EXPANSION OF WATER. 
789 
The discordances which these tables exhibit are partly due to errors in the assumed 
expansions of brass, glass and mercury, on which, by the nature of the experiments, 
the value of the expansion of water is made to depend. 
Stampfer deduced the expansion of water from the apparent weight of a hollow 
cylinder of brass suspended in water. The coefficient of the linear expansion of the 
brass was found to be 0*0000 192, by experiments in which the variations of tem- 
perature amounted to from 38° to 62° (the absolute temperatures are not given). At 
about 17° Mr. Sheepshanks found the coefficient of expansion of cast brass equal to 
0*00001722. This is 0*00000153 less than the mean coefficient of expansion from 0° 
to 100°, assuming the latter to be 0*00001875. The error of the assumed expan- 
sion of the cylinder at ordinary atmospheric temperatures will probably be not quite 
so large. If taken equal to 0*00000133, the correction will be — 0*000004(^ — 4). 
Despretz experimented with thermometers filled with water. The expansion of 
the glass was inferred from the apparent expansion of mercury in the thermometer 
from 0° to 28°, using for the coefficient of the expansion of mercury 0*00018018, 
the value obtained by Dulong and Petit. But the expansion of mercury from 0 ° to 
28° is 0*005032 according to Regnault*. The resulting mean coefficient of expan- 
sion is 0*00017971. Hence the expansions obtained by Despretz must be dimi- 
nished by 0*00000047(^—4). Pierre and Kopp, who employed the same method, 
deduced the expansion of the glass from the apparent expansion of the mercury from 
0° to 100°, assuming* its absolute expansion between those points to be 0*01 8018. But 
the absolute expansion of mercury from 0° to 100° is 0 018 153. The glass used by 
Pierre contained oxide of lead, and probably had very nearly the same rate of 
expansion at both high and low temperatures. It is not known how far the glass 
used by Kopp possessed this property. Hence these expansions require the addition 
of 0*00000135(^—4). The observations of Plucker and Geissler extend only to 
12 °. They were made with a thermometric apparatus the capacity of which is com- 
pensated by mercury so as to be invariable, or very nearly so. Assuming the expan- 
sion of mercury from 0° to 100° to be 0*018018, the cubic expansion of the glass 
fi'om 0° to 100°, deduced from the apparent expansion of mercury, is 0*002818. 
But according to Regnault'^ the coefficient of the cubic expansion of a glass free 
from lead was 0*00002761 from 0° to 100°, and 0*00002628 from 0° to 10°. It is 
therefore probable that the coefficient of the cubic expansion uf the glass has been 
taken 0*00000133 too great. Also the quantity of mercury used for compensating 
the expansion of the glass will be too small in the ratio of 0*000179714, the rate of 
expansion of mercury from 0° to 10°, to 0*000181 53, the rate of expansion of mercury 
from 0° to 100°. Hence, upon the whole, the expansion must be diminished by 
0*0000013(^-4). 
The ratios of the maximum density of water to its density at f, according to the 
* Memoires de ITnstitut, tome xxi. p. 328. t p. 237. 
5 L 2 
