1905-6.] A New Form of Harmonic Synthetiser. 
229 
In any actual instrument the dimensions are such that powers 
of r/Z greater than the second may be neglected, hence we have 
from (20) and (21) with (16) (and 19) 
This completes the determination of the comparison S.H., and, 
precisely as in the former case, it may be shown that it is a curve 
having its time axis depressed by a distance - r 2 /(4Z) below the 
time axis of the actual curve. The displacement that should 
accordingly be given to the time axis when drawing in the latter 
on the paper has already been explained. 
The interpretation of equation (22) is this. To make the 
average error as small as possible, the curve drawn by any one 
of the wheels of the instrument, the amplitude of the eccentric 
pin of which, according to the present theory, is r, ought to 
be regarded as a slightly inaccurate representation of a true 
S.H. curve, the amplitude of wdiich is not r, but r^l — 
The value of the average deviation can now be found by putting 
the values of p and v into equation (17) ; or, what comes to the 
same thing, by putting the values for m and n given by (20) and 
(21) into equation (18). 
There results, 
TT TT TT 
<dt \ ■ ■ • (24) 
Btt ) 
4 
Now if, as before, powers of rjl greater than the second may 
be neglected, then it follows from equation (16) that powers of 
ft/ a greater than the second may also be neglected ; hence from (15) 
e = p cos t + v + ^/a[l - @ cos t - cos 2 t\ 
a 2a 2 
Were this expression for e to be substituted in equation (24), 
and the integration then performed, it would be found that none 
of the terms would survive the process except the last. Therefore 
(24) may be written 
