80 



Mr. A. Schuster on the Elementary Treatment 



two straight lines, LL 1 , NF (fig. 2), draw the perpendicular 

 P 0, and divide the wave into rectangular strips such that the 



Fisr. 2. 



M 



M„M 



M 



K 



resultant phase of two successive strips shall be opposite, the 

 phase of alternate strips agreeing with that of the whole 

 effect at P. It is obvious how to find the positions of the 

 points M ra , M n _! when these are not close up to ; for as the 

 whole resultant has a phase which corresponds to a distance 



PO + -x, and as, except for the central strips, the resultant 

 o 



phase at P will be very nearly that corresponding to the 



arithmetical mean of the extreme distances, we shall satisfy 



the condition by making 



4n— 5 



PM w _ 1=i > + 

 PM n = P + 



8 

 4n-l 



\ 



We shall assume that this is allowable until we come to the 



central strip; so that PM 1 = p+-^-X. This division differs 



from that usually adopted, and herein consists the great 

 advantage of the method of reduction which I propose. 



We divide, then, the central line K into elements such 

 that 3\ 



PM 1 = PO +~, 



o 



PM 2 =PM 2 + J, 



PM 3 =PM 2 + y 



It has already been shown that, after the first few elements, 

 the resultant vibration due to the elementary strips is that 



corresponding to a distance P+ a- If this is true for all 



