214 Proceedings of Royal Society of Edinburgh. [sess. 
the device. If in making a change in the amplitude by this 
method it were arranged that the phase of one of the S.H.Ms. 
should be increased just as much as the phase of the other was 
diminished, then the periodic time would remain always 
invariable, for in that case 
y = cos (t + a) + J cos ( t - a), 
y = cos a . cos if. ..... (2) 
Now if the side wheels were each to he driven from the crown 
wheel, the latter being driven from the motor belt, then on moving 
the axle through an angle a each of the side wheels would he 
rotated through a ; and as these latter rotate in opposite directions, 
this means that one of them would have its phase increased by a, 
and the other its phase diminished by a. An arrangement of 
weighted jockey pulleys would take up the slack of the motor belt 
when the crown-wheel axle was shifted ; and it should he arranged 
to do so on both the advancing and retreating sides of the belt 
equally, as otherwise the crown wheel would on these occasions 
change its phase relative to the rest of the machine, which of 
course is inadmissible. 
§ 4. Mechanism connected icith the Pen and Paper 
(see Plate, fig. 2). 
The paper used is obtained in long rolls, and is 4 inches wide. 
In the instrument the roll turns loosely on a fixed upright pin, and 
the paper is allowed to unwind of itself. First of all it passes round 
an upright revolving drum driven by a belt from a “stepped” pulley 
on the machine. Two rubber-shod wheels press the paper band 
against the drum and ensure its gripping the latter. The electric 
driving motor runs at a greater or less speed from instant to instant 
according to the amount of work it is doing, and therefore it is 
necessary that the motion of the hand of paper should he produced, 
not by an independent clock-work arrangement or like device, but 
by something connected with the general mechanism, so as to vary 
similarly in speed. The rate of the drum relative to the other 
mechanism may be varied by using the several steps of the pulley, 
that is to say, the horizontal scale of the trace may be altered at 
will. The vertically moving pen is so placed that it writes on the 
paper soon after it leaves the winding drum, and the strip then 
