79 
of Edinburgh, Session 1866 - 67 . 
been carefully excluded ; and, therefore, any assistance which can 
be obtained from mechanical measurements must be acceptable as 
affording a test for confirmation of the results. 
If we attempt to find the specific gravity of any potable water 
by means of the balance, we encounter very great obstacles ; the 
extreme delicacy of the weighing, and the uncertainty introduced 
hy changes of temperature during the process, render the direct 
method almost valueless ; since both the expansion of the water 
and that of the glass vessel in which it is contained would need 
to be allowed for. But, by taking advantage of the peculiarity of 
water in regard to changes of temperature, we can obtain an ex- 
tremely sensitive indicator of changes in its composition. 
Let us prepare a glass ball, adjusted in its specific gravity so 
that it will just float in pure water between the temperature of 
melting ice and 5 degrees of the centigrade thermometer (be- 
tween 32° and 42° of Fahrenheit’s), and placing a delicately 
graduated thermometer along with it in a jar of cold water, let the 
whole be allowed slowly to become warmer. The effect of an in- 
crease of temperature at first is to produce a contraction in the 
water, and at the same time a slight expansion in the glass of the 
ball ; and the result is that, when the temperature becomes such 
that the two specific gravities are alike, the ball begins to float 
upwards. By placing the ball of the thermometer at some dis- 
tance from the bottom of the vessel, we can note the temperature 
at the instant when the ball passes it ; let this temperature be t v 
As the water continues to grow warmer its density augments, 
but more and more slowly, until it reach its maximum ; after this 
the water begins to expand, and eventually the glass ball, which 
had risen to the top, begins to descend. If we note the tempera- 
ture £ a , at which the ball again passes the thermometer bulb, we 
shall have, in the difference t a — t x between the two temperatures, 
an argument by help of which to compute the relative densities of 
the water and the glass. 
Since the expansion of water on either side of its state of maxi- 
mum density is proportional to the square of the change of tem- 
perature from that point, if we were to measure, on the line of 
abscissas, equal distances to represent the degrees of temperature, 
and were to lay off ordinates to represent the corresponding volumes 
