between the viscosity of liquids and their chemical nature. 399 
through a capillary tube of known size under definite conditions of temperature, 
pressure, &c. By suitably arranging the experimental conditions, the relative times 
of flow, or, as they have been somewhat inaptly termed, the relative times of transpi¬ 
ration, through the same tube may be considered as proportional to the coefficients of 
viscosity. 
Hence it happens that the historical treatment of the investigations which are 
related to that described in this paper opens with some account of the researches 
which have been undertaken to obtain the so-called transpiration-times of liquids. It 
has to be borne in mind, in dealing with this part of the subject, that in many cases 
the observers were apparently unaware that they might obtain relative measures of 
viscosity by the method they employed. They simply ascertained the time of flow of 
a liquid, and considered this value as a physical constant under the experimental 
conditions. In most cases, as will be made clear subsequently, these conditions were 
probably not such as would admit of the transpiration-time being regarded as a 
relative measure of the coefficient of viscosity—that is, of the real physical constant 
which was influencing the experiments. 
That the flow of liquids, and especially of water, through channels, conduits, and 
pipes should have received so much attention in the early days of experimental 
science is, of course, due to the economic importance of the subject. The main result 
of these observations was to show that the resistance offered to the flow of the liquid 
was as the square of the velocity, the velocity being in these cases considerable. 
About fifty years ago, however, Poiseuille, starting from physiological con¬ 
siderations, attempted to discover the law of the flow in tubes of very narrow bore 
where the velocity of exit was but small, and here he found the resistance to vary 
not as the square of the velocity, but directly as the velocity. It was thus evident 
that the character of the motion of a liquid in a capillary tube where the velocity is 
small, diflered essentially from that occurring in the cases of rapid flow in tubes of 
large diameter. As is well known, Poiseuille found that the volume of liquid, in 
cub. millims., which flows in the unit of time through a tube of circular section, the 
walls of which it wets, may be expressed by the formula V = K H/B, in which 
D is the diameter in millims. of the tube, L its length in millims., H the pressure in 
millims. of mercury, and K (which Poiseuille regarded as a measure of the fluidity 
of the liquid) a constant which varies with the nature of the liquid and its 
temperature. 
The meaning and validity of this empirical expression have been established by 
the theory of hydrodynamics, and it has been shown that from observations made 
by Poiseuille’s method, under suitable conditions and with certain corrections, to be 
explained hereafter, the viscosity of a liquid may be ascertained."^' 
* Stokes, ‘Cambridge PLil. Trans.,’ 8, 304, 1847; G. Wiedemann, ‘ Pogg. Ann.,’ 99, 177, 1856; 
E. Hagenbach, ‘ Pogg. Ann.,’ 109, .385, I860; Stefan, ‘ Wien. Ber.,’ 46, II., 495, 1862 ; Codette, ‘ Ann. do 
Chimie et de Pbys.’ (6), 21, 433, 1890; Wilbeeeokce, ‘Pbil. Mag.’ (5), 31, 407, 1891. 
