154 REPORT — 1861. 



from If cubic feet per minute to 39, the coefficient c renriains almost abso- 

 lutely constant; and thus the theoretic anticipation that the quantity should 

 be proportional, or very nearly so, to the f power of the depth is fully con- 

 firmed by experiment. The mean of these six values of c is •3064- ; but, being 

 inclined to give rather more weight, in the determination of the coefficient 

 as to its amount, to some of the experiments made this year than to those of 

 last year, I adopt "305 as the coefficient, so that the formula for the right- 

 angled notch without floor will be 



Q=-305 nt 



My experiments on the right-angled notch with the level floor, fitted as 

 already described, comprised the flow of water for depths of 2, 3, 4, 5, and 

 6 inches. They indicate no variation in the value of c for different depths 

 of the water, but what may be attributed to the slight errors of observation. 

 The mean value which they show for c is '308 ; and as this differs so little 

 from that in the formula for the same notch without the floor, and as the 

 difference is within the limits of the errors of observation, and because some 

 consecutive experiments, made without and with the floor, indicated no 

 change of the coefficient on the insertion of the floor, I would say that the 

 experiments prove that, with the right-angled notch, the introduction of the 

 floor produces scarcely any increase or diminution on the quantity flowing for 

 any given depth, but do not show what the amount of any such small increase 

 or diminution may be, and I would give the formula 



Q=-305 H* 

 as sufficiently accurate for use in both cases. The experiments in both 

 cases were made with care, and are without doubt of very satisfactory accu- 

 racy ; but those for the notch without the floor are, I consider, slightly the 

 more accurate of the two sets. 



The experiments with the notch with edges sloping two horizontal to one 

 vertical showed an altered feature in the flow of the issuing vein as com- 

 pared with the flow of the vein issuing from the right-angled notch. The 

 edges of the vein, on issuing from the notch with slopes two to one, had 

 a great tendency to cling to the outside of the iron notch and weir-board, 

 while the portions of the vein issuing at the deeper parts of the notch would 

 shoot out and fall clear of the weir-board. Thus, the vein of water assumed 

 the appearance of a transparent bell, as of glass, or rather of the half of 

 a bell closed in on one side by the weir-board and enclosing air. Some 

 of this air was usually carried away in bulibles by the stream at bottom, 

 and the remainder continued shut up by the bell of water, and existing under 

 slightly less than atmospheric pressure. The diminution of pressure of the 

 enclosed air was manifested by the sides of the bell being drawn in towards 

 one anotlier, and sometimes even drawn together, so as to collapse with 

 one another at their edges which clung to the outside of the weir-board. 

 On the full atmospheric pressure being admitted, by the insertion of a knife 

 into the bell of falling water, the collapsed sides would instantly spring out 

 again. The vein of water did not always form itself into the bell ; and when 

 the bell was formed, the tendency to the withdrawal of air in bubbles was 

 not constant, but was subject to various casual influences. Now it evidently 

 could not be supposed that the formation of the bell and the diminution of 

 the pressure of the confined air could occur as described without producing 

 some irregular influences on the quantity flowing through the notch for any 

 particular depth of flow, and this circumstance must detract more or less 

 from the value of the wider notches as means for gauging water in compa- 

 rison with the right-angled notch with edges inclined at 45° with the hori- 



