First, that there is a constant interchange of air taking place, the cold air descending, spreading itself out over the surface of the earth, becoming warm, and ascending in other places. Second, that the centres of the two columns are generally separated from each other by a distance which may be from 500 feet to 20 miles. Third, that the centres of greatest action are not in spots, but in lines which may be approximately straight, but sometimes abound in many sinuosities. Fourth, that this action is constantly taking place over both the sea and the land; that the soaring of birds, the phenomenon which has heretofore been so little understood, may be accounted for on the hypothesis that the bird seeks out an ascending column of air, and while sustaining itself at the same height in the air, without any muscular exertion, it is in reality falling at a considerable velocity through the air that surrounds it. It has been supposed by some scientists that birds may take advantage of some vibratory or rolling action of the air. I find, however, from careful observation and experiment, that the motion of the wind is comparatively steady, and that the short vibratory or rolling action is always very near to the earth and is produced by the air flowing over hills, high buildings, trees, etc. Tools and instruments used by mechanicians are very often made of the material most used in their profession; for instance, a blacksmith’s tools are generally of iron, a carpenter’s tools largely of wood, and a glass-blower uses many things made of glass, and so on. Mathematicians are no exception to this general rule, and seem to imagine that everything can be accomplished by pure mathematical formulæ. It appears that Prof. Langley was at times considerably puzzled by the extraordinary behaviour of birds, and was led to believe that they took advantage of some vibratory or oscillating movement of the air; he called it “the internal work of the air.” I have been very much amused in a recent mathematical work that I have read, in which the writer seeks to solve all questions by pure mathematics. In this case, notwithstanding that all of the factors are unknown and unknowable, still, with the use of about two pages of closely written algebraic formulæ, he appears to have solved the whole question. Just how he arrived at it, however, is more than I am able to understand. If a kite is flown only a few feet above the ground, it will be found that the current of air is very unsteady. If it is allowed to mount to 500 feet the unsteadiness nearly all disappears, while if it is allowed to mount further to a height of 1,500 or 2,000 feet, the pull on the cord is almost constant, and, if the kite is well made, it remains practically stationary in the air.