ON THE GAUGING OF WATER BY TRIANGULAR NOTCHES. 155 



Each barrel had a valve in the bottom, covering an aperture six inches 

 square, and the valve could be opened at pleasure, and was capable of 

 emptying the barrel very speedily. The capacity of the two barrels jointly 

 was about 230 gallons, and. their content up to marks fixed near the top for 

 the purpose of the experiments was accurately ascertained by gaugings 

 repeated several times with two- or four-gallon measures with narrow necks. 



By tilting the small trough so as to deliver the water alternately into the 

 one barrel and the other, and emptying each barrel by its valve while the other 

 was filling, the process of measuring the flowing water could be accurately 

 carried on for as long time as might be desired. With this apparatus, quan- 

 tities of water up to about 38 cubic feet per minute could be measured with 

 very satisfactory accuracy. 



The experiments of which I have now to report the results were made on 

 two widths of notches in vertical plane surfaces. The notches were accu- 

 rately formed in thin sheet iron, and were fixed so as to present next the 

 water in the pond a plane surface, continuous with that of the weir-board. 



The one notch was right-angled, with its sides sloping at 45° with the 

 horizon, so that its horizontal width was twice its depth. The other notch 

 had its sides each sloping two horizontal to one vertical, so that its horizontal 

 width was four times its depth. 



In each case experiments were made both on the simple notch without a 

 floor, and on the same notch with a level floor starting from its vertex, and 

 extending for a considerable distance both up stream and laterally. The 

 floor extended about 2 feet on each side of the centre of the notch, and about 

 2g feet in the direction up stream, and this size was sufficient to allow the 

 water to enter on it with only a very slow motion — so slow as to be quite 

 unimportant. The height of the water surface above the vertex of the 

 notch was measured by the sliding hook at a place outside the floor, where 

 the water of the pond was deep and still. 



The principal results of the experiments on the flow of the water in the 

 right-angled notch without floor are briefly given in the annexed table, the 



quantity of water given in column 2 for each height of 2, 3, 4, 5, 6, and 7 

 inches being the average obtained from numerous experiments comprised in 

 two series, one made in 1860, and the other made in 1861, as a check on the 

 former set, and with a view to the attainment of greater certainty on one or 

 two points of slight doubt. The second set was quite independent of the 

 first, the various adjustments and gaugings being made entirely anew. The 

 two sets agreed very closely, and 1 present an average of the two sets in the 

 table as being probably a little more nearly true than either of them sepa- 

 rately. The third column contains the values of the coefficient c, calculated 

 for the formula Q=cH^, from the several heights and corresponding quantities 

 of water given in the first and second columns, H being the height, as mea- 

 sured vertically in inches from the vertex of the notch up to the still-water 

 surface of the pond, and Q being the corresponding quantity of water in 

 cubic feet per minute, as ascertained by the experiments. It will be ob- 

 served from this table that, while the quantity of water varies so greatly as 



