1918-19.] A “Duplex” Form of Harmonic Synthetiser. 239 
shown in its entirety.) The right-hand member of (4) may be expressed as 
a series — 
* = - I cos 0 (1 - cos 2 % 2 1 ^1 + • cos 0 
+ (I + - cos2 ^ - ! ■ cos * ^ ^ 
where 
2p 
2_ 2^TT (6) 
The turning values of e regarded as a function of 9 are determined by the 
equation 
° dO 
de 
sin 0 
(0 
d cos 0 
The factor sin 6 leads to 6 = 0 or tt, values which are evident a priori 
because of our choice of comparison S.H.M. The other factor gives 
