The ordinary paddles of a steamer impel a mass of water horizontally backward by impact alone, but screw propellers use reaction somewhat disguised, and only to a limited extent.  The full use and advantages of reaction for screw propellers were not generally known until after the publication of papers by the present writer in the “Proceedings” of the Institution of Naval Architects for 1867 and 1868, and more fully in the “Transactions” of the Society of Engineers for 1868.  Since that time, by the author of these investigations then described, by the English Admiralty, and by private firms, further experiments have been carried out, some on a considerable scale, and all corroborative of the results published in 1868.  But nothing further has been done in utilizing these discoveries until the recent exigencies of modern naval warfare have led foreign nations to place a high value upon speed.  Some makers of torpedo boats have thus been induced to slacken the trammels of an older theory and to apply a somewhat incomplete form of the author’s reaction propeller for gaining some portion of the notable performance of these hornets of the deep.  Just as in turbines a combination of impact and reaction produces the maximum practical result, so in screw propellers does a corresponding gain accompany the same construction.

[Illustration:  Fig. 1.]

[Illustration:  Fig. 2.]

Turbines.—­While studying those effects produced by jets of water impinging upon plain or concave surfaces corresponding to buckets of turbines, it simplifies matters to separate these results due to impact from others due to reaction.  And it will be well at the outset to draw a distinction between the nature of these two pressures, and to remind ourselves of the laws which lie at the root and govern the whole question under present consideration.  Water obeys the laws of gravity, exactly like every other body; and the velocity with which any quantity may be falling is an expression of the full amount of work it contains.  By a sufficiently accurate practical rule this velocity is eight times the square root of the head or vertical column measured in feet.  Velocity per second = 8 sqrt (head in feet), therefore, for a head of 100 ft. as an example, V = 8 sqrt (100) = 80 ft. per second.  The graphic method of showing velocities or pressures has many advantages, and is used in all the following diagrams.  Beginning with purely theoretical considerations, we must first recollect that there is no such thing as absolute motion.  All movements are relative to something else, and what we have to do with a stream of water in a turbine is to reduce its velocity relatively to the earth, quite a different thing to its velocity in relation to the turbine; for while the one may be zero, the other may be anything we please.  ABCD in Fig. 1 represents a parallelogram of velocities, wherein AC gives the direction of a jet of water starting at A, and arriving at C at the end of one second or