H. 8S. I. SMAIL. CLXXXI. 
has used this and other methods for deep rivers, says! ‘‘All 
the objections to the surface float apply with greater force 
to the double float, and additional ones peculiar to itself.’’ 
Prof. HK. C. Murphy of Cornell University, says, ‘‘It is 
impossible to determine the exact position or depth of the 
lower fioat,’” and this is the great difficulty that the author 
has found with this method. Again the upper float may 
drag the lower one or vice versa. 
Slope formula.—The mean velocity may be computed 
from the slope of the water surface, the dimensions of the 
cross section and a knowledge of the roughness of the sides 
and bottom. The one most largely used is Kutter’s— 
41°6 + 1811 in °00281 ie 
Se n Ss / Rs 
~ 1 + (41°6 + °00281) oe 
Seo ivehs 
Where v = mean velocity in feet per second. 
s = surface slope. 
= hydraulic radius. | 
n = aratio varying from °009 for well planed wooden 
channel to ‘035 for rivers in bad order, over- 
grown with weeds or covered with stones. — 
v 
ou 
| 
It is claimed that this formula applies to streams of all 
sizes, from small sewers to large rivers, its constants being 
determined from gaugings by Bazin, Humphreys and Abbot, 
Cunningham and many others. 
There is no doubt as to its accuracy where applied to 
artificial channels with constant cross section, but it is 
absolutely valueless for a natural stream of any size, and 
this same remark applies to all general formulas, from the 
great difficulty in measuring the slope. The author has 
endeavoured to measure the slope at different gauging sites, 
* Journal Franklin Inst., Vol. ux11., p. 167. 
? Water Supply and Irrigation Papers, United States, No. 64, p. 15. 
