364 
Proceedings of the Royal Society 
at A and B will increase. If the motion be sufficiently con- 
tinued, the greater angle A will become a right angle, and then 
B will have reached its maximum. Should the motion be still 
further continued, A becomes obtuse and B decreases ; till, when 
the rods have entirely closed, A becomes 180° and B becomes 
zero. Continuing the angular motion, A becomes a reverse angle, 
and B appears on the opposite side of AB. Thus the alternate 
increase and decrease of the smaller angle B resembles the changes 
of the angle NZA (fig. 1), when the motion is oscillatory. And 
at the same time the continual development of the angle at B 
Fig. 2. 
C 
A P B 
E 
C Q D 
Fig. 3. 
resembles the change of NZA when the heavy body over-passes 
the zenith point. The resemblance is a close one, for if we suppose 
CAB to increase with a velocity proportional to the distance PB, 
intercepted by the perpendicular CP, its variations are then 
exactly analogous to those of the angle NZA, when a heavy body 
revolving in a circle whose diameter is proportional to AC, has its 
velocity at the lower point equal to that obtained by falling 
through a distance proportional to CB. And similarly the varia- 
tions of the smaller angle B are analogous to the oscillations of a 
heavy body in another circle, the greatest height being to the 
whole diameter in the ratio of AC to CB. 
When AC is very small in comparison with CB, the maximum 
angle Bis also small; that is to say, the arrangementrepresents an 
oscillation in a small arc ; but when the two rods are nearly of 
equal lengths, as in the case of CE, ED (fig. 3), the maximum 
value of D approaches to a right angle, and the arrangement 
represents an oscillation extending to nearly the whole ciroum- 
