OF ARTS AND SCIENCES. 53 



It may be that variations of 0.0002 ft. were overlooked, though such 

 were detected at Station No. 5. 



To obtain as definite an idea as we may of the precision necessary 

 to obtain accurate results with a piezometer, let the results obtained 

 at the several orifices of the first group be worked up separately. 

 The heights of the piezometers above and below the surface of the 

 stream will be expressed approximately as follows : — 



Station No. 4. West side, — 0.00004 U 2 East side, — 0.00006 U 2 

 Station No. 8. West side, -t- 0.00022 U 2 East side, + 0.00006 U 2 , 

 Station No. 9. East side, •+- 0.00002 U 2 



Applying as well as we may the results obtained in the second group 

 of experiments, and assuming the variation in height to be propor- 

 tional to the angle of inclination with the plane of the side, of the 

 horizontal elements of the surface bounded by the edge of the orifice, 

 it will be seen that an extreme variation from the plane of the side 

 in the length of any of the longer of these elements of 0.0004 ft., 

 0.0002 ft., 0.0003 ft., 0.0002 ft., and 0.0002 ft., respectively at the 

 several orifices, in the order in which they have been named, will 

 account for the several variations in the height of the piezometric 

 columns above or below the surface of the stream ; and a less varia- 

 tion from the plane of the side, in the length of any of the shorter 

 horizontal elements of the circular orifices, would serve to account 

 for them. 



It will be observed that the heights by the piezometer whose orifice 

 was 0.334 ft. long horizontally indicated more nearly than those with 

 smaller orifices the actual height of the stream. 



From these results, it is evident that it is entirely within the 

 practicable limits of construction to make piezometers that will indi- 

 cate the true height of the stream, within the practicable limits of 

 observation. 



