422 
MESSRS. T. E. THORPE AND J. W. RODGER ON THE RELATIONS 
Conditions Deteemining the Dimensions of the Appaeatus. 
The fundamental measurement which rep^ulated the degree of accuracy aimed at, 
and therefore the dimensions of the apparatus, was that of time. Since a comjiara- 
tively large number of liquids was to be examined, and since it was considered to be 
necessary to make, as a rule, twenty-four observations on the same liquid in order 
that the law of the change of viscosity with temperature might be ascertained, 
it was desirable that the times of flow should be as shoi’t as possible, consistent with 
an accuracy sufficient to satisfy the requirements of the research. Considering the 
conditions of the problem, we may assume an accuracy of one part in- 1000 as 
sufficient ; indeed, when we have regard to the imperfection and uncertainty of the 
theory, this degree of accuracy is probably the utmost that we can at present legiti¬ 
mately aspire to. Since the watch was graduated into fifths of a second, and could 
be read to one-tenth, it followed, on the assumption that one-fifth of a second was the 
probable error in time of an estimation, and that two observations were to be taken 
at each temperature, that the minimum time of an observation, even at the highest 
temperature, should never be less than three minutes. At the lower temperatures, 
where the efflux times would be greater, the same absolute error in time, other things 
being equal, would of course have a smaller percentage effect. 
On the basis of Poiseuille’s observations, we first made a trial apparatus, and with 
such a working volume of liquid as seemed suitable (determined approximately in the 
manner given below), we ascertained the size of capillary needed to give an efflux 
time of three minutes in the case of water at 100°. Observations with benzene, 
which is less viscous at its boiling-point than water, showed that the same apparatus 
could still be made to give efflux times within the minimum limit with liquids much 
less viscous than water at its boiling-point, provided that means were devised for 
slightly altering the pressure under which the flow took place. With the knowledge 
acquired by the use of this model the apparatus described was designed. 
As regards the volume of liquid to be taken, it is obvious that, other dimensions being 
constant, the larger the volume of liquid employed, the smaller is the percentage effect 
of an error in the time ; on the other hand, the larger the volume the greater becomes 
the difficulty of keeping the temperature uniform during the flow and of ensuring 
that the whole of the liquid has taken up the temperature of the bath. A relatively 
small volume meets the requirements, and it may be made to give sufficiently long 
times by using long and narrow capillary tubes. But in the case of a small apparatus 
the relative amount of liquid which adheres to the walls is greater than in a large 
apparatus of similar shape. On the assumption of the degree of accuracy above given 
we are thus able to fix the minimum limit. Considering all things the best volume 
to take appeared to be about 2‘5 c.c. So small a quantity had the further advantage 
that it enabled observations to be made on liquids which were difficult to obtain in 
large quantities in a state of sufficient purity. The shape of the vessel had also to be 
