[Illustration: One of the earliest attempts to steer a spherical balloon by retarding its speed with the drag-rope, and adjusting the sail to the passing wind.] A cubic foot of hydrogen weighs but 0.0056 lbs., and it will therefore be pushed upward in air by the difference in weight, or 0.0751 lbs. per cubic foot. A cubic foot of coal gas weighs about 0.0400 lbs., and is crowded upward in air with a force of 0.0407 lbs. [Illustration: Apparatus to illustrate the principle of Archimedes. At the left, the small solid glass ball and large hollow glass sphere are balanced in the free air. When the balance is moved under the bell-glass of the air pump (at the right), and the air exhausted, the large sphere drops, showing that its previous balance was due to the upward pressure of the air, greater because of its larger bulk.] It is readily seen that a very large bulk of hydrogen must be used if any considerable weight is to be lifted. For to the weight of the gas must be added the weight of the containing bag, the car, and the network supporting it, the ballast, instruments, and passengers, and there must still be enough more to afford elevating power sufficient to raise the entire load to the desired level. Let us assume that we have a balloon with a volume of 20,000 cubic feet, which weighs with its appurtenances 500 pounds. The hydrogen it would contain would weigh about 112 pounds, and the weight of the air it would displace would be about 1,620 pounds. The total available lifting power would be about 1,000 pounds. If a long-distance journey is to be undertaken at a comparatively low level, this will be sufficient to carry the necessary ballast, and a few passengers. If, however, it is intended to rise to a great height, the problem is different. The weight of the air, and consequently its lifting pressure, decreases as we go upwards. If the balloon has not been entirely filled, the gas will expand as the pressure is reduced in the higher altitude. This has the effect of carrying the balloon higher. Heating of the contained gas by the sun will also cause a rise. On the other hand, the diffusion of the gas through the envelope into the air, and the penetration of air into the gas bag will produce a mixture heavier than hydrogen, and will cause the balloon to descend. The extreme cold of the upper air has the same effect, as it tends to condense to a smaller bulk the gas in the balloon. To check a descent the load carried by the gas must be lightened by throwing out some of the ballast, which is carried simply for this purpose. Finally a level is reached where equilibrium is established, and above which it is impossible to rise.