What speed my "No. 6" made on those Mediterranean flights was not published at the time because I had not sought to calculate it closely. Fresh from the troubling time limit of the Deutsch prize competition I amused myself frankly with my air-ship, making observations of great value to myself, but not seeking to prove anything to anyone.

The speed problem is, doubtless, the first of all air-ship problems. Speed must always be the final test between rival air-ships, and until high speed shall be arrived at certain other problems of aerial navigation must remain in part unsolved. For example, take that of the air-ship's pitching (tangage). I think it quite likely that a critical point in speed will be found, beyond which, on each side, the pitching will be practically nil. When going slowly or at moderate speed I have experienced no pitching, which in an air-ship like my "No. 6" seems always to commence at 25 to 30 kilometres (15 to 18 miles) per hour through the air. Now, probably, when one passes this speed considerably—say at the rate of 50 kilometres (30 miles) per hour—all tangage or pitching will be found to cease again, as I myself experienced when flying homeward on the wind in the voyage last described.

Speed must always be the final test between rival air-ships, because, in itself, speed sums up all other air-ship qualities, including "stability." At Monaco, however, I had no rivals to compete with. Furthermore, my prime study and amusement there was the beautiful working of the maritime guide rope; and this guide rope, dragging through the water, must of necessity retard whatever speed I made. There could be no help for it. Such was the price I must pay for automatic equilibrium and vertical stability—in a word, easy navigation—so long as I remained the sole and solitary navigator of the air-ship.

Nor is it an easy task to calculate an air-ship's speed. On those flights up and down the Mediterranean coast the speed of my return to Monaco, wonderfully aided by the wind, could bear no relation to the speed out, retarded by the wind, and there was nothing to show that the force of the wind going and coming was constant. It is true that on those flights one of the difficulties standing in the way of such speed calculations—the "shoot the chutes" (montagnes Russes) of ever-varying altitude—was done away with by the operation of the maritime guide rope; but, on the other hand, as has been said, the dragging of the guide rope's weight through the water acted as a very effectual brake. As the speed of the air-ship is increased this brake-like action of the guide rope (like that of the resistance of the atmosphere itself) grows, not in proportion to the speed, but in proportion to the square of it.

On those flights along the Mediterranean coast the easy navigation afforded me by the maritime guide rope was purchased, as nearly as I could calculate, by the sacrifice of about 7 or 8 kilometres (4 or 5 miles) per hour of speed; but with or without maritime guide rope the speed calculation has its own almost insurmountable difficulties.

From Monte Carlo to Cap Martin at 10 o'clock of a given morning may be quite a different trip from Monte Carlo to Cap Martin at noon of the same day; while from Cap Martin to Monte Carlo, except in perfect calm, must always be a still different proposition. Nor can any accurate calculations be based on the markings of the anemometer, an instrument which I, nevertheless, carried. Out of simple curiosity I made note of its readings on several occasions during my trip of 12th February 1902. It seemed to be marking between 32 and 37 kilometres (20 and 23 miles) per hour; but the wind, complicated by side gusts, acting at the same time on the air-ship and the wings of the anemometer windmill—i.e. on two moving systems whose inertia cannot possibly be compared—would alone be sufficient to falsify the result.

When, therefore, I state that, according to my best judgment, the average of my speed through the air on those flights was between 30 and 35 kilometres (18 and 22 miles) per hour, it will be understood that it refers to speed through the air whether the air be still or moving and to speed retarded by the dragging of the maritime guide rope. Putting this adverse influence at the moderate figure of 7 kilometres (4½" miles) per hour my speed through the still or moving air would be between 37 and 42 kilometres (22 and 27 miles) per hour. Rather than spend time over illusory calculations on paper I have always preferred to go on materially improving my air-ships. Later, when they come in competition with the rivals which no one awaits more ardently than myself, all speed calculations made on paper and all disputes based on them must of necessity yield to the one sublime test of air-ship racing.

Where speed calculations have their real importance is in affording necessary data for the construction of new and more powerful air-ships. Thus the balloon of my racing "No. 7," whose motive power depends on two propellers each 5 metres (16½" feet) in diameter, and worked by a 60 horse-power motor with a water cooler, has its envelope made of two layers of the strongest French silk, four times varnished, capable of standing, under dynamometric test, a traction of 3000 kilogrammes (6600 pounds) for the linear metre (3·3 feet). I will now try to explain why the balloon envelope must be made so very much stronger as the speed of the air-ship is designed to be increased; and in so doing I shall have to reveal the unique and paradoxical danger that besets high-speed dirigibles, threatening them, not with beating their heads in against the outer atmosphere, but with blowing their tails out behind them.

Although the interior pressure in the balloons of my air-ships is very considerable, as balloons go, the spherical balloon, having a hole in its bottom, is under no such pressure: it is so little in comparison with the general pressure of the atmosphere, that we measure it, not by "atmospheres," but by centimetres or millimetres of water pressure—i.e. the pressure that will send a column of water up that distance in a tube. One "atmosphere" means one kilogramme of pressure to the square centimetre (15 lbs. to the square inch), and it is equivalent to about 10 metres of water pressure, or, more conveniently, 1000 centimetres of "water." Now, supposing the interior pressure in my slower "No. 6" to have been close up to 3 centimetres of water (it required that pressure to open its gas valves), it would have been equivalent to 1/333 of an atmosphere; and as one atmosphere is equivalent to a pressure of 1000 grammes (1 kilogramme) on one square centimetre the interior pressure of my "No. 6" would have been 1/333 of 1000 grammes, or 3 grammes. Therefore on one square metre (10,000 square centimetres) of the stem head of the balloon of my "No. 6" the interior pressure would have been 10,000 multiplied by 3, or 30,000 grammes i.e.—30 kilogrammes (66 lbs.).

How is this interior pressure maintained without being exceeded? Were the great exterior balloon filled with hydrogen and then sealed up with wax at each of its valves, the sun's heat might expand the hydrogen, make it exceed this pressure, and burst the balloon; or should the sealed balloon rise high, the decreasing pressure of the outer atmosphere might let its hydrogen expand, with the same result. The gas valves of the great balloon, therefore, must not be sealed; and, furthermore, they must always be very carefully made, so that they will open of their own accord at the required and calculated pressure.

This pressure (of 3 centimetres in the "No. 6"), it ought to be noted, is attained by the heating of the sun or by a rise in altitude only when the balloon is completely filled with gas: what may be called its working pressure—about one-fifth lower—is maintained by the rotary air pump. Worked continually by the motor, it pumps air continually into the smaller 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 speed tends to reduce strain, so that the faster the air-ship goes the less will it be liable to burst out 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 (22 to 27 miles) per hour without giving the slightest hint of strain. 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 from outside pressure, and with positive relief from interior 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 (25 miles) per hour, or 80 kilometres (50 miles).

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 continuous, 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. (See Fig. 12.)

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 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 definitely. It has two propellers, each 5 metres (16½" feet) 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 Clement motor will, if my expectations are fulfilled, give it a speed of between 70 and 80 kilometres (40 and 50 miles) 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 (30 miles) per hour such an air-ship will surely be able to go out daily during more than ten months in the twelve.