88 Mr Dalton on the Vision of Colours. 



the major axis makes with O A, it will make its complement 

 with O B, and we shall have 



O A 2 = a? cos 2 <p + ty sin2 p, 



O B 2 = a 2 sin 2 <p + Ifi cos 2 <p, 



and therefore O A 2 -f O B 2 = a- + W. Hence the intensity is 



independent of the difference of origin, and therefore the rays 



do not interfere. 



This remarkahle circumstance is commonly accounted for by 

 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 direc- 

 tions, the expression for the square of the velocity in each of 

 those directions consisting of two parts, one of which is constant, 

 and the other depends on the cosine of an arc increasing pro- 

 portionally to the time ; the square of the resultant velocity, 

 therefore, consists 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 in- 

 tensity 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 

 integrated, the variable part will vanish when the integral is 

 extended to the whole time of a vibration. 



Art. X. — Extraordinary facts relating' to the Vision of Co- 

 lours : with Observations. By Mr John Dalton.* 



It has been observed, that our ideas of colours, sounds, tastes, 

 From Memoirs nf Lit. and Phil. Sac. of Manchester, vol v. part i. 



