GEEK WARNING – the following post is not for the scientifically challenged !

I started cleaning the pendulum. The clock has a 66″ compensating pendulum. The “compensating” part refers to the fact the pendulum automatically adjusts for climate changes.

The challenge is that the pendulum expands and contracts as the air temperature increases and decreases. Thus, when the air temperature rises the pendulum becomes longer and the clock slows. When the temperature drops, everything is in reverse and the clock speeds up.

All substances of which pendulums can be made expand by heat, and consequently every pendulum naturally goes slower in hot weather than in cold; and though the lengthening of the rod is far too small to measure, except by most delicate experiments, it is enough to make a difference of a minute a week between moderate winter and summer heat (40? and 70?) with a common iron wire pendulum, and in five days with a brass one, and a minute in three weeks even with a wooden rod, which varies the least of all materials.

Material	Expansion	lbs/in3
Flint Glass	0.0048	0.1166
Platinum	0.0056	0.76
Steel Rod	0.0064	0.28
Cast Iron	0.0066	0.26
Iron Rod	0.0070	0.28
Brass	0.0100	0.30
Copper	0.0106	0.32
Silver	0.0115	0.38
Lead	0.0165	0.41
Zinc	0.0160	0.253
Mercury	0.1000	0.49

Let “l” (as usual) be the length from the top of the spring to the c.o.[center of oscillation]; “r” the length to the bottom of the zinc tube, which rests on the nut at the bottom of the rod; “z” the zinc tube to be found; “s” the iron tube, which may or may not = “z”, as just now explained; “c” the height from the bottom to the c.o.

Then for a steel rod, and a lead bob resting on the bottom, we must have

• .016z + .0165c = .0064r + .007s

But now s = z, assuming all the bottoms to coincide, as they always do nearly; and we know by experience c to be about 4?5 in. for a 9-in. bob, and r about 44 in a 1-sec. pendulum, and we may introduce them at once, bearing in mind that the moment you translate one algebraic letter into inches all the rest become numbers of inches only. Then transposing all the unknown and known terms to opposite sides, equation A becomes

• (.016 ? .007)z = .2816 ? .0742 = .2074

which gives z = 23; but it is safer to begin with the tubes a little longer, in case the compensation is not found quite enough, as they are easy to shorten, but impossible to lengthen.

When the bob is fixed, or may be considered fixed, at its c.o., the equations will be, first, for a steel rod and lead bob fixed at its middle,

• .016z = .0064r + .007s = .0064r + .007(s ? c), . . .B

and for iron rod and bob,

• .016z = .007(r + 2 + c). . . .C

Rate (sec)	“l”	“r”	“z”	Bob	Weight (lbs)
1.25	61	68.5	48.5	14×8	200
1.5	88	98	68	15×9	300
1.5	88	96.5	61	14×8 (lead)	300
2.0	156.5	173	125	20×12	700

Source: “A Rudimentary Treatis of Clocks, Watches and Bells” by Edmund Beckett, 1903

If you want the full story, I strongly recommend Beckett’s book. If freely available as an ebook.

If you are still with me, the pendulum for my clock has a rate of 1-1/4 seconds. It is made with a 3/8″ center rod of steel, inside a zinc tube 47-3/4″ long, which is inside a steal outer cylinder.The pendulum bob is approximately 100 lbs and rests on a collar at the bottom of the outer most tube.

The graphic depicts the zinc tube in red. Thus, the center rod “hangs” from the clock frame. The zinc tube rests on a flange at the end of the rod. The outer steel tube rests on the top of the zinc tube. It has a cap at the top small enough for the rod to pass through but holds the zinc tube. The pendulum box rests on a flange at the bottom of the outer tube.

Thus the stress travels from the bob up the outer tube which rests on the zinc tube – so the stress pressing down through the zinc tube. The zinc tube rests on a flange at the bottom of the center steel rod so now the stress travels up the steel rod to the pendulum mounting point.

You can picture, as the temperature increases, the center steel rod and the steel outer tube increase “downward” but the zinc tube is increasing “upward”. These expansions cancel each other out !

Aren’t you glad you asked what a “compensating pendulum” is ?!