The reader is reminded that these are simply deductions from the equations given in “Aerodynamics,” and that these deductions have not been verified by direct trial, such as would show that no new conditions have in fact been introduced in this new application. While, however, these deductions cannot convey any confidence beyond what is warranted by the original experiments, in their general trustworthiness as working formulæ at this stage of the investigations, we may, I think, feel confidence. I may, in view of its importance, repeat my remark that the relation of area and weight which obtain in practice, will depend upon yet other than these theoretical considerations, for, as the flight of the free aerodrome cannot be expected to be exactly horizontal nor maintained at any constant small angle, the [p044] data of “Aerodynamics” (obtained in constrained horizontal flight with the whirling-table) are here insufficient. They are insufficient also because these values are obtained with small rigid planes, while the surfaces we are now to use cannot be made rigid under the necessary requirements of weight, without the use of guy wires and other adjuncts which introduce head resistance. Against all these unfavorable conditions we have the favoring one that, other things being equal, somewhat more efficiency can be obtained with suitable curved surfaces than with planes.[22] I have made numerous experiments with curves of various forms upon the whirling-table, and constructed many such supporting surfaces, some of which have been tested in actual flight. It might be expected that fuller results from these experiments should be given than those now presented here, but I am not yet prepared to offer any more detailed evidence at present for the performance of curved surfaces than will be found in Part III.[23] I do not question that curves are in some degree more efficient, but the extreme increase of efficiency in curves over planes understood to be asserted by Lilienthal and by Wellner, appears to have been associated either with some imperfect enunciation of conditions which gave little more than an apparent advantage, or with conditions nearly impossible for us to obtain in actual flight. All these circumstances considered, we may anticipate that the power required (or the proportion of supporting area to weight) will be very much greater in actual than in theoretical (that is, in constrained horizontal) flight, and the early experiments with rubber-driven models were in fact successful only when there were from three to four feet of sustaining surface to a pound of weight. When such a relatively large area is sought in a large aerodrome, the construction of light, yet rigid, supporting surfaces becomes a nearly insuperable difficulty, and this must be remembered as consequently affecting the question of the construction of boiler, engines and hulls, whose weight cannot be increased without increasing the wing area. [p045]