BETWEEN THE VISCOSITY OE LIQUIDS AND THEIR CHEMICAL NATURE. 435 
V = TrU’p/STyZ, 
and thus, that 
77 = 7rll^j9/8V^. 
It is also possible to obtain the same expression for 77 by integrating the simplest of 
the fundamental hydrodynamical equations of Naviee, (‘ Mem, A.cad. des Sciences,’ 
vol. 6 , 1822), after making the assumptions that when a permanent current of liquid 
passes through a tube the velocities of the molecules are parallel to the axis of the 
tube and zero at the sides (Couette, ‘ Bull, des Sci. Phys.,’ 1888). 
If, instead of considering a tube of indefinite length, and the loss of pressure taking 
place between two sections of such a tube, we deal with a system consisting of two 
reservoirs, connected by a tube of finite length, the difference of pressure measured 
being that between the two reservoirs, then the above formula will in general not apply 
unless suitable corrections be introduced. This arises from the fact that the observed 
difference of pressure will, in general, not be entirely spent in overcoming viscosity 
within tlie tube, for, besides this cause of loss of pressure, the following have to be 
taken into account:— 
(1.) If the liquid flows through the tube with a finite velocity, at the entrance to 
the tube pressure will be spent in imparting kinetic energy to the liquid. 
( 2 .) Owing to modifications of the stream-lines, especially at the entrance, i)ressure 
will be spent to some small extent in overcoming friction outside the tube, in the 
neighbourhood of its ends. 
It is possible to arrange the experimental conditions so that corrections for these 
disturbing causes may be neglected. The observations made by Poiseuille, with 
long and narrow tubes, are in perfect accord with the preceding formula. In these 
experiments the velocity of efflux was so small that the kinetic energy correction v/as 
inappreciable, and, owing to the length and narrowness of the tubes, the pressure 
spent in friction outside the tubes was negligible in comparison with that s})ent 
within them. When, however, the velocity of efflux is considerable, and the tube is 
as short as that of our glischrometer, the magnitudes of these disturbing effects have 
to be ascertained and, if necessary, corrections have to be applied. 
( 1 .) A correction for the kinetic energy imparted to the liquid was first deduced 
by PIagenbach Pogg. Ann.,’ 109, 385, 1860). His conclusion may be thus stated. 
If, in the formula for an indefinitely long tube, I be taken as the length of a finite 
tube, and the difference of pressure between the reservoirs which the tube connects, 
then the value of this correction, which has to be a})plied to the formula, is 
in which p is the density of the liquid. 
In a communication (‘i\nn. de Chim. Phys.’ (G), 21, 433, 1890), which must be 
regarded as containing the most complete theoretical discussion, which has hitherto 
appeared, of the formula applicable to the case of a finite tube, Couette finds that 
3 K 2 
