260 
If to one of these screens a pencil be attached it will trace 
out on the other screen the curve 
x= acos (Ft+a)—beos (+48), 
Ty T. 
y= asin (= t+ a) —bsin( 248). 
Ty T. 
The constants in this can be arranged at pleasure as in the 
former curve. 
It is manifest that ifa=6 and t,=7, the curve is reduced 
to a point, and the. corresponding vibration to rest, ze. the 
composition of the two motions of the paper and pencil pro- 
duce rest. 
This may be taken as an example of interference. 
The pencil and every point in the paper are describing the 
same circle, so that there is no relative motion, and the pencil 
does not travel over the paper. 
The above curve is the epitrochoid, which includes the 
epicycle as a particular case. By crossing the band we make 
T, negative, and obtain the equation to the hypotrochoid in- 
cluding the hypocycloid as a particular case. 
In this case the curve cannot be reduced to a point, but x 
may be equal to zero during the motion, or y may be, 2. ¢. we 
may reduce the vibration to either one of two straight lines at 
right angles to each other. 
Prof. CAYLEY mentioned a machine by M. Perigal for de- 
scribing curves in a somewhat similar manner. Dr Hubert 
Airy had drawn similar curves with a pendulum. 
Mr GLAISHER said that the above machine, exhibited in 
1848 at the Royal Society, drew curves of more complexity 
than that of Mr Ellis. He described the machine and gave a 
brief sketch of its origin. 
