532 Prof. Arthur Schuster on 



contained in the disturbance is not equal to the sum of the 

 energies contained in its different parts. 



If such a succession of waves as we have been speaking 

 of were to fall on the retina of our eye, a colour-effect might 

 be produced by the combination where none is produced by 

 the individual disturbance. In that case there is interference ; 

 but it will be shown that the interference is due to some 

 resonance effect in the eye, but does not exist objectively. 



1 8. We proceed to discuss the nature of interference pro- 

 duced when some point of a screen is illuminated by two 

 different sources of light. Let the velocity due to each source 

 separately be expressed as functions of the time,/(i) and <j>{t), 

 the velocity at any time due to the superposition of the two 

 disturbances is/(£) +0(0? an d the excess of kinetic energy of 

 the combination over the sum of the energies due to each 

 separately will be proportional to 



[/(o +</>«] 2 - lao* + * w 2 ] = m) * («) • 



The value of 



%) — 00 



may be taken as a measure of the a interference." In order 

 to express this in a form suitable for our purpose, we make 

 use of the well-known proposition expressed by the equation 



T . ., ,-, v C* „ x sinA# _ —/(0), if /3 positive and a=( 



Limit (A = oo) fix) dx = \ 2 J K " ^ * 



J- * lOif£>*>0. 



From this we easily obtain, if u is a positive quantity, 



J sin /i ( x —~ u) 



M u-u) dx = ^ W • 



Let ¥(\i } X 2 ) be a function of two independent variables, and 

 consider the integral 



J CO /*oo /*co 

 I I F(X,, X 3 )cos ic(\ 1 —\ 2 )d\ 1 d\ 2 die. 

 -ooj -cojo 



Performing the integration with respect to k, we find 

 Limit '(*=•) rj'^X,) "^y cPl^; 



and this, with the help of the above relation, becomes 



J CO 

 F(X 1? \>) dki, 



