called upon to embar- 

 rass ourselves with these extravagant conclusions ? The defini- 

 tion of intensity was invented for the special purpose of explain- 

 ing the phenomena of interference, or, to speak more precisely, 

 to determine the points of maximum and minimum intensity in 

 interfering rays; and whether we take the simple power of the 

 amplitude or its square as the measure of intensity, the positions 



