of Edinburgh , Session 1866-67. 
67 
3. On Compensation Pendulums of two Pieces. By 
Edward Sang, Esq. 
Three or four years ago, wishing to make some experiments on 
time-keepers, and desiring for that purpose to have a compensa- 
tion pendulum fitted to my clock, I turned my attention to pen- 
dulums composed of two pieces, having different rates of expan- 
sion. 
Such compensation pendulums are now pretty common ; the 
idea which has led to their construction being this, — that if the 
pendulum rod be made of material having a very small rate of 
expansion, and if the bob or weight be of a substance much more 
expansive, then the upward expansion of the one may be made to 
compensate for the downward expansion of the other, and so the 
going of the clock may remain unaffected by changes of tempera- 
ture. 
On designing the arrangement, and on proceeding to make the 
calculation, according to the received expansions of deal and lead, 
I was much surprised to find the solution of the resulting equation 
to be impossible ; and the surprise was the greater, because I had 
understood that of clocks constructed with such pendulums, the 
compensation had been verified by actual observations. There 
is not sufficient disparity between the expansibilities of deal and 
lead. 
A very slight glance at the subject is sufficient to show, 
that if it be impossible to construct such a pendulum with 
a deal rod of great tenuity, and with an enclosing cylinder 
of lead also of inappreciable diameter, it must be im- 
possible to make one with the parts having appreciable 
diameters ; since the lateral expansion of the parts tends 
to augment the length of the corresponding simple 
pendulum. 
Let us then suppose an exceedingly thin rod AB, of some 
slightly expansive substance, suspended by the end A, and 
having on the lower end B a small projection or seat, on 
which the end of a cylinder BC of heavy and expansive metal 
rests. Then neglecting the weight of the inner rod, and the radius 
Fig. 1. 
Al 
Bill 
