300 Prof. K. Pearson, On plane waves of the [May 25, 



medium, it might after transition be found to be accompanied by a 

 strong heat ray. Further, we might be led to question whether 

 the heat of a very hot body be not due to its giving off at the 

 same time a mass of chemical or even violet rays ; whether with 

 Mr Langley the 'real colour of the sun be not blue"? 



On the other hand the occurrence of terms with an amplitude 

 containing t might suggest the breaking up of the wave, or the 

 impossibility of transmitting a wave of a velocity k which is inde- 

 pendent of the intensity and of the wave length. 



6. (c) Let us look at the matter from a somewhat different 

 standpoint, and assume 



u = A cos — (z — kt), 



A, 



where k is not equal to k. 

 We find 



d\i 2 d 2 u A^tt* 2tt, j^AHtt* 6tt, ... 



W~ K M = — ^vcos-iz-W + ^-vcos-iz-kt), 



d 2 u ( „ -4V \ d'u A'*tt % bV. 1A 



w-[ K+ -^ v )d? = ^r VC0S i, { *- kt) - 



Hence approximately 



. 27T, ... , 3 7r 3 v . %tt , ... 

 u = A cos — (z — kt) — A —s jr- t sm — - (z — kt), 



A2 2 



where k 2 = k? + 8 v. 



A, 



From this we can again draw curious deductions. If a wave be 

 transmitted into a medium for which v is not zero, its velocity will 

 depend upon its wave length and its intensity. Its velocity 

 increases with its intensity as seems natural. Let k' be the 



velocity of a wave in a second medium, and suppose rp = p, the 



coefficient of refraction, then 



s s 

 ^ = r + ^ + ^+ etc., 



where r, s, s', etc. are certain constants, of which s, s'. . . depend partly 

 on the intensity of the wave*. It will be observed that this result 



* ' It has, however, long been the opinion of some philosophers that there are 

 rays of different colours which have the same degree of refrangibility, and that 

 there are rays of the same colour with different degrees of refrangibility.' Airy, 

 Undulatory Theory, p. 157. Will the refrangibility being a function of the intensity 

 elucidate this ? 



