It is inevitable that in so complex a study some repetition should present itself, especially in the narrative form chosen as the best method of presenting the subject to the reader. Each of these chapters, then, will contain its own historical account of its own theme, so that each subject can be pursued continuously in the order of its actual development, while, since they were all interdependent and were actually going on simultaneously, the order of dates which is followed in each chapter will be a simple and sufficient method of reference from one to the other. EXPERIMENTS WITH SMALL MODELS In order to understand how the need arises for such experiments in fixing conditions which it might appear were already determined in the work “Experiments in Aerodynamics,”[8] it is to be constantly borne in mind, as a consideration of the first importance, that the latter experiments, being conducted with the whirling-table, force the model to move in horizontal flight and at a constant angle. Now these are ideal conditions, as they avoid such practical difficulties as maintaining equilibrium and horizontality, and for this reason alone give results more favorable than are to be expected in free flight. Besides this, the values given in “Aerodynamics” were obtained with rigid surfaces, and these surfaces themselves were small and therefore manageable, while larger surfaces, such as are used in actual flight, would need to be stiffened by guys and like means, which offer resistance to the air and still further reduce the results obtained. It is, therefore, fairly certain, that nothing like the lift of 200 pounds to the horse-power for a rate of 40 miles an hour,[9] obtained under these ideal conditions with the whirling-table, will be obtained in actual flight, at least with plane wings. The data in “Aerodynamics” were, then, insufficient to determine the conditions of free flight, not alone because the apparatus compels the planes to move in horizontal flight, but because other ideally perfect conditions are obtained by surfaces rigidly attached to the whirling-table so as to present an angle to the wind of advance which is invariable during the course of the experiment, whereas the surfaces employed in actual flight may evidently change this angle and cause [p007] the aerodrome to move upward or downward, and thus depart from horizontal flight so widely as to bring prompt destruction.