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22 into the small interior balloon. As much of this air as is needed to preserve the outer balloon's rigidity remains inside the little interior balloon ; but all the rest pushes its way out into the atmosphere again through its air-valve—which opens at a little less pressure than do the gas-valves.

Let us now return to the balloon of my "No. 6." The interior pressure on each square metre of its stem-head being continuously about 30 kilogrammes, the silk material composing it must be normally strong enough to stand it ; nevertheless it will be easy to see how it becomes more and more relieved of that interior pressure as the air-ship gets in motion and increases speed. Its striking against the atmosphere makes a counter-pressure against the outside of the stem-head. Up to 30 kilogrammes to the square metre, therefore, all increase in the air-ship's speeds tends to reduce strain—so that the faster the air-ship goes, the less will it be liable to burst its head!

How fast may the balloon be carried on by motor and propeller before its head-stem strikes the atmosphere hard enough to more than neutralise the interior pressure ? This, too, is a matter of calculation ; but, to spare the reader, I will content myself with pointing out that my flights over the Mediterranean proved that the balloon of my " No. 6" could safely stand a speed of 36 to 42 kilometres per hour without giving the slightest hint of strain ; but had I wanted an air-ship of the proportions of the " No. 6 " to go twice as fast, under the same conditions, its balloon must have been strong enough to stand four times its interior pressure of 3 centimetres of "water," because the resistance of the atmosphere grows, not in proportion to the speed, but in proportion to the square of the speed.

The balloon of my " No. 7" is not, of course, built in the precise proportions of that of my " No. 6" ; but I may mention that it has been tested to resist an interior pressure of much more than 12 centimetres of "water"—in fact, its gas-valves open at that pressure only. This means just four times the interior pressure of my "No. 6." Comparing the two balloons in a general way, it is obvious, therefore, that with no risk and, indeed, with positive relief from outside pressure on its stem, or head, the balloon of my "No. 7" may be driven twice as fast as my easy-going Mediterranean pace of 42 kilometres per hour—or 80 kilometres !

I say with relief from outside pressure on the balloon's stem, or head ; and this brings us to the unique and paradoxical weakness of the fast-going dirigible. Up to the point where the exterior shall equal the interior pressure, we have seen how every increase of speed actually guarantees safety to the stem of the balloon. Unhappily it does not remain true of the balloon's stern-head. On it the interior pressure is also continuons ; but speed cannot relieve it. On the contrary, the suction of the atmosphere behind the balloon as it speeds on increases also, almost in the same proportion as the pressure caused by driving the balloon against the atmosphere. And this suction, instead of operating to neutralise the interior pressure on the balloon's stern-head, increases the strain just that much, the pull being added to the push. Paradoxical as it may seem, therefore, the danger of the swift dirigible is to blow its tail out rather than its head in !

How is this danger to be met ? Obviously by strengthening the stern part of the balloon-envelope. We have seen that when the speed of my "No. 7" shall be just great enough to completely neutralise the interior pressure on its stem, or head, the strain on its stern-head will be practically doubled. For this reason I have doubled the balloon material at this point.

I have reason to be careful of the balloon of my "No. 7." In it the speed problem will be attacked definitively. It has two propellers, each 5 metres in diameter. One will push, as usual, from the stern, while the other will pull from the stem, as in my "No. 4." Its 60- horse-power Clément motor will—if my expectations are fulfilled—give it a speed of between 70 and 80 kilometres per hour. In a word, the speed of my "No. 7" will bring us very close to practical everyday aerial navigation ; for, as we seldom have a wind blowing as much, even, as 50 kilometres per hour, such an air-ship will surely be able to go out daily during more than ten months in the twelve.