Hypothesis of Colour Vision ivith Mechanical Illustrations. 341 



.and 0'4yu,, the colours being red, green, and violet respectively. 

 Possibly a nearer imitation would be afforded if the range 

 were still less. 



4. Mathematical Theory. 



It is obviously desirable to associate some specified values 

 of the dampings with the " resonators " postulated, and then 

 •derive mathematically the consequent resonance curves. 



The equatioji of motion of forced vibrations may be 

 written 



where y is the displacement of an element of the responder, 

 2k is the frictional resisting force per unit mass per unit 

 velocity, p 2 is the elastic force per unit mass per unit dis- 

 placement, f is the maximum value per unit mass of the 

 harmonic impressed force of frequency n/2rr ; the frequency 

 natural to the responder, if devoid of friction, being 

 P/2tt. 



The complete solution of this equation may be written 



fs'mhit — d>) a z/ • / \ /«\ 



^=7(^^*«7 2 I +A<; s,n (i '-"°" °° 



(Displacement) (Forced Vibration) (Free Vibration) 



where 



tan ^ = ^T^> q } '=p 2 -k\ .... (a) 



and A and a are arbitrary constants depending upon initial 

 conditions. 



We are here concerned with incident radiations of variable 

 frequency nj2ir throughout the visible spectrum, but with 

 only three assumed values for the frequencies of the 

 respotulers. These may be denoted by pi/2v, p^lrr. pJ2ir 

 respectively, and their wave-lengths by X ls X 2 ? ^s- 



Then, if v be written for the speed of light, we shall have 

 p 1 \i/v=27r or 



2itv 2irv ... 



Pi= Y~ and n= — (4) 



where x is written for the variable wave-length of the 

 incident light. 



From equation (2) we may obtain the value of 8, the 



