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 any other division of time. At a scale of 1/40 in. to 1 ft., AC represents 80 ft., the fall due to 100 ft. head, or at a scale of 1 in. to 1 ft., AC gives 2 ft., or the distance traveled by the same stream in 1/40 of a second. The velocity AC may be resolved into two others, namely, AB and AD, or BC, which are found to be 69.28 ft. and 40 ft. respectively, when the angle BAC—generally called x in treatises on turbines—is 30 deg. If, however, AC is taken at 2 ft., then A B will be found = 20.78 in., and BC = 12 in. for a time of 1/40 or 0.025 of a second. Supposing now a flat plate, BC = 12 in. wide move from DA to CB during 0.025 second, it will be readily seen that a drop of water starting from A will have arrived at C in 0.025 second, having been flowing along the surface BC from B to C without either friction or loss of velocity. If now, instead of a straight plate, BC, we substitute one having a concave surface, such as BK in Fig. 2, it will be found necessary to move it from A to L in 0.025 second, in order to allow a stream to arrive at C, that is K, without, in transit, friction or loss of velocity. This concave surface may represent one bucket of a turbine. Supposing now a resistance to be applied to that it can only move from A to B instead of to L. Then, as we have already resolved the velocity A C into AB and BC, so far as the former (AB) is concerned, no alteration occurs whether BK be straight or curved. But the other portion, BC, pressing vertically against the concave surface, BK, becomes gradually diminished in its velocity in relation to the earth, and produces and effect known as "reaction." A combined operation of impact and reaction occurs by further diminishing the distance which the bucket is allowed to travel, as, for examples, to EF. Here the jet is impelled against the lower edge of the bucket, B, and gives a pressure by its impact; then following the curve BK, with a diminishing velocity, it is finally discharged at K, retaining only sufficient movement to carry the water clear out of the machine. Thus far we have considered the movement of jets and buckets along AB as straight lines, but this can only occur, so far as buckets are concerned, when their radius in infinite. In practice these latter movements are always curves of more or less complicated form, which effect a considerable modification in the forms of buckets, etc., but not in the general principles, and it is the duty of the designer of any form of turbine to give this consideration its due importance. Having thus cleared away any ambiguity from the terms "impact," and "reaction," and shown how they can act independently or together, we shall be able to follow the course and behavior of streams in a turbine, and by treating their effects as arising from two separate causes, we shall be able to regard the problem without that inevitable confusion which arises when they are considered as acting conjointly. Turbines, though driven by vast volumes of water, are in reality impelled by countless isolated jets, or streams, all acting together, and a clear understanding of the behavior of any one of these facilitates and concludes a solution of the whole problem.

Experimental researches.—All experiments referred to in this paper were made by jets of water under an actual vertical head of 45 ft., but as the supply came through a considerable length of ½ in. bore lead piping, and many bends, a large and constant loss occurred through friction and bends, so that the actual working head was only known by measuring the velocity of discharge. This was easily done by allowing all the water to flow into a tank of known capacity. The stop cock had a clear circular passage through it, and two different jets were used. One oblong measured 0.5 in. by 0.15 in., giving an area of 0.075 square inch. The other jet was circular, and just so much larger than ¼ in. to be 0.05 of a square inch area, and the stream flowed with a velocity of 40 ft. per second, corresponding to a head of 25 ft. Either nozzle could be attached to the same universal joint, and directed at any desired inclination upon the horizontal surface of a special well-adjusted compound weighing machine, or into various bent tubes and other attachments, so that all pressures, whether vertical or horizontal, could be accurately ascertained and reduced to the unit, which was the quarter of an ounce. The vertical component p of any pressure P may be ascertained by the formula—

where alpha is the angle made by a jet against a surface; and in order to test the accuracy of the simple machinery employed for these researches, the oblong jet which gave 71 unit when impinging vertically upon a circular plate, was directed at 60 deg. and 45 deg. thereon, with results shown in Table I., and these, it will be observed, are sufficiently close to theory to warrant reliance being placed on data obtained from the simple weighing machinery used in the experiment.

In the first trial there was a distance of 1½ in. between the jet and point of its contact with the plate, while in the second trial this space was diminished to ½ in. It will be noticed that as this distance increases we have augmented pressures, and these are not due, as might be supposed, to increase of head, which is practically nothing, but they are due to the recoil of a portion of the stream, which occurs increasingly as it becomes more and more broken up. These alterations in pressure can only be eliminated