on the Hypothesis of Undulations, 333 



in this theory by the formula *q»ih rf^rf« ot e^rf 3vr«. 



v=msinrr- (w^at + c) +m'sin— y {cc—at-rc'). 

 Let 



m'=m + ^, i-=|(l + y,andi=l(i-^). 



Then, the time being given, the expression may be put under 

 the form 



v = 2msm{-j- +Cilcosf-y- H-Cg I +/ism( — p +C3 j. A 



At present we will leave out of consideration the term contain- 

 ing /JL. The other term taken by itself shows that the axis of x 

 will be cut by the curve at a series of points separated by the 

 common interval L, which is an harmonic mean between \ and 

 X', and at another series of points separated by the common 

 interval /. As the ratio of the greatest and least values of \ for 

 light is nearly that of 3 to 2, / will be at least equal to 5L. 

 Hence the second series of recurrences will always be slower than 

 the first ; and in case \' be not much larger than \, they will be 

 much slower. The following considerations will show that in 

 this case this second trigonometrical factor will have little or no 

 sensible effect on the quality of the compound light. It is known 

 from experiment, that if a stream of light be interrupted at short 

 intervals by breaks, the sensation of light is still continuous. 

 Suppose, therefore, the parts of the curve contiguous to those 

 points of its intersection with the axis of ic which depend on the 

 second factor, to be suppressed ; the remaining portions will have 

 the quality of regularity of recurrence which is necessary to pro- 

 duce colour, and the colour will plainly correspond to the wave- 

 length L, which is intermediate to X and X'. The suppressed 

 portions, not satisfying the condition of regularity of intervals, 

 may cause a sensation of whiteness, and thus have the effect of 

 diluting the colour. These theoretical deductions agree exactly 

 with a law first given by Newton as a result of experiment, viz. 

 that " if any two colours be mixed, which in the series of those 

 generated by the prism are not too far distant from one another, 

 they, by their mutual allay, compound that colour which in the 

 said series appeareth in the midway between them.^^ This law 

 is confirmed by the experiments of M. Helmholtz. (Phil. Mag. 

 S. 4. vol. iv. p. 532.) 



According to the theory, the condition that m = m! must be 

 approximately fulfilled. The effect of the term containing //, will 

 be to introduce irregularity of intervals, and therefore whiteness ; 



