"Every body which is immersed in a fluid is acted upon by an upward force, exactly equal to the weight of the fluid displaced by the immersed body."
That is, a body will be at rest if immersed in a fluid of equal specific gravity or equal weight, volume for volume; if the body has less specific gravity than the fluid in which it is immersed it will rise; if it has a greater specific gravity it will sink. Therefore, if the total weight of a balloon is less than the weight of all the air it displaces it will rise in the air. It is, then, necessary to fill the balloon with some gas whose specific gravity is enough less than, that of the air to make the weight of the gas itself, the bags, and the attachments, less than the weight of the air displaced by the whole apparatus. The gases usually employed are hydrogen, coal gas, and hot air.
At atmospheric pressure and freezing temperature, the weight of a cubic foot of air is about .08 pound; the weight of a cubic foot of hydrogen is about .005 pound, under the same conditions. According to the law of Archimedes, a cubic foot of hydrogen would be acted upon by a force equal to the difference, or approximately .075 pound, tending to move it upwards. In the same way, a cubic foot of coal gas, which weighs .04 pound, would be acted upon by an upward force of .04 pound.
It is evident, then, that a considerable volume of gas is required to lift a balloon with its envelope, net, car, and other attachments.
Further, it requires almost twice as much coal gas as hydrogen, under the same conditions, for we have seen that the upward force on it is only half as great. The lifting power of hot air is less than one-eighth as great as that of hydrogen at the highest temperature that can possibly be used in a balloon.
Fig. 3. Montgolfier Balloon
The general type of lighter-than-air machines may be divided into aerostats (ordinary balloons, which are entirely dependent on wind currents for lateral movement, and which are often the chief features at country fairs) and dirigible balloons or aeronats (air swimmers). Dirigible balloons employ the gas bag for maintaining buoyancy, and have rudders to guide them and propellers to drive them forward through the air in much the same way that ships are driven through the water.
The First Balloon. For several years, Joseph and Steven Montgolfier had been experimenting with a view to constructing a balloon: in the first place by filling bags with steam; then by filling bags with smoke, and finally by filling bags with hydrogen. These attempts were all failures, for the steam rapidly condensed and the smoke and hydrogen leaked through the pores in the bags. They finally hit upon the idea of filling the bag with hot air, by means of a fire under its open mouth. Several balloons were burned up, but the next was always made larger, until, at their first public exhibition on June 5, 1783, the bag had become over 35 feet in diameter. On this occasion, it rose to a height of between 900 and 1,000 feet, but the hot air was gradually escaping, and at the end of ten minutes the balloon fell to the ground.
The Montgolfiers then went to Paris, where, after suffering the loss of a paper balloon by rain, they sent up a waterproofed linen one carrying a sheep, a duck, and a rooster in a basket. A rupture in the linen caused the three unwilling aeronauts to make a landing at the end of about ten minutes. The Montgolfiers received great honor, and small balloons of this type became a popular fad. One of these balloons is shown in Fig. 3, making an ascension.