248 



REPORT 1876. 



4«. 



Fig. 4. 



4 6. 



motion does not deviate mucli from perpendicularity to the plane of the 

 orifice. Lower down in the plane of the orifice the direction of the 

 water's motion will approach still more nearly to being perpendicular to 

 that plane ; bnt there the pressure will be considerably in excess of the 

 atmospheric pressure, and so the velocity will be considerably less than that 

 due by gravity to a fall through the vertical distance from the still-water 

 surface-level down to the stream-line in the plane of the orifice. At places 

 still further down in the orifice the flow comes to be obliquely upwards ; 

 and this obliquity is so great as to render the normal component very 

 much less than the actual velocity, while the actual velocity itself is 

 less than that due by gravity to the depth of the particle below the still- 

 water surface-level. At this region of the flow then, for both reasons, the 

 ordinates of the time curve are less than those of the parabola. Lastly, at 

 the very bottom of the orifice, or immediately over the top of the crest of 

 the notch, the water issues into contact with the atmosphere, and so attains 

 to atmospheric pressure, and must therefore have the velocity due by gravity 

 to its depth below the still-water surface-level. Here, however, its direction 

 of flow is necessarily tangential to the plane face of the vessel from which 

 it is shooting away, and consequently is vertically upwards. Hence the 

 normal component of its motion is zero, and so the ordinate of the true 

 curve at that place is zero in length, instead of the normal component 

 being greater at the bottom of the orifice than at any higher level, and 

 instead of that component being properly represented by the ordinate there 

 of the parabola. 



Like explanations to those already given might be offered for other forms 

 of orifices (for circular or triangular orifices or V-notches, and for orifices 

 in general which may be in vertical or horizontal or inclined plane faces, 

 or in faces of other superficial forms than the plane), and it might be 

 shown that in general the ordinary modes of treating the subject are very 

 faulty. 



The examples already discussed may suffice to direct attention to the 

 faulty character of the ordinarilj^ advanced theories, and to give some sug- 

 gestions of directions in which reforms are requisite. 



I will now proceed to offer some improved investigations which are appli- 



