Brlggs.] 'jlv) [Nov. 3, 



be confirmed by the discussions of tlio late transit of Venus, the accuracy 

 of my cliemical estimate of Sun's ifiass and distance* will be likewise con- 

 firmed. 



Tlie generalization of Faraday, as con-oborated by the measurements of 

 Weber, Kolilrausch, and Clerk Maxwell, is thus extended to include gravi- 

 tation, as well as electrostatic and electrodynamic action, in the same 

 category of central force with light (VI), by means of an identical limit- 

 ing vis viva. The simple mathematical correlations make the generalization 

 still broader, so as to embrace heat (IV), chemism, cosmical and molecular 

 aggregation, dissociation, rotation and revolution (V-X), and all central 

 forces (I-X). 



The Flow of Water Through an Opening in a Pierced Plate. 



By Robert Briggs. 



{Bead before the American Philosophical Society, November 3(Z, 1876.) 



The consideration of the subject of the vena contractu, or section of a 

 vein of water emerging from an orifice under certain conditions, is made a 

 portion of the proceedings of the Philosophical Society of Glasgow, and 

 appears in their volume X, page 145 et seq. Four papers are published, 

 the first of which is an extract from a letter of William Froude, Esq., C. 

 E., F. R. S. , to Sir William Thomson, dated Cheston Cross, Torquay, 20th 

 December, 1875. Mr. Froude is quotedf * * * * "One result I 

 ■^ jt^ have tried came out well : — The discharge through 



an introverted cylinder [tube] with keen edge. 

 ^ Here, by theory, the section of the jet ought to 



be exactly half of the aperture. For tiie conserva- 

 tion of stream line energy obliges the velocity to be 

 that due to the head, while the conservation of 

 ■^■"^ momentum requires that the pressure on the aper- 

 ture (which is here the sole operative pressure set- 

 ing in the ultimate direction of the velocity gene- 

 rated) is only sufficient to create as much momen- 

 tum, say, per second as will be resident in the length 

 delivered per second, of a column of discharge, of half the sectional area 

 of the aperture, if its velocity is that due to the head. 



"The cylinder was quite smooth outside and the edge quite keen. The 



•area ratio came out 0.503, 0.502, «&c., instead of 0.500, and the little excess 



was obliterated, if the head was counted, to about one-fourth the diameter 



below the edge ; as indeed it ought to be (I won't swear to the exact figure 



* Proc. ft. P. A., xil, xiil, loc. cit. 



+ The entire article Is quoted, the hiatus Indicated by asterisks exist in the 

 published Proceedings of the Glasgow Society. 



