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.