Mr Watts’ Ohservatims on the Resistance of Fluids. SI 9 
— ^ 
And since we are at liberty to suppose 
is 
have R = x 
^•M 
Thus, it appears, that the resistance II is in the duplicate 
ratio of the velocity as it ought to he ; and therefore, the vali- 
dity of the proposition under consideration is completely esta- 
blished. 
The value of R in the two preceding equations, may be re- 
duced to known measures by means of the equation v — gh \ 
for, by substituting this value of v in the equation (S), it be- 
comes 
^(b.^^gh 4} ^hh 
M 
but is the volume of a prism of the fluid whose base is 
and whose height is 4^; and 4^6^ is the mass of fluid which 
has the surface b for its base, and 4 times the height due to the 
velocity v for its altitude ; therefore, by assuming M equal to 
unity, the resistance R will be equal to the mass of a prism of 
the fluids whose base is the area of the fluid vein^ and whose 
height is four times the fall productive of the eflluent velociiy.. 
This result corresponds with the formula given by Daniel, 
Bernoulli, in the 2d volume of the Comment. Petropol. in. 
the year 1727 ; although he afterwards calls this determination 
in question in his subsequent theory of Hydrodynamics, as he 
found that it gave a resistance four times greater than experl. 
ment. 
But however this may be, it nevertheless appears at least to 
be confirmed by the experiments of d’Ulloa; for he found,^ 
that the resistance of a board one foot square, and immersed in 
a stream, moving at the rate of two feet per second, was 15^ 
pounds avoirdupois, — a result very nearly corresponding with 
that deduced from the preceding formula, which gives for rain-- 
water about 15 ^^5 lb. weight avoirdupois. 
Notwithstanding, it is necessary to avow, that this resistance 
greatly exceeds all the values given by other authors : it is in 
fact more than double the resistance assigned by the members, 
of the Academy of Sciences at Paris, whose determination is ge« 
