1905 - 6 .] A New Form of Harmonic Eynthetiser. 217 
then the greatest deviation should be minimised, because of the 
chance that the measurements are being made just at the placer 
where the greatest deviation occurs. Hence in the case of any 
given instrument it is desirable to know the value both of its 
greatest deviation and also of its average deviation. 
§ 7. Expression for the Greatest Deviation of the Pen. 
In fig. 6 let S be an eccentric pin fixed in the rotating wheel 
A and let SRQ be a perfectly flexible wire turning abruptly 
round an infinitely thin pin R, its end Q being constrained to- 
0 
Fig. 6. 
For the sake of clearness , in each of the above figures the size of the wheel 
has been greatly exaggerated relative to the total height. For the 
same reason , in fig. 7 the three pulleys are slioivn without flanges. 
move in the horizontal line RQ. If Q have a sufficient force 
applied to it to keep the wire always taut, then as the wheel 
revolves, Q will describe approximately the S.H.M. •which i& 
produced by resolving the circular motion of the pin S in a 
vertical direction. 
Calling e the deviation at any time t ( i.e . the distance of the 
actual position of Q from its proper position at any time t), and 
writing for shortness RO = Z and OS = r, we have, 
e = RS - RM = + r 2 - 2 Ir cos t) -l + r cos t . (3) 
de lr sin t ^ . 
dt J(l 2 + ?- 2 — 2/r cos t) 1 Sm 
