1903] 
HARMONICS OF ORDER UNITY. 
405 
Since with definition (4) f 2 g 2 K 2 = 1, 
r , . 4 vie 3 cos /3 cos 7 
Il (COS) = 7 L 
3 sin 8 /3 
In “ Harmonics ” this harmonic is defined by 
(/*) = A (/*)-/*; Ci (</>) = V(i - /3 cos 2c/>) 
.(5) 
.( 6 ) 
Now we must take for /and <7 values such as to bring the two definitions 
into accord. This is the case if 
and f 2 g 2 k- = 1 + /3. 
Hence /j (cos) = | 7 rM (1 + /3) (7) 
agreeing with the result on p. 277 of “ Harmonics” for the case i = 1, s= 0, 
type OEC. 
( 2 ) The Sectorial Cosine Harmonic. 
I define this thus :— 
pp (^) = (1 _ /c* sin 2 of =/(k ' 2 + k 2 cos 2 of 
QL 1 1 (</>) = cos </> =g (k 2 — k 2 sin 2 </>/ 
.(8) 
where/= 1 , g — — . 
By symmetry with the last result 
T , . . 47 rJc 2 cos 8 cos 7 
/j 1 (cos) = 
47 r/r 3 cos /3 cos 7 
3 sin 3 /3 J a 3 sin 3 /3 
In “ Harmonics ” I defined the functions thus :— 
.(9) 
1+0 
\h 
(&! 1 ((f)) = COS cf) 
i 
x —ß-^V 
....( 10 ) 
/1 _j_ 2 
If we take f= y -—, g* = 1 , the two definitions agree, and we have 
A 1 (cos) = IttM = AttM (1 + 2/3 + 2/3 2 ) (11) 
This agrees with the result on p. 277 of “Harmonics” with i = l, s — 1, 
type OOC.