The motion of the points P_1P_2 ... is here made harmonic by aid of a
series of excentric disks arranged so that for one revolution of the first
the other disks complete 2, 3, ... revolutions. They are all driven by one
handle. These disks take the place of the templets described before. The
distances NG are made equal to the amplitudes a_1, a_2, a_3, ... The
drawing-board, moved forward by the turning of the handle, now receives a
curve of which (2) is the equation. If all excentrics are turned through a
right angle a sine-series can be added up.
It is a remarkable fact that the same machine can be used as a harmonic
analyser of a given curve. Let the curve to be analysed be set off along
the levers NG so that in the old notation it is
y" = f(x),
whilst the curves y' = [phi](x[xi]) are replaced by the excentrics, hence
[xi] by the angle [theta] through which the first excentric is turned, so
that y'_k = cos k[theta]. But kh = x and nh = [pi], n being the number of
springs s, and [pi] taking the place of c. This makes
k[theta] = (n/[pi])[theta].x.