The change from my model is only a change in the framework made possible by dispensing with the boiler, water tank, and steam engine. In this little work, I have dealt at considerable length with air currents, the flight of birds, and the behaviour of kites, perhaps at the expense of some repetitions; as the resemblance between kite flying and the soaring of birds is similar in many respects, repetitions are necessary. To those who go to sea in ships, it is necessary to know something of the currents they are liable to encounter; if it be a sailing ship, certainly a knowledge of the air currents is of the greatest importance, and so it is with flying machines. If flights of any considerable distance are to be made, the machine is liable at any time to encounter very erratic air currents, and it has been my aim in discussing these three subjects—air currents, birds, and kites—to bring them before the would-be navigators of the air, in order that they may anticipate the difficulties they have to deal with and be ready to combat them. Then, again, there has been almost an infinite amount of discussion regarding the soaring of birds and the flying of kites. Many years ago, after reading numerous works on the subject of flight, I became a close observer myself, and always sought in my travels to learn as much as possible. I have attempted to discuss this subject in simple and easily understood language, and to present sufficient evidence to prevent the necessity of any further disputes. I do not regard what I have said as a theory, but simply as a plain statement of absolute and easily demonstrated facts. During the last few years, a considerable number of text-books and scientific treatises have been written on the subject of artificial flight, the most elaborate and by far the most reliable of these being the “Pocket-Book of Aeronautics,” by Herman W. L. Moedebeck, Major und Battaillonskommandeur im Badischen Fussartillerie Regiment No. 14; in collaboration with O. Chanute and others. Translated by W. Mansergh Varley, B.A., D.Sc., Ph.D., and published by Whittaker & Co. This work does not, however, confine itself altogether to flying machines, but has a great deal of information which is of little or no value to the builder of true flying machines; moreover, it is not simple enough to be readily understood by the majority of experimenters. In some other works which I have recently examined, I find a confusing mass of the most intricate mathematical calculations, abounding in an almost infinite number of characters, and extending over hundreds of pages, but on a close examination of some of the deductions arrived at, I find that a good many of the mathematical equations are based on a mistaken hypothesis, and the results arrived at are very wide of the truth. I have shown several diagrams which will explain what I mean. What is required by experimenters in flying machines—and there will soon be a great number of them—is a treatise which they can understand, and which requires no more delicate instruments than a carpenter’s 2-foot rule and a grocer’s scales. The calculations relating to the lift, drift, and the skin friction of an aeroplane are extremely simple, and it is quite possible to so place this matter that it can be understood by anyone who has the least smattering of mathematical knowledge. Mathematics of the higher order expressed in elaborate formulæ do very well in communications between college professors—that is, if they happen to be agreed. When, however, these calculations are so intricate as to require a clever mathematician a whole day to study out the meaning of a single page, and if when the riddle is solved, we find that these calculations are based on a fallacy, and the results in conflict with facts, it becomes quite evident to the actual experimenter that they are of little value. For many years, Newton’s law was implicitly relied upon. Chanute, after going over my experimental work, wrote that Newton’s law was out as 20 is to 1—that is, that an aeroplane would lift twenty times as much in practice as could be shown by the use of Newton’s formula. Some recent experiments, which I have made myself, at extremely high velocities and at a very low angle, seem to demonstrate that the error is nearer 100 to 1 than 20 to 1. It will, therefore, be seen how little this subject was understood until quite recently, and even now the mathematicians who write books and use such an immense amount of formulæ, do not agree by any means, as will be witnessed by the mass of conflicting controversy which has been appearing in Engineering during the last four months. When an aeroplane placed at a working angle of, say, 1 in 10 is driven through the air at a high velocity, it, of course, pushes the air beneath it downwards at one-tenth part of its forward velocity—that is, in moving 10 feet, it pushes the air down 1 foot. A good many mathematicians rely altogether upon the acceleration of the mass of air beneath the aeroplane which is accelerated by its march through the air, the value of this acceleration being in proportion to the square of the velocity which is imparted to it. Suppose now that the aeroplane is thin and well-made, that both top and bottom sides are equally smooth and perfect; not only does the air engaged by the under side shoot downwards, but the air also follows the exact contour of the top side, and is also shot downwards with the same mean velocity as that passing on the underneath side, so if we are going to consider the lifting effect of the aeroplane, we must not leave out of the equation, the air above the aeroplane, which has quite as much mass and the same acceleration imparted to it, as the air below the aeroplane. Even calculations made on this basis will not bring the lifting effect of an aeroplane up to what it actually does lift in practice; in fact, the few mathematicians who have made experiments themselves have referred to the actual lifting effect of aeroplanes placed at a low angle and travelling at a high velocity as being unaccountable. Only a few mathematicians appear to have a proper grasp of the subject. However, three could be pointed out who understand the subject thoroughly, but these are all mathematicians of the very highest order—Lord Kelvin, Lord Rayleigh, and Professor Langley. In placing before the public, the results of my experiments and the conclusions arrived at, it is necessary to show the apparatus which I employed, otherwise it might be inferred that my conclusions were guesswork, or mathematical calculations which might or might not be founded on a mistaken hypothesis; this is my excuse for showing my boiler and engine, my rotating arm, and my large machine. I do not anticipate that anyone will ever use a steam engine again, because any form of a boiler is heavy; moreover, the amount of fuel required is much greater than with an internal combustion engine, and certainly seven times as much water has to be dealt with. However, the description which I am giving of my apparatus will demonstrate that I had the instruments for doing the experimental work that I have described in this work. In the Appendix will be found a description of my machine, and some of my apparatus. The conclusions which I arrived at were written down at the time with a considerable degree of care, and are of interest because they show that, at that date, I had produced a machine that lifted considerably more than its own weight and had all of the essential elements, as far as superposed aeroplanes, fore and aft horizontal rudders, and screw propellers were concerned, common to all of the successful machines which have since been made. The fact that practically no essential departure has been made from my original lines, indicates to my mind that I had