214 
Proceedings of the Poyal Society of Edinburgh. [Sess. 
their widest part was practically 7*4 cms. ; from this we find the corre- 
sponding cross-sectional areas to be 43 square centimetres. By trial it was 
found that 70 c.c. of water were sufficient to fully charge one of the tubes 
and also its cistern to a level coincident with its greatest diameter. Now 
let the cisterns be charged, the one with 70 c.c. of distilled water and the 
other with an equal volume of sea- water ; further, let the density of the sea- 
water be so great that the total difference in the lengths of the two columns 
is equal to 50 mm. A difference so large as this would, with tubes having 
an internal diameter of 5 mm., be equal to a volume of 1 c.c. ; this would 
cause the waters in the cisterns to deviate slightly from a common level ; 
and from the data given above it can be shown that the deviation would 
be 0*2 mm. ; hence, to obtain the true value of the density, it would be 
necessary to allow for this. As, however, the instrument is chiefly intended 
to be used differentially, a standard sea- water of known density taking 
the place of the distilled water, the differences in the heights of the water 
columns will generally be quite small, and need never exceed 5 mm. The 
latter value would reduce the correction from 0*2 mm. to 0*02 mm., and this 
would only affect the density determination by 2 in the fifth decimal place. 
So small an error may be safely neglected. 
After the apparatus had been set up, it was cleaned by successively 
charging the tubes with fuming nitric acid, distilled water, strong alcoholic 
solution of potash, and, lastly, with distilled water : each liquid was kept 
in the tube for a considerable time. It is believed that the glass was thus 
very thoroughly freed from foreign matter. 
The tubes having thus been cleaned, one of the cisterns was charged 
with 70 c.c. of water, some of which was then drawn up into the attached 
tube and adjusted by trial until the column of water was 1000 mm. long, 
as determined by a cathetometer. The cross threads of the microscope M 
were then made to coincide with the meniscus, and a reading taken. In 
this way it was discovered that the micrometer reading corresponding 
to a column of water 1000 mm. long was 42*00 mm., this being the mean 
of a number of determinations. In order to ascertain the length of a 
column of water at any other time, it is only necessary to determine how 
much it differs from this standard reading. 
Determination of the Density of a Standard Sea- Water. 
In order to measure the density of a water which is subsequently to 
be accepted as a standard, the following method of procedure was adopted. 
The cisterns were placed in their normal positions and charged, the 
