1819.] and on the Laws of the Communication of Heat. 123 
of the level. This datum was sufficient to enable us to correct 
the observations in which the level was deranged. 
The processes employed for regulating such instruments are 
too well known to require any details here. [tis known that by 
the requisite turnings of the telescope, both upon itself and on 
its rings, and by observations in the different azimuths in which 
it may be placed, by turning the axis of the instrament, we have 
it in our power to render that axis vertical, and the optical axis 
of the telescope horizontal. 
Let us return now to the apparatus of the dilatation. The 
micrometer was placed upon a marble plane, T, supported by 
mason work. The axis of the instrument was at an equal dist- 
ance from the centres of the tubes, A B and A’ B’, and the point, 
R. Hence we could measure immediately the excess of the 
height of this point above the summits of the columns of mer- 
cury ; that is to say, the heights r — A andr — A’, callmgr 
the absolute height of R. To be certain that the refraction 
across the tubes produced no deviation in the vertical direction, 
we placed artificial horizons im the centre of each, on which we 
directed our telescope, and we ascertained that the comeidence 
of the wire was not altered whether we raised or turned the tube. 
Nothing further remained than to ascertain 7. But this 
height remained constant in all the experiments, since the bar 
supporting the arch, R, was always surrounded with ice. To 
measure it, a vertical graduated rule was employed, the zero of 
which was placed upon the iron bar, M N. This rule, constructed 
for another purpose with very great care, gave the height within, 
the tenth of a millimetre. But the heights measured above the 
bar, M N, are too great ; for h, h’, and r, ought to be reckoned 
from the axis of the horizontal tube. Hence from the height 
given by the rule, we must subtract half the total thickness of 
the tube. 
To enable the reader to judge of the accuracy to which these 
different operations lead, let us state one of the measures taken 
at 100°. The height of the arch, R, above the axis of the hori- 
zontal tube was 0°58520 metre, the heights r — h,r — h’, were 
respectively 0°03855 and 0:02875; therefore h = 0-54395, 
and h’ — A = 000980. And consequently the mean coeflicient 
of the absolute dilatation of mercury between 0° and 100° = 
stzx: Wesee by this, that an error of two or three tenths ofa 
millimetre on the measure of » would produce onty an uncer- 
tainty of two or three unities in the denominator of the preceding 
fraction. Thus by a particular effect of the disposition of our 
apparatus, those measures susceptible of the least precision can 
only occasion errors that may be entirely overlooked. Supposing 
that even the iron bar were a little deranged by the effect of the 
fire (though we always took care to make it horizontal by means 
of the levels), it would produce but very little effect upon the 
final result. 
