*Air Resistance vs. Speed.* Unless a voyage is to be governed in its direction entirely by the wind, the dirigible must possess a means of moving contrary to the latter. The moment this is attempted, resistance is encountered, and it is this resistance of the air that is responsible for the chief difficulties in the design of the dirigible. To drive it against the wind, it must have power; to support the weight of the motor necessary, the size of the gas bag must be increased. But with the increase in size, the amount of resistance is greatly multiplied and the power to force it through the air must be increased correspondingly. The law is approximately as follows: _Where the surface moves in a line perpendicular to its plane, the resistance is proportional to the extent of the surface, to the square of the speed with which the surface is moved through the air, and to a coefficient, the mean value of which is 0.125._ This coefficient is a doubtful factor, the figure given having been worked out years ago in connection with the propulsion of sailing vessels. Its value varies according to later experimenters between .08 and .16, the mean of the more recent investigations of Renard, Eiffel, and others who have devoted considerable study to the matter, being .08. This is dwelt upon more in detail under "Aerodynamics" and it will be noted that the values of the coefficient _K_, given here, do not agree with those stated in that article. They serve, however, to illustrate the principles in question. In accordance with this law, doubling the speed means quadrupling the resistance of the air. For instance, a surface of 16 square feet moving directly against the air at a speed of 10 feet per second will encounter a resistance of 16 X 100 (square of the speed) X 0.125 = 200 pounds pressure. Doubling the speed, thus bringing it up to 20 feet per second, would give the equation 16 X 400 X 0.125 = 800 pounds pressure, or with the more recent value of the coefficient of .08, 512 pounds pressure. The first consideration is accordingly to reduce the amount of surface moving at right angles. The resistance of a surface having tapering sides which cut through or divide the molecules of air instead of allowing them to impinge directly upon it, is greatly diminished; hence, Meusnier’s principle of elongation. If we take the same panel presenting 16 square feet of surface and build out on it a hemisphere, its resistance at a speed of 10 feet per second will be exactly half, or a pressure of 100 pounds. By further modifying this so as to represent a sharp point, or acute-angled cone, it will be 38 pounds. There could accordingly be no question of attempting to propel a spherical balloon. [Illustration: Fig. 6. Giffard Dirigible]