ON THE GAUGING OF yV^ATER BY TRIANGULAR NOTCHES. 151 



On Experiments on the Gauging of Watei' by Triangular Notches. By 

 James Thomson, M.A., Professor of Civil Engineering, Queen's 

 College, Belfast. 



In 1858 I presented to the Association an interim Report on the new me- 

 thod which I had proposed for the gauging of flowing water by triangular (or 

 V-siiaped) notches, in vertical plates, instead of the rectangular notches, with 

 level bottom and upright sides, in ordinary use. I there pointed out that the 

 ordinary rectangular notches, although for many purposes suitable and con- 

 venient, are but ill adapted for the measurement of very variable quantities 

 of water, such as commonly occur to the engineer to be gauged in rivers and 

 streams ; because, if the rectangular notch be made wide enough to allow the 

 water to pass through it in flood times, it must be so wide that for long 

 periods, in moderately dry weather, the water flows so shallow over its crest, 

 that its indications cannot be relied on. I showed that this objection would 

 be removed by the employment of triangular notches, because, in them, when 

 the quantity flowing is small, the flow is confined to a narrow and shallow 

 space, admitting of accurate measurement ; and as the quantity flowing 

 increases, the width and depth of the space occupied in the notch increase 

 both in the same ratio, and the space remains of the same form as before, 

 though increased in magnitude. I proposed that in cases in which it might 

 not be convenient to form a deep pool of quiet water at the upstream side of 

 the weir-board, the bottom of the channel of approach, when the triangular 

 notch is used, may be formed as a level floor, starting exactly from the ver- 

 tex of the notch, and extending both up stream and laterally so far as that 

 the water entering on it at its margin may be practically considered as still 

 water, of which the height of the surface above the vertex of the notch may 

 be measured in order to determine the quantity flowing. 1 indicated theo- 

 retic considerations which led to the anticipation that in the triangular 

 notch, both without and with the floor, the quantity flowing would be pro- 

 portional, or very nearly so, to the ^ power of the height of the still-water 

 surface above the vertex of the notch. As the result of moderately accurate 

 experiments which I had at that time been able to make on the flow in a right- 

 angled notch, without floor, I gave the formula Q=0'317 H^, where Q is the 

 quantity of water in cubic feet per minute, and H the head of water, as 

 measured vertically, in inches, from the still- water level of the pool down to 

 the vertex of the notch. This formula I submitted at that time tempo- 

 rarily, as being accurate enough for use for many ordinary practical pur» 

 poses for the measurement of water by notches similar to the one experi- 

 mented on, and for quantities of water limited to nearly the same range as 

 those in the experiments (from about two to ten cubic feet per minute), but 

 as being subject to amendment by future experiments which might be of 

 greater accuracy, and might extend over a wider range of quantities of water. 

 Having been requested by the General Committee of the Association to 

 continue my experiments on this subject, with a grant placed at my dis- 

 posal for the purpose, 1 have, in the course of last summer and of the present 

 summer, devoted much time to the carrying out of more extended and more 

 accurate experiments. The results which I have now obtained are highly 

 satisfactory. I am confident of their being very accurate. 1 find them to 

 be in close accordance with the law which had been indicated by theoretical 

 considerations ; and I am satisfied that the new system of gauging, now by 

 these experiments made completely ready for general application, will prove to 

 be of great practical utility, and will aff'ord, for a large class of cases, import- 

 ant advantages over the ordinary method — for such cases, especially, as the 

 very varying flows of rivers and streams. 



