on the Hypothesis of Undulations. 465 



hold good with reference to an axis passing through the centre 

 of gravity of all of them. Possibly this circumstance may be 

 the physical reason that the above accelerative force is effective 

 only so far as it varies as the distance from the axis, which law 

 is more exactly true in proportion as the distance from the axis 

 is less. It is also worthy of remark that the above expression 

 contains A 2 in the denominator of its factor. Nothing, however, 

 respecting the intensity of the sensation of light can be inferred 

 from this circumstance, since we do not even know why the eye 

 is insensible to vibrations for which the value of X is not included 

 within certain limits. All that we can assert is that, ceteris 

 paribus, the intensity of an individual ray is dependent on the 

 constant m. 



The circular functions which are factors in the expressions for 

 V and a indicate regular periodicity in the dynamical effects of 

 the vibrations; and as we know from experiment that such 

 periodicity in respect to sound corresponds to the sensation of 

 the pitch of a musical note, we may conclude analogically that 

 regular periodic vibrations of the sether have the effect of produ- 

 cing the sensation of colour. The kind of colour depends on the 

 number of vibrations in a given time, which again depends on 

 the value of X and that of the absolute constant ica. Conse- 

 quently the symbol X, originating in a priori reasoning applied 

 to the supposed sether, may be regarded as the exponent of colour. 



So also the symbol c, the value of which depends on the velo- 

 city wata given point of the axis at a given time, corresponds 

 to a physical reality named the phase of a vibration, the meaning 

 of which will be best understood by what will presently be said 

 respecting the interference of vibrations. 



The mutual independence of rays of light, exhibited by the fact 

 that the same parts of space may be simultaneously traversed by 

 rays from different origins without any perceptible disturbance 

 of each other, is at once and satisfactorily explained by the 

 law of the coexistence of small vibrations. This law applies to 

 the sethereal undulations of the present theory, because the equa- 

 tions which express their properties were deduced from linear 

 differential equations with constant coefficients. See arts. 22, 

 26, and 38. 



The same law of the coexistence of small undulations serves 

 to explain the observed interference of rays of the same colour 

 under certain circumstances. To take a simple example, let two 

 sets of primitive undulations have coincident axes and the same 

 value of X. Then, according to that law, the velocity at any 

 point of the common axis will be given by the expression 



m sin — - {/cat — z + c) + ml sin — {jcat—z -f d) • 



A. A. 



