ON RECENT RESEARCHES IN HYDRODYNAMICS. 19 
- face of the solid, the tangential force on this plane, referred to a unit of 
‘surface, shall be in the same direction with, and proportional to the velocity 
with which the fluid flows past the surface of the solid. The condition ob- 
eeened by Poisson is essentially the same. 
_ Dubuat stated, as a result of his experiments, that when the velocity of 
Toxater flowing through a pipe is less than a certain quantity, the water adja- 
> _ cent to the surface of the pipe is at rest*. This result agrees very well with 
an experiment of Coulomb’s. Coulomb found that when a metallic dise was 
made to oscillate very slowly in water about an axis passing through its 
centre and perpendicular to its plane, the resistance was not altered when 
the dise was smeared with grease; and even when the grease was covered 
_ with powdered sandstone the resistance,was hardly increased}. This is just 
what one would expect on the supposition that the water close to the disc is 
_ earried along with it, since in that case the resistance must depend on the 
~ internal friction of the fluid; but the result appears very extraordinary on 
the supposition that the fluid in contact with the disc flows past it with a 
nite velocity. It should be observed, however, that this result is compatible 
‘with the supposition that a thin film of fluid remains adhering to the dise, in 
onsequence of capillary attraction, and becomes as it were solid, and that 
the fluid in contact with this film flows past it with a finite velocity. If we 
‘consider Dubuat’s supposition to be correct, the condition to be assumed in 
the case of a fluid in contact with a solid is that the fluid does not move re- 
latively to the solid. This condition will be included in M. Navier’s, if we 
‘suppose the coefficient of the velocity when M. Navier’s condition is ex- 
pressed analytically, which he denotes by E, to become infinite. It seems 
probable from the experiments of M. Girard, that the condition to be satis- 
ed at the surface of fluid in contact with a solid is different according as the 
fluid does or does not moisten the surface of the solid. 
___M.Navier has applied his theory to the results of some experiments of 
-M. Girard’s on the discharge of fluids through capillary tubes. His theory 
shows that if we suppose E to be finite, the discharge through extremely 
all tubes will depend only on E, and not on A. The law of discharge at 
ich he arrives agrees with the experiments of M. Girard, at least when the 
es are extremely small. M. Navier explained the difference observed by 
: Girard in the discharge of water through tubes of glass and tubes of 
opper of the same size by supposing the value of E different in the two 
es. This difference was explained by M. Girard himself by supposing that 
n film of fluid remains adherent to the pipe, in consequence of molecular 
ion, and that the thickness of this film differs withthe substance of which 
tube is composed, as well as with the liquid employed{. If we adopt 
vier’s explanation, we may reconcile it with the experiments of Coulomb 
supposing that E is very large, so that unless the fluid is confined in a 
harrow pipe, the results will depend mainly on A, being sensibly the 
ne as they would be if E were infinite. 
There is one circumstance connected with the motion of a ball-pendulum 
scillating in air, which has not yet been accounted for, the explanation of 
Which seems to depend on this theory. It is found by experiment that the 
orrection for the inertia of the air is greater for small than for large spheres, 
t is to say, the mass which we must suppose added to that of the sphere 
a greater ratio to the mass of the fluid displaced in the former, than in 
atter case. According to the common theory of fluid motion, in which 
* See the Table given in tom. i. of his Principes d’Hydraulique, p.93. 
+ Mémoires de l'Institut, 1801, tom. iii. p. 286. 
} Mémoires de l’Académie des "Sciences, tom. i. pp. 203 and 234, 
C2 
