It seems hardly necessary in this day and generation to explain that a balloon rises because it is lighter than the air it displaces, but it does seem astonishing that a balloon weighing several tons may yet be lighter than an equal volume of air. We do not ordinarily think of air as having any weight. We know that the ocean of air bears on the earth with a pressure of about 14½ pounds per square inch, or about a ton per square foot at sea level. This amounts to 28 millions tons per square mile and, when we multiply this figure by the number of square miles of surface in the total area of the earth, we find that the whole ocean of air has a weight of 5,500,000,000,000,000 tons--a figure which is far beyond our conception, but it does impress us with the fact that air is a ponderable substance. Of course, the atmosphere that exerts a pressure of 14½ pounds per square inch is scores of miles deep, but even a small quantity of air has appreciable weight. If weighed in a vacuum a cubic foot of air would tip the scales at 1¼ ounces, and 100 cubic feet would weigh close to 8 pounds. The air in an empty room 10 feet square and with a 10-foot ceiling weighs nearly 80 pounds at a temperature of 32 degrees Fahrenheit. In other words, if we had a box measuring 10 feet on each side and weighing less than 80 pounds in a vacuum it would float in the atmosphere when the thermometer was down to the freezing point, provided there was no air in the box to weigh it down. Vacuum balloons were proposed long before the time of the Montgolfier, but the problem was to construct a vessel strong enough to resist the crushing pressure of the atmosphere. The best bracing for the walls of the vessel is some gas dense enough to exert a pressure equal to that of the atmosphere but whose weight is less than that of the air. The weight of the vessel must then not exceed the difference between the weight of the gas and an equal volume of air. The Montgolfier brothers used heated air to keep their box or envelope distended. Air expanded by heat is lighter than cold air. However, it does not make a very good filler because 1,000 cubic feet of air heated to 212 degrees Fahrenheit weighs 59 pounds, leaving only 21 pounds on a freezing cold day for the absolute weight of our 1,000-cubic-foot box. Coal gas, on the other hand, weighs about 40 pounds per 1,000 cubic feet at 32 degrees Fahrenheit, while the same volume of hydrogen weighs only 5½ pounds. If coal gas were used to brace our box against the pressure of the air we should have a surplus of about 40 pounds for the weight of the box, while hydrogen would allow us 74½ pounds. Of course, the weight of a volume of gas depends upon its density. No matter how small a weight of gas we placed in the box it would fill the box completely, but when we speak of a 1,000 cubic feet of gas or hydrogen we mean a volume sufficiently dense to bear against the container with the same pressure that the atmosphere presses outside; _i.