362 On the Measure of Temperature. [Dec. 
screw D. Tlie whole apparatus turns on a vertical axis, which is supported on a 
triangular plate of thick brass, furnished with three foot screws. 
The nature of this instrument, it may be seen, allows of our measuring the differ- 
ence of height of two points, though not situated in the same vertical. For this 
purpose, it is only necessary, after having directed the microscope on one of the 
points, to turn it on its axis till it point to the other. It is then raised or depressed, 
the proper quantity which is measured on a scale engraved on the opposite face of 
the ruler, by the aid of a vernier, moved by the piece M N P R S The application 
of a micrometer screw would, perhaps, have been preferable, bat for the dispatch re- 
quired in our experiments ; and as the vernier allowed of our estimating the fifti- 
eth of a millimetre, it appeared capable of sufficient exactness. 
To give to this instrument all the nicety required, it was necessary that the smal- 
lest differences of level should be appreciable, and that in turning the microscope 
from one direction to another, it should preserve its horizontal position, or at least 
that account might be taken of any derangement which might occur. The first point 
was attained by giving sufficient power to the microscope ; and for the second, the 
great care with which the level had been constructed, and the solidity' of its support, 
which was unconnected with the rest of the apparatus, may he considered to have 
fulfilled this condition. Nevertheless, we had determined before hand, the difference 
of height answering to a change of inclination of one division of the level, regard being 
had to the distance of the observed columns. This determination enabled us to 
correct those observations in which any derangement of the level had been ob- 
served. 
The methods by which sucli instruments are adjusted, arc too familiar to require 
any detail from us. It is well known, that by proper reversal of the microscope, as 
well as by observations in different azimuths, while the instrument is turned ou its 
axis, tlie latter is adjusted to the vertical, and the former to the horizontal line. 
We will now return to the observation of the expansion. The micrometer was 
placed od aslab of marble T supported by masonry, the axes of the instrument was 
then at equal distances from the centres of the tubes A 13 and A 'H' and of the index 
R — the height then of this point above the summits of the columns was easily mea- 
sured, that is to say r — A and r — /;' for the height of the index In order to be cer- 
tain that refraction through the tubes had no effect in the vertical plane, we 
placed in the centre of each a small well defined object on which we directed the 
cross wire of the microscope, and we convinced ourselves that the coincidence of 
the wire was nowise disturbed, whether the tube was taken away altogether, or 
merely turned round. 
We had still to determine r. Now this height must he constant in all the experi- 
ments, as the stem which carried the index was always surrounded by ice. To 
measure it we made use of a graduated vertical ruler, the zero of which was placed 
on the iron bar M N this ruler, originally made for a different purpose, and with the 
utmost c re, gave results true to the 10th of a millimetre. The heights, however, 
measured by it arc all in excess, because A, A', and r, should he reckoned from the 
axis of the horizontal tube; we had, therefore, to subtract from the height given by 
the ruler the semi-diameter of the tube. 
To give an idea of the exactness belonging to these different operations, we may 
give the particulars of the incus uremeuts made at 100°. The height of the index, 
above the axis of the horizontal tube was in metres 0,5825 the heights r — A r — A' 
were severally 0,0.1855 and 0,02875; thus A was 0,54305 and h — h' 0,00980, and 
consequently the mean coefficient of the true or absolute expansion of mercury be- 
tween 0° and 100° = s l Ei! . We may sec by this that an error of two or three tenths 
of a millimetre in the value of r would only affect the preceding denominator by 
2 or 3 units. So that in consequence of the peculiar arrangement of our apparatus, 
the measurement in which least exactness was attainable, was precisely that which 
could never occasion errors that might not fairly be neglected ; even the iron bar 
might have been a little disturbed by the action of the heat (although care was al- 
ways taken to set it truly horizontal by means of the levels) without affecting much 
the final result. 
It is iu this particular, that our apparatus appears to be superior, both inexactness 
of result and simplicity of construction, to those adapted to the measurement of the 
expansion of solids. In fact, in these latter, the slightest derangement of the fixed 
point, durir g the very long interval of an experiment, not only alfects the total length 
of the ruler or bar, but the expansion itself is also augmented or diminished thereby, 
inducing errors of the greatest moment. Whereas in our experiments it is evident, 
that eveu were the heights h and h! to become affected in the manner we have spo- 
ken of, still the quantity h — A' which is the measure of the expansion, cannot be; for 
