OF ARTS AND SCIENCES. 43 



of the stream ; and, when turned so that the particles of water with- 

 draw from it, the surface of the piezometer stands lower than the sur- 

 face of the stream. Assuming that the variation is as the square of 

 the mean velocity of the stream, the excess in height of the piezo- 

 metric surface at the west box of Station No. 5 may be expressed 

 approximately by heights equal to 0.0002 U' 2 , in which U stands for 

 the mean velocity of the stream at the station ; and the excess in 

 height at the east box of Station No. 5 may be expressed approxi- 

 mately by heights equal to 0.00032 U 2 ; and the depression at Station 

 No. 9 may in like manner be expressed by 0.00008 U' 2 . 



Orifices parallel. Passages inclined. 



At Stations No. 7 and No. 10, the planes of the edges of the ori- 

 fices were, within the limits of careful observation, either in the plane 

 of the sides of the trough, as at Station No. 7, or parallel with this 

 plane, and within 0.0004 ft. from it, as at Station No. 10; but at 

 these stations the passages from the orifices, beginning at the plane of 

 their edges, were not normal to this plane, but made therewith an 

 acute horizontal angle. 



At Station No. 7, on the west side, the angle was 45° up stream, 

 and on the east side was 45° down stream. At Station No. 10, on 

 the west side, the angle was 30° down stream, and on the east side 

 was 30° up stream. 



At Station No. 7, the orifices were made by boring through the 

 sides of the trough, at the proper angle, holes 0.021 ft. in diameter ; 

 and, though cut with great care, it was found at the end of the experi- 

 ments that the acute edge of each was slightly ragged, but no projec- 

 tion into the trough was perceptible. 



At Station No. 10, the orifices were made with the same sized hole 

 in plates of brass, carefully finished, and set into the sides of the 

 trough flush ; but the swelling of the wood in the thickness of the 

 plate, which was 0.01 ft., caused it to project 0.0003 ft. or 0.0004 ft. 

 beyond the surface of the plates all around. The plates were 0.083 ft. 

 high and 0.125 ft. long. 



The results given in the tables for these stations are represented in 

 Fig. No. 3, Plate No. 3. 



Here we see that on the east side at Station No. 7, and on the 

 west side at Station No. 10, in which cases the particles of water 

 turning 45° and 30° respectively from their course would flow 

 directly through the passage into the piezometric reservoirs, the sur- 

 faces of the reservoirs stand higher than the surface of the stream, 



