246 



REPORT 1876. 



3 a, 



Fig. 3. ' 



3 6. 



a unit ol liorizontal length of the orifice. Although the exact form of this 

 true curve is untnown, yet we maj' observe that it must have its ordinates 

 each less than the ordinate for the same level in the parabola. 



The truth of this may be perceived through considerations such as the 

 following. First, it is to be noticed that for the very top and the very bottom 

 of the orifice, instead of the ordinates B D and C E of the parabola, the ordi- 

 nates of the true curve must be each zero ; because, at each of these two 

 places, the direction of the motion is necessarily'tangential to the plane of the 

 orifice *, and so the velocity-component normal to the plane of the orifice 



* The assertion here made, to the efTect that the directions of the stream-lines which 

 form the external surface of the jet on its leaving the edge of the orifice must, at the edge, 

 be tangential to the plane of the orifice when the orifice is in a plane face, or must in 

 general be tangential to the marginal narrow band or terminal lip of the internal or water- 

 confining face of the plate or nozzle in which the orifice is formed, can be clearly and easily 

 proved, although, strangely, the fact has been and is still very commonly overlooked. 

 Even MM. Poucelet and Lesbros, in their delineations of the forms of veins of water 

 issuing i'rom orifices in thin plates, after elaborate observations and measurements of those 

 forms, represent the surface of the issuing fluid as making a sharp angle with the plane 

 wetted face in leaving the edge ("Experiences Hydrauliques sur les Lois de I'Ecoule- 

 ment de I'Eau," a Memoir read at the Academy of Sciences in November 1829, and pub- 

 lished in the Memoires, Sciences Mathematiques et Physiques, tome iii.). Other writers 

 on Hydraulics put forward very commonly representations likewise erroneous. Weisbach, 

 for instance, in his valuable works (Ingenieur ur.d Maschinen-Mechanik, vol. i. § 313, fig. 

 427, date 1846 ; and Lehrbucli der theoretischen Mechanik, 5th ed. date 1875, edited by 

 Hermann, § 433, fig. 772), has assumed (not casually, but with deliberate care, and after 

 experimenial measurements made by himself), as the best representation which, with avail- 

 able knowledge of the laws of contraction of jets of water, can be given for the form of the 



