1. The object of this paper is to explain the principles upon which the flapping flight of birds depend and to show how the velocities, power expended and gliding angles can be approximately calculated. The birds are considered to be flying on a horizontal course with constant velocity. The calculations have been made for five birds, the Teal, the Grouse, the Common Swift, the Starling and the Stork, but the formulae given can of course be used for any bird.

2. The results obtained seem to show that:—

1st.—As regards velocities, the very high speeds given by some writers are by no means so impossible as is generally supposed.

2nd.—The power expended at these high speeds is much less than the estimates usually made.