12 
At the bottom they were curved a little inwards. Measure- 
ments were taken from the summit of the curve. When 
in such cylinders we have short columns of fluid, the depth 
not being uniform, the colour is not uniform over the whole 
area as we look through the cylinder at an external white 
surface. Manifestly the colour at the sides is more intense 
than at the middle, but for purposes of comparison we must 
restrict our attention to the middle. It is not easy to 
confine attention to a limited portion of a coloured area so 
as to receive no impression from, the remainder of the area 
without some provision. Hence it is necessary to limit the 
field of view at the bottom of the cylinder — this was done 
either by placing small porcelain discs on a black ground 
and holding the cylinder so that its axis passed through the 
centre of the disc — or still better by covering the bottom of 
the cylinder with a black external plate having a small hole 
(about quarter of an inch diameter) in its centre. With 
such a provision columns seemed in some cases to satisfy 
the experiment, which otherwise would have given the 
impression of too dark a colour. In these experiments I 
used a method for determining colours indicated in my last 
paper, regarding the proper colour as the mean of two sets 
of determinations, one set giving too great and the other 
too small values. Thus the determination of colour has 
some analogy with the method used by old geometers for 
determining areas bounded by curved lines; considering 
them as the limits of internal and external polygons. In 
these experiments A denotes the number of cubic c. of 
caramel solution mixed with water ; B the length of the 
column; and C the number of cubic centimetres thence 
