Large balloons, however, are structurally weak: and more is lost by the extra bracing necessary than is gained by reduction of head end resistance. It is probable that the Zeppelin represents the limit of progress in this direction; and even in that balloon, if it had not been that the adoption of a rigid type necessitated great structural strength, it is doubtful if as great a length would have been fixed upon, in proportion to the diameter. The frictional resistance of the air gliding along the surface of the envelope, moreover, invalidates any too arbitrary conclusions. This, as in the aeroplane, varies nearly as the square of the velocity, and is usually considerably greater than the direct head end resistance. Should the steering gear break, however, and the wind strike the _side_ of the balloon, the pressure of the wind against this greatly increased area would absolutely deprive it of dirigibility. A stationary, drifting, or "sailing" balloon may as well have the spherical as well as any other shape: it makes the wind a friend instead of a foe and requires nothing in the way of control other than regulation of altitude. Independent Speed and Time Table The air pressure, direct and frictional resistances, and power depend upon the _relative_ velocity of flying machine and air. It is this relative velocity, not the velocity of the balloon as compared with a point on the earth's surface, that marks the limit of progression. Hence the speed of the wind is an overwhelming factor to be reckoned with in developing an aerial time table. If we wish to travel east at an effective speed of thirty miles per hour, while the wind is blowing due west at a speed of ten miles, our machine must have an independent speed of forty miles. On the other hand, if we wish to travel west, an independent speed of twenty miles per hour will answer. [Illustration: THE SANTOS-DUMONT DIRIGIBLE NO. 2 (1909)] Again, if the wind is blowing north at thirty miles per hour, and the minimum (relative) velocity at which an aeroplane will sustain its load is forty miles per hour, we cannot progress northward any more slowly than at seventy miles' speed. And we have this peculiar condition of things: suppose the wind to be blowing north at fifty miles per hour. The aeroplane designed for a forty mile speed may then face this wind and sustain itself while actually moving backward at an absolute speed (as seen from the earth) of ten miles per hour.