12. for the lowest = p (1 + 1·72 m6);
13. the counterweight = π x2 (p (1 + 2m) - 56 n12);
14. the weight of the equalizing chain = 112800 p π m x2.
For example, let the diameter of the gas-holder be 30 feet, the height 15 (the contents in cubic feet will be 10,597), p = 4 pounds; then the counterweight for a height of an inch and a half of water pressure = 3532 pounds; the weight of the chain for a length of 15 feet = 395 pounds. Were no counterweight employed, so that the gas-holder pressed with its whole weight upon the gas, then the height of the equivalent column of water in its highest position = 2·56 inches; and in its lowest, 2·33. The counterweight may hence be lessened at pleasure, if the height of the pressing water-column n be increased. The weight of the equalising or compensating portion of the chain remains the same. When n = 2 inches, for instance, the counterweight = 1886 pounds.
The velocity with which the gas passes along the mains for supplying the various jets of light, may be further regulated by opening the main-cock or slide-valve in a greater or less degree.
Gasometers whose height is greater than their semi-diameter, are not only more costly in the construction, but require heavier counterweights and equilibration chains.
The above estimate is made on the supposition of the gas in the gas-holder being of the same specific gravity as the atmospherical air, which would be nearly true with regard to oil gas under the ordinary pressure. But coal gas, whose specific gravity may be taken on an average at about 0·5, exercises a buoyancy upon the top of the gas-holder, which of course diminishes its absolute weight. Supposing the cubic foot of gas to be = 0·0364 pounds, the buoyancy will be = 0·0364 π x3 pounds; a quantity which deserves to be taken into account for large gasometers. Hence,
15. the weight of the gas-holder in its highest position = 3 p π x2 - 0·1143 x3;
16. the counterweight = π x2 (3 p - 56 n12) - 0·1143 x2;
17. The weight of the chain for the length x, = 112800 p π x2 0·1143 x32;