360 
On the Measure of Temperature. 
[Dec. 
It is founded on the incontestable principle in Hydrostatics, viz. that when 
two liquid masses communicate by a lateral tube, the vertical heights of their 
surfaces are in an inverse ratio to their densities. If then we can contrive to mea- 
sure the heights of two columns of mercury, contained in the branches of a glass 
syphon in a reversed position, one being surrounded by melting ice, while the 
other may he raised to any desired temperature, we can easily deduce the expan- 
sions we are in search of. 
If h and h f represent the vertical heights of the two columns, the pressures of 
which correspond to the temperatures t and t' we shall have, putting d and d! the 
corresponding densities. 
hd = h’d! 
Now d and d ' are in an inverse ratio to the volumes v and v' which the same 
mass of liquid would occupy in raising it to the successive temperatures t and i 
Then 
v h* 
from which we get for the mean coefficient of expansion between / and / 
k ' — h 
Every thing then depends on the exact measurement of the temperatures and of 
the height of the columns. It is scarcely necessary to remark, that in this way we 
obtain the absolute or true expansion of the liquid, since as the shape of the con- 
taining vessel exercises no influence whatever on the pressure of its contents, neither 
can any expansion affecting them influence it. 
Boyle was the first who proposed this method as a means of comparing the specific 
gravities of fluids. Other experimenters have thought of applying it to the measure 
of expansions, and it is probable, that in the lower temperatures it is as applicable 
as it is exact ; but when we come to temperatures of 300° and more, it is certainly 
of very difficult application. 
In order to render intelligible the following description of apparatus which we 
used, we have drawn an outline of it, (Fig. J, Plate VI.) in which, however, the prin- 
cipal parts only are drawn ; the reader can easily supply what is omitted. 
The bent tube which contains the mercury, lias two vertical branches A B and 
A' B' which communicate by a horizontal tube B B' exactly levelled, and haring 
the same diameter as well as thickness of glass throughout. We had taken the 
precaution to ascertain beforehand, that the pressure was readily communicated 
from one branch to the other, through the horizontal tube, and that the friction 
against its sides in no degree interfered with the re-establishment of the level when 
that had been disturbed. 
Each of the two vertical branches is formed, as we may see in the figure, of two 
tubes of different diameters properly united. In using a smaller diameter for the 
lower tube, we diminish the quantity of mercury, and by using a larger diameter 
for the upper tube, we guard against any inequality of the capillary depression 
which might be occasioned, by the difference of temperature in the two legs. 
The horizontal tube rests on a strong iron bar, M N shaped like a T and sup- 
ported by its three legs on a very thick table. The upper surface of the bar has 
been worked quite true, and carries two spirit-levels placed at right angles, which 
are adjusted by means of screws placed at the four corners of the table. Close to 
each of the vertical tubes, there rises an. iron arm carrying a ring with screw, which 
serves to hold the tube in a fixed position. Not to crowd the paper too much, we 
have only drawn the iron arm along side the tube A B It is terminated, as is 
shown in the sketch, by a small beut piece of iron, the point of which R is meant 
to serve as an index. 
The bent tube being thus adjusted in all its parts, it remained, so to arrange the 
apparatus, as to communicate the requisite temperature to each of the columns, No- 
thing was easier in the case of the column A B, which it was desired should beat 0 Q . 
1 he object was effected by surrounding it with a large cylinder of cast iron, cemented 
below to the bar of iron all round, and filling the cylinder with ice up to the surface 
ol. the mercury in the tube. A small window F had been made and applied to the 
cylinder, which was occasionally opened when observing, in order to take out a 
Pule ot the jcc, so that the surface of the column might be better observed. Thermo- 
ters, which were immersed from time to time in the mercury, satisfied us, that every 
part of the column was actually of the temperature 0*. 
I hat part i t the apparatus again, which is meant to contain the bath for heating 
the column A B , presented the greatest difficulties in its arrangement. It was neces- 
