AND ITS APPLICATION TO MR. B. TOWER’S EXPERIMENTS. 
165 
value of any such considerations depends on whether the calculated behaviour of the 
ideal fluid is found to agree with the behaviour of the actual fluids—whether taking 
a particular fluid, a value of p can be found such that the values of f calculated by 
equation (1) agree with the values of f determined by experiments for all values of 
a and u. 
In the mathematical theory of viscous fluid, p is assumed to be constant for a 
particular fluid. This supposition is sometimes justified by reference to some assumed 
dynamical constitution of fluids; but apart from such hypotheses there is no more 
ground for supposing a constant value for p than there is for supposing a particular law 
of gravitation, in other words, there is no ground at all. If a particular value of 
p is found to bring the calculated results into agreement with all experimental results, 
then this value of p defines a property of actual fluids, and of course it has been with 
this object that the mathematical theory of p has been studied. 
The chief question as regards p is a simple one — within a particular fluid is p 
constant ? In other words, is viscosity a property of a fluid like inertia which is 
independent of its motion ? If it is, our equations may be useful ; if it is not then 
the introduction of p into the equations renders them so complex that it is almost 
hopeless to expect anything from them. 
Another question of scarcely less practical importance relates to the character 
of p near the bounding surfaces of the fluid. If p is constant in the fluid, does it 
change its value near the boundary of the fluid ? Is there anything like slipping 
between the fluid and a solid boundary with which it is in contact ? 
As regards the answers to these questions the present position is somewhat as 
follows:— 
11. The Two Viscosities. 
The genera] experience that the resistance varies as the square of the velocity is an 
absolute proof that p is not constant unless a restricted meaning be given to the 
definition of viscosity, excluding such part of the resistance as may he due, in the 
way explained by Prof. Stokes,'" to internal eddies or cross streams, however insensible 
these may be, so long as they are not simply molecular motions. 
On the other hand in the definite experiments made by Colomb, and particularly 
by Poiseuille, it was found that the resistance was proportional to the velocity, and 
therefore that p was absolutely constant— i.e., independent of the velocity.! 
To meet this discordance it has been supposed that p varied with the rate of distor¬ 
tion— i.e,, is a function of u-Ja , but is sensibly constant when uja is small.| 
To assume this, however, is to neglect Poiseuille’s experiments, in which he found 
for water the resistance absolutely proportional to the velocity in a tube '6 mm. 
* Stokes’s Reprint, vol. i., p. 99. 
t Paris Mem. Savans Etrang., tom. 9 (1846), p. 434. 
f Lamb’s “ Motion of Fluids,” 1879, Art. 180. 
