THE EXPANSION OE SEA-WATER BY HEAT. 
417 
This Table amply verifies the accuracy of the general formula over the range of the 
experiments ; and it has accordingly been employed to calculate Table XV., in which 
the results of the investigation are summed up. 
The values of the functions of t on which the value of v depends were first determined 
for every integral value of t between 0° and 36°, and the value of f{s) was calculated when 
s was put equal to T02 and 1-03, and also for several intermediate values of the variable. 
The different numbers given by \f/(7) were multiplied by the values of f(s) in succession, 
and the results being added (algebraically) to the corresponding values of (p (t), gave the 
values of v for the selected temperatures and specific gravities. 
The specific gravities at the different temperatures (<r) were then obtained by means 
of the formula 
<TV=S. 
Writing this in the form 
<T ~p{t)+^(t)(j) + qsy 
it is easy to show, by considering the different possible values of <p(t), ip(t), and s, that 
^ is for the range of the observations so nearly constant that no error greater than 
•00002 could be introduced into the calculated specific gravities by the assumption that 
it is independent of s ; and the values of a calculated for the different selected values of 
s prove that this superior limit is really considerably in excess of the true error, and 
that therefore we may with safety assume that is constant. 
We are therefore able to give in Table XV. all the data necessary to calculate the 
specific gravity of sea-water of any degree of salinity at any temperature between 0° and 
36°. Column II. contains the specific gravities at the temperatures given in column I. 
of a solution the specific gravity of which at 0°C. is T02000 ; column III. contains the 
numbers which must be subtracted from those in column I. for each increase of l o, 0 
over the temperatures opposite to which they are placed ; and column IY. the numbers 
which must be added for each increase of -00001 of the specific gravity of the solutions 
at zero. At the head of columns III. and IY. are the numbers of ciphers which must 
be prefixed to the figures written in them in the unit place. 
