in reference to the Phoneido scope. 85 



that at one point all the waves shall be in the same phase. We 

 have 



h~ l z= cos \%Tr\- l ivt— rcos(0 — «)j-] 



+ cos[27r\ -1 jitf + rcos(0— «)]■] 



+ cos[27r\- l {vt—rcos(0 + u)\~\ I 



+ cos \_27rX- 1 \vt + r cos (0 + a)}] 



= 4 cos (27r\ -1 ^) cos (2irX~ l a: cos a) cos (27rX -1 ?/ sin a). 



The ventral segments occur when the quantities have the 

 values given in the following table: — 



\~ l vt 



X~ l X COS OL 



X~ l ysinu 



I 



I 



l + h 



m 



m + i 



m + \ 



n 



n + i 



n 



l+i 



m 



n + ± 



The ventral segments are divided into two sets : all one set 

 vibrate together ; and all the other set vibrate in the opposite 

 direction. 



The nodal lines are two sets of straight lines, whose equa- 

 tions are 



4# cos a = (2m + 1)X 

 and 



4y sin a = (2n + 1)X. 



Hence the nodal lines divide the film into oblongs whose 

 length and breadth are 



X , X 



2 cos a 



and 



2 sin a 



and a ventral segment lies in the centre of each oblong. 

 When the directions of the waves are J_ each other, a = 45 , 

 and the oblongs become squares. This form is shown in fig. 5. 

 When two waves of equal amplitude meet at an angle = 2a, 

 the equation is 



hr l z — cos [27r\- j J vt — r cos [6 — a) Y\ 



+ cospTrX- 1 ^— rcos(0 + a)£] 



= 2 cos l27rX~ 1 (vt— # cos a) J- . cos (27rA, -1 ?/sina). 



The nodal lines are the straight lines 



4ysina = (27i + l)\. 



When a =90°, we get two waves meeting each other in the 

 same direction. The equation becomes 



h-h = 2 cos (2ttX- 1 i?0 cos (2ttX~ 1 ?j). 



