The general theory of their action may be explained in the following propositions:—
1. The spouting force of water is theoretically equal to its gravity.
2. The percussive force of spouting water can be fully utilised if its motion is altogether arrested by the vanes of a wheel.
3. The force of the water is greatest by its striking against planes at right angles to its course.
4. Any force resulting from water rebounding from the vanes parallel to their face, or at any angle not reverse to the motion of the wheel, is lost.
5. This rebounding action becomes less as the columns of water projected upon the wheel are increased in number and diminished in size.
6. To meet the conditions of rotation in the wheel, and to facilitate the escape of the water without dragging, after it has expended its force upon the vanes, the reversed curves of the turbine is the best-known arrangement.
It is, of course, very difficult to deal with so complex a subject as the present one with words alone, and the reader is recommended to examine drawings, or, what is better, water-wheels themselves, keeping the above propositions in view.
Modern turbine wheels have been the subject of the most careful investigation by able engineers, and there is no lack of mathematical data to be referred to and studied after the general principles are understood. The subject, as said, is one of great complicity if followed to detail, and perhaps less useful to a mechanical engineer who does not intend to confine his practice to water-wheels, than other subjects that may be studied with greater advantage. The subject of water-wheels may, indeed, be called an exhausted one that can promise but little return for labour spent upon it—with a view to improvements, at least. The efforts of the ablest hydraulic engineers have not added much to the percentage of useful effect realised by turbine wheels during many years past.