ARTIFICIAL AND NATURAL FLIGHT. CHAPTER I. INTRODUCTORY. It has been my aim in preparing this little work for publication to give a description of my own experimental work, and explain the machinery and methods that have enabled me to arrive at certain conclusions regarding the problem of flight. The results of my experiments did not agree with the accepted mathematical formulæ of that time. I do not wish this little work to be considered as a mathematical text-book; I leave that part of the problem to others, confining myself altogether to data obtained by my own actual experiments and observations. During the last few years, a considerable number of text-books have been published. These have for the most part been prepared by professional mathematicians, who have led themselves to believe that all problems connected with mundane life are susceptible of solution by the use of mathematical formulæ, providing, of course, that the number of characters employed are numerous enough. When the Arabic alphabet used in the English language is not sufficient, they exhaust the Greek also, and it even appears that both of these have to be supplemented sometimes by the use of Chinese characters. As this latter supply is unlimited, it is evidently a move in the right direction. Quite true, many of the factors in the problems with which they have to deal are completely unknown and unknowable; still they do not hesitate to work out a complete solution without the aid of any experimental data at all. If the result of their calculations should not agree with facts, “bad luck to the facts.” Up to twenty years ago, Newton’s erroneous law as relates to atmospheric resistance was implicitly relied upon, and it was not the mathematician who detected its error, in fact, we have plenty of mathematicians to-day who can prove by formulæ that Newton’s law is absolutely correct and unassailable. It was an experimenter that detected the fault in Newton’s law. In one of the little mathematical treatises that I have before me, I find drawings of aeroplanes set at a high and impracticable angle with dotted lines showing the manner in which the writer thinks the air is deflected on coming in contact with them. The dotted lines show that the air which strikes the lower or front side of the aeroplane, instead of following the surface and being discharged at the lower or trailing edge, takes a totally different and opposite path, moving forward and over the top or forward edge, producing a large eddy of confused currents at the rear and top side of the aeroplane. It is very evident that the air never takes the erratic path shown in these drawings; moreover, the angle of the aeroplane is much greater than one would ever think of employing on an actual flying machine. Fully two pages of closely written mathematical formulæ follow, all based on this mistaken hypothesis. It is only too evident that mathematics of this kind can be of little use to the serious experimenter.