8 The Astronomer Royal on the 



e, 2-405, 5'52, S'Si, nearly; and that the successive maximum 

 values of E^ correspond to the values of e, O'OO, 3"85, 701, 

 10*15, nearly; and that the corresponding maximum values 



ofE* are nearly 1, — , — , — . 



I will now proceed to point out the practical application of 

 this table. 



First, suppose the value of — - ( i^A'-^ + 6'^ — ^^h'^ + a^j 



to be small, or not exceeding a few multiples of tt. 



In this case no considerations can be introduced which tend 

 to simplify the expression for the intensity of the light. If 

 the light be heterogeneous, it will be necessary to form the 



numerical values of e^, e„, E^, E,;, and — ( \^/r + b^ 



— Vfr + a^) for each different colour, and to substitute 



9 _ / 



them in the expression E^^+E/— 2 E, E,, .cos — ( yh- + U^ 



— \/h^ + ct^y It is easily seen that the greatest intensity of 



light under any circumstances is (E, + EJ^ and the least is 



(E, - E,)^. 



Secondly, suppose the value of— ( V h^ + b^— \/ h^-\- a A 



to amount to many multiples of ir. 



Whatever care be taken to make light homogeneous, it is 

 practically impossible to make it homogeneous or even nearly 



so. Therefore the value of ^ ( "^ h^ + b^ — '^ h^ i- a^ will 



vary, perhaps to the amount of many multiples of it, for the 

 different values of \ corresponding to the different kinds of 

 light in the stream of light which is the sutyect of experiment. 

 And this may happen even when the portion of the spectrum 

 corresponding to the light used is so short that there is no 

 conspicuous chjinge of colour. In aggregating the effects of 

 these, it is to be observed that, for points near to the central 

 normal of the circular plate, the change produced in e^ and ^^, 

 by the change of X is very small, and the only variation which 



needs to be considered is that of cos — \ 'v/F+^— s/W^^ >•• 



As the arc included in this quantity changes its value by se- 

 veral multiples of t, the cosine will have equal values repeat- 



