16 On the Intensity of Light, &c. 



observing, that since the component velocities are at right angles 

 to each other, the square of the actual velocity must be the sum 

 of their squares ; but this proves the proposition only when the 

 greatest velocities are simultaneous, which happens only in the 

 cases of a complete accordance or of a difference of a semi- 

 undulation in the interfering portions. 



It may be observed also, that the method usually given for 

 finding the intensity of the vibration resulting from two or more 

 rectilinear vibrations proceeds upon no certain grounds. All the 

 vibrations may be reduced to two in rectangular directions, the 

 expression for the square of the velocity in each of their direc- 

 tions consisting of two parts, one of which is constant, and the 

 other depends on the cosine of an arc increasing proportionally 

 to the time : the square of the resultant velocity, therefore, con- 

 sists also of a constant part, and a part depending similarly on 

 the time ; and it is assumed that the intensity of the resulting 

 vibration is proportional to the former, which is true only in 

 the very particular cases just mentioned, if the intensity be 

 measured by the square of the greatest velocity. 



This assumption, however, gives a correct result ; and the 

 reason that it does so is obvious from the principle laid down in 

 the commencement ; for if the expression for the square of the 

 velocity be multiplied by the differential of the time and inte- 

 grated, the variable parts will vanish when the integral is ex- 

 tended to the whole time of a vibration. 



