1906-7.] On the Application of a Differential Densimeter. 211 
of the two columns of liquid are measured. As the densities of the two 
liquids are inversely as the heights of the two columns, we have — 
h _ D 
H “ d’ 
in which h and H are the respective heights of the columns of distilled 
water and liquid, and d and D their corresponding densities. 
In its primitive form, the apparatus suffers from several defects, and 
these render even an approximately accurate density -determination 
extremely difficult, if not an impossibility. We observe (1) that no attempt 
is made to keep the contents of the tubes at the same temperature. (2) 
The air enclosed in the upper part of the apparatus may, and generally 
does, vary in temperature during the course of measurement ; any 
such variations cause the liquid columns to alter in height, thus leaving 
the observer in doubt as to their true values. (3) In order to measure the 
heights of the columns, readings must he taken (preferably by means of 
a telescope and vertical scale, the latter being set up between the two 
columns) for the surface of the liquid in each cistern, in addition to those 
for the meniscus in each tube, or four readings in all. Hence, in addition 
to a certain inexactness, the method becomes quite laborious when a 
number of measurements are undertaken. (4) Finally, we note that the 
limbs of the apparatus are generally too short for accurate work. 
The Differential Densimeter. 
In order to minimise the several errors inherent in Hare’s original 
apparatus, and also to reduce the labour of experimenting, some six or 
seven modifications were constructed and tested. After numerous experi- 
ments, four of these proved unsuitable, and were consequently rejected. In 
each of the rejected forms, an attempt was made to introduce some kind 
of constant-level overflow cistern, but without success. A form of appar- 
atus yielding values which were in close agreement with those obtained 
by means of pyknometers. is shown in fig. 1. 
The apparatus consists of two glass tubes S, K, each having an internal 
diameter of about 3 mm. and a length of 1200 mm. ; these tubes, having 
obliquely perforated taps t, p, are sealed to the bulbs b , b ; each bulb has 
a capacity of about 25 c.c., and their upper ends are joined by an inverted 
U-tube into the bend of which a three-way tap T is sealed. One of the two 
free branches of this tap communicates with an exhausted copper globe E, 
having a capacity of 42 litres ; the other communicates with a suitable 
