MECHANICS AND USEFUL ARTS. * 57 



small, the flow is confined to a small space, admitting of accurate measure- 

 ment; and that the space for the flow of the water increases as the quantity 

 to be measured increases, but still continues such as to admit of accurate 

 measurement. 



Farther, the ordinary rectangular notch, when applied for the gauging of 

 rivers, is subject to a serious objection from the difficulty or impossibility of 

 properly taking into account the influence of the bottom of the river on the 

 flow of the water to the notch. If it were practicable to dam up the river sr 

 deep that the water would flow through the notch as if coming from a reser 

 voiv of still water, the difficulty would not arise. This, however, can seldom 

 be done in practice; and, although the bottom of the river may be so far 

 below the crest as to produce but little effect on the flow of the water when 

 the quantity flowing is small, yet when the quantity becomes great, the " ve- 

 locity of approach" comes to have a very material influence on the flow of 

 the water, but an influence which it is usually difficult, if not impracticable, 

 to ascertain with satisfactory accuracy. In the notches now proposed, of 

 triangular form, the influence of the bottom may be rendered definite, and 

 such as to affect alike (or, at least, by some law that may be readily deter- 

 mined by experiment) the flow of the water when very small, or very great, 

 in the same notch. The method by which I propose that this may be ef- 

 fected, consists in carrying out a floor, starting exactly from the vertex of 

 the notch, and extending both up-stream and laterally, so as to form a bot- 

 tom to the channel of approach, which will both be smooth and will serve 

 as the lower bounding surface of a passage of approach, unchanging in form, 

 while increasing in magnitude at the places, at least, which are adjacent to 

 the vertex of the notch. The floor may either be perfectly level, or may 

 consist of two planes, whose intersection would start from the vertex of the 

 notch, and, as seen in the plan, would pass up stream perpendicularly to the 

 direction of the weir-board; the two planes slanting upwards from their in- 

 tersection more gently than the sides of the notch. The level floor, although 

 theoretically not quite so perfect as the floor of two planes, would probably, 

 for most practical purposes, prove the more convenient arrangement. 



With reference to the use of the floor, it may be said, in short, that by a 

 due arrangement of the notch and the floor, a discharge orifice and channel 

 of approach may be produced, of which (the upper surface of the water 

 being considered as the top of the channel and orifice) the form will be un- 

 changed, or but little changed with variations of the quantity flowing; very 

 much less, certainly, than is the case with rectangular notches. The laws 

 regulating the quantities of water flowing in such orifices as have now been 

 described, come naturally next to be considered. Without, however, in the 

 present interim report, attempting to enter on a detailed discussion of theo- 

 retical considerations on this subject, I shall here merely advert briefly to 

 the principal results and methods of reasoning. 



By theory I have been led to anticipate that the quantity flowing in a given 

 notch should be proportional, or very nearly so, to the ^ power of the lineal 

 dimensions of the cross section of the issuing jet, or to the ^ power of the 

 head of water over the vortex of the notch. This head is to be understood, 

 in the case of water flowing from a still reservoir, as being measured verti- 

 cally from the level water surface in the reservoir down to the vertex of the 

 notch; or in the case of water flowing to the notch with a considerable ve- 

 locity of approach over a floor arranged as above described, the head is to be 

 considered as measured vertically from the water surface, where the motion 



