BETWEEN THE VISCOSITY OF LIQUIDS AND THEIR CHEMICAL NATURE. 423 
considered. As regards rapidity of acquiring a constant temperature, a Jong cylinder 
is better than a sphere ; in the case of a sphere, however, less liquid adheres to the 
walls than in that of a cylinder of equal capacity. Experiments made witii water 
determined the relations of length and breadth of cylinder such that the observations 
should not be influenced, within the limits of accuracy aimed at, by the liquid left 
adhering to the walls. 
Having fixed the working volume, the other factors to be considered in maintaining 
the time of flow at any temperature within the three minutes limit were the pressure 
and the dimensions of the cap)illary tube. 
As already stated the pressure employed was a head of water. The minimum 
head should be capable of measurement with an accuracy well within 1 in 1000. 
The scales of the manometer were divided into millimeters and could be easily read 
by a lens to 0'2 millim. The minimum pressure head usually employed was about 
too centims., which was found a convenient height to measure ; hence the error in 
readinof the manometer did not exceed 1 in 5,000. 
The dimensions of the capillary could now be fixed from Poiseuille’s observations 
and from the results of the experiments with the model. Since the time of flow 
depends on both the length and radius, it is obvious that the same time could be 
obtained by means of tubes of very different dimensions. It was advisable, however, 
to have the length as short as possible consistently with the considerations given 
below, for then the limbs of the apparatus could be placed near together, and could 
be kept more readily at the same temperature, and the temperature, indicated by 
a thermometer placed between them, could be taken as that of each. The length 
chosen was about 5 centims., and with this length the radius had to be about 
•008 centim. 
It will be obvious from fhe above dimensions that the velocity of flow of liquids 
which have efflux times near the minimum limit is considerable. 
Mean velocity = 
V _ 2-5 
7rr~t IT X (’008)® X 180 
= 66 centims. per second. 
In connection with this relatively high velocity two questions present themselves ; 
(1) The formula used in obtaining the coefficient of viscosity is deduced on the 
assumption that the motion of the fluid within the tube is linear, and tliat the 
stream does not break up into eddies. Osborne Eeynolds (‘ Phil. Trans.,’ 1883 
and 1886) has shown, experimentally, that if the velocity of efflux is greater than 
that given by the expression V = 2000 ') 7 / 2 r(i, the motion is j^robably turbulent, and 
therefore the formula will not hold. In this expression rj is the viscosity coefficient, 
and d the density of the liquid ; r is the radius of the tube. By taking 
observations under different pressures, it has been shown, as is described later, that 
the flow in the apparatus employed J^y us is linear. In the case of water the 
critical velocity at 100° in our apparatus is about 400 centims. a second, the velocity 
