4 
THE VOYAGE OF H.M.S. CHALLENGER. 
volume of air displaced by the part of the instrument which protrudes above the surface 
of the liquid. In the case of our hydrometer the maximum volume of air displaced 
would be not more than 1 c.c., weighing about 0'0012 grm. The maximum error 
therefore due to this cause would be the same as that caused by an error of one-tenth 
of a scale division on the stem of the hydrometer. As this reading cannot be made with 
certainty to less than half a division the correction for displaced air may be omitted. 
The effective weight, therefore, of the hydrometer is constant, and is 160'2128 grms. In 
order from its reading, when floating in a liquid, to know the volume of the liquid displaced 
by this weight, we must know to what variations the volume of the instrument is subject. 
These are due solely to changes of temperature. 
In determining the volume of the instrument at different temperatures, we confine 
our attention to the body of the instrument and neglect the stem, because it is immersed 
to a variable extent, and even if completely immersed, its bulk is so small that the 
variations of it may be neglected. 
The coefficient of expansion w^as determined by floating the instrument in distilled 
water of different temperatures and observing the displacement. For water of tempera- 
ture below 15° C., the hydrometer was loaded with the small brass table, which weighed 
0 836 grm. 
Table II. 
Showing the Volumes of the Body of the Instrument at 
Different Temperatures. 
With Brass Table. 
Without Brass Table. 
Temperature of water (* C.), 
t 
4-5 
60 
11-4 
15-7 
20-1 
25-9 
Weight of hydrometer (grms.), 
W 
161 0488 
160-2128 
Reading of do., .... 
r 
13-2 
13-2 
9-2 
98-7 
85-2 
63-6 
' Volume (c.c.) of stem immersed ) 
(100 -r) 0-00865, . 
V 
0-751 
0-751 
0-777 
0-011 
0-128 
0-315 
Volume of W grms. water at /*, . 
V 
161-049 
161-054 
161-110 
160-361 
160-487 
160-704 
Volume of body of hydrometer at /* (V - v), 
v, 
160-298 
160-303 
160-333 
160-350 
160-359 
160-389 
If these values for the volume of the body at the different temperatures be 
laid off as ordinates, the corresponding temperatures being abscissae, a straight line 
ran lx* drawn, passing through the points representing the observations at 4 0, 5, 6°, 
15 7 and 25 '9, and giving a higher value by 0 01 c.c. at 20°T C., and a lower 
