a Barometer, depending on its capillary Action. 105 
2. sin? = Ve, The depression of the mercury in the baro- 
meter is =. (Suppl. Th. del’ Act. Cap. p.59...) The for- 
mule for z, and for & (p. 60) give the following series, which 
haye been employed for depressions less than *S millimetre : 
& = — (2'8960566.u? 4 3-1700532.u* + 5°1018673.0° + 
$-7838040.« + 10-2719206.u'.,.), and tangV = — 
(1-1870866.z + 3,7721132 .u? + 5.8S00186.u5 4- 7.6868940.w7 
+ 9°'2719206.u? + ...): the coefficients of the powers of u 
being here represented by their logarithms, for the assistance of 
the calculation; and the figures distinguished by a horizontal 
stroke being negative indices. In this manner, by assigning to 
z such a value that V should be between four and six decimal 
degrees, the corresponding ordinates have been very accurately 
determined for this inclination of the end of the curve: hence, 
by means of the preceding formule, these ordinates have been 
ealculated for V = 6°, and this angle has been successively in- 
creased by two degrees at each step still it became 12°, and 
then by four degrees as far as V = 52°. , 
In order to arrange the results obtained by this method in a 
table calculated for equal increments of the diameter of the tube, 
I have observed that the differences of the logarithins of the de- 
pressions form in this case a series which varies but very slowly. 
By means of this property, | have obtained without difficulty 
the following table, the principal calculations having been 
obligingly furnished me by Mr. Bouvard: and the same property 
will also serve for the interpolation of the table. 
We find in Nicholson’s Journal for October 1809, a similar 
table, formed by the expansion of the expressions for z and 
sin V into a series, and founded on elements differing but little 
from those which we have employed. ‘These two tables agree 
very nearly with each other, and with that which Lord Charles 
Cavendish had deduced from experiments. But the method 
which we have just explained appears to me to be more 
accurate {??], and more convenient for calculation [??]5 it has 
besides the advantage {??] of showing the influence of the varia- 
tion of the angle of contact of the surface of the mereury with 
the tube on the capillary action. Jt is well known that by the 
friction of the mercury against the sides of the tube, and per- 
haps also by a peculiar viscosity of the liquid, the angle is liable 
to 
