A THEORY OF COLOUR VISION 383 



was 2 'oo sec. Both records show the simple pendulum starting 

 from an approximate state of rest. 



The vibrators in the retina are not allowed to pursue their 

 motion undisturbed. They may start from rest, but before 

 many periods have elapsed they may break free from their 

 points of attachment, or they may be brought to rest by an 

 impact. Thus as typical of their motion we may take a piece 

 of one of the curves given in Fig. 5. I have studied two por- 

 tions of the lower curve very carefully, namely from the end 

 of the first to the end of the ninth inch, and from the end of 

 the first to the end of the twenty-first inch. The first portion 

 gives the rise of the amplitude from zero to its maximum value. 

 The second portion gives practically the whole curve. 



According to Fourier's integral theorem, any curve may be 

 represented as the sum of an infinite number of sine curves. 

 In the special case here considered when the original curve is 

 approximately periodic, although sine curves of all possible 

 wave-length take part in its composition, those with approxi- 

 mately the same wave-length as the original curve have much 

 the greatest amplitude. For example, the wave-length of the 

 original curve, as obtained with the kymograph, seemed 

 about 1 *7 in. It can consequently be regarded as due to the 

 superposition of sine curves of wave-length ro, ri, 1*2, 1-3 

 up to 2*4 in., the sine curves in the middle of the range having 

 the greatest amplitudes. If we take the constituent sine 

 curves twice as close, i.e. every twentieth inch apart, when 

 added together they will reproduce the original curve with 

 greater accuracy. 



Just as the original motion may be regarded as built up 

 of an infinite number of sine motions, the energy of the original 

 motion may be regarded as distributed over these different 

 sine motions. Lord Rayleigh has shown how to calculate the 

 proportion that falls to each. 1 I made the calculation for 

 both the 8-in. length and the 20-in. length of the lower curve 

 in fig. 5. It was rather a tedious calculation, but as the 

 details of the procedure may be interesting, I describe them 

 in the following paragraph with special reference to the 20-in. 

 length. 



The curve was reproduced on squared paper, divided in 

 tenths of an inch, and the value of the ordinate measured 



1 Collected Works, vol. iii. p. 268. 



