| Wood expands | .0004 | of its length between 32° and 212° F. |
| Steel expands | .0011 | of its length between 32° and 212° F. |
| Lead expands | .0028 | of its length between 32° and 212° F. |
| Brass expands | .0020 | of its length between 32° and 212° F. |
| Zinc expands | .0028 | of its length between 32° and 212° F. |
| Tin expands | .0021 | of its length between 32° and 212° F. |
| Antimony expands | .0011 | of its length between 32° and 212° F. |
| Total length of pendulum to adjusting nut 46 inches. | ||
| Total length of steel to adjusting nut 2 inches. | ||
| Total length of wood to adjusting nut 44 inches. | ||
| .0011 × 2 = | .0022 | inch, expansion of our steel. |
| .0004 × 44 = | .0176 | inch, expansion of our wood. |
| .0198 | total expansion of rod. | |
We have 7 inches as half the diameter of our bob .0198 ÷ 7 = .0028, ²⁄₇, which we find from our tables is very close to the expansion of zinc, so we will make the bob of that metal. Now let us check back; the upward expansion of 7 inches of zinc equals .0028 × 7 = .0196 inch, as against .0198 inch downward expansion of the rod. This gives us a total difference of .0002 inch between 32° and 212° or a range of 180° F. This is a difference of .0001 inch for 90° of temperature and is closer than most pendulums ever get.
The above figures are for dry, clear white pine, well baked and shellacked, with steel of average expansion, and zinc of new metal, melted and cast without the admixtures of other metals or the formation of oxide. The presence of tin, lead, antimony and other admixtures in the zinc would of course change the results secured; so also will there be a slight difference in the expansion of the rod if other woods are used. Still the jeweler can from the above get a very close approximation.
Fig. 5. Zinc bob and wood rod to replace
imitation gridiron pendulum.
Such a bob, 14 inches diameter and 1.5 inches thick, alike on both sides, with an oval hole 1 × .5 inches through its center, [see Fig. 5], would weigh about 30 to 32 pounds, and would have to be hung from a cast iron bracket, [Fig. 6], bolted through the clock case to the wall behind it, so as to get a steady rate. It would be nearly constant, as the metal is spread out so as to be quickly affected by temperature; and the shape would hold it well in its plane of oscillation, if both sides were of exactly the same curvature, while the weight would overcome minor disturbances due to vibration of the building. It would require a little heavier suspension spring, in order to be isochronous in the long and short arcs and this thickening of the spring would need the addition of from one and a half to two pounds more of driving weight.
Fig. 6. Cast iron bracket for heavy pendulums and movements.