212 



fall established immediately below a bridge about 100 feet from 

 the turbine. This process gives very precise results, if the 

 necessary precautions be taken. The formula for the number 

 of cubic feet passed in a second is Q = CxZxfl^|% when C 

 is a coefficient varying from 3-550 to 3-206, according to the 

 ratio of the overfall's width to the channel in which it is 

 placed. The first belongs to the case when they are equal, 

 the second when that ratio does not exceed I to 3. L is the 

 breadth of the overfall in feet, and H ihe depth of the water 

 in it. This should be measured so far behind it as to be 

 exempt from the curvature assumed by the surface as the 

 water rushes towards the aperture. The measures were taken, 

 for convenience, at the overfall itself, and it was found by trial 

 that they require to be multiplied by 1*111, in the circum- 

 stances of this overfall, to reduce them to those due to the un- 

 disturbed surface. This formula, however, assumes that the 

 water-way above is so large, that the velocity of arrival at the 

 overfall is insensible. If not, the result must be multiplied by 



/ 0-I395xz<-\ 

 V ( 1 + — -jj ) ; u being this velocity, which Dr. Ro- 

 binson obtained by dividing the approximate quantity of water 

 given by the formula, by the water-way of the channel. This 

 last was found, by a careful section, to be 12- 18 feet + | of a 

 foot for every inch of water in the overfall. The results ob- 

 tained are, he believes, quite as exact as direct measurement 

 could afford. The fall was ascertained by measuring, at the 

 beginning and end of each experiment, the distance of the 

 upper surface of the water below a point fourteen feet above 

 the top of the turbine, and also the depth of water over that 

 top (the wheel being always submerged). The power of the 

 fall is expressed in horse power, whose unit is 33,000. 



Tlie resistance in ordinary work is, first, the friction of 

 the machinery, and secondly, the weight of the beetles ; these 

 he at first thought could easily be valued, and thus give a 

 measure of the efficiency of the machine. As, however, the 



