ved, and the system tends to assume the singular form which d. I have several times repeated the experiment, varying as much as possible, and the same effects are always pro

this memoir I shall point out another process for obtaining it is an extremely simple one, and has moreover the advanall the systems in a complete state.

ing our observations upon polyhedric liquids, I shall remark -r prism may be employed to produce the phenomena of disway a beautiful solar spectrum may be obtained by means of id faces. But as the effect only depends upon the excess of tion of the oil above that of the alcoholic liquid, to obtain a ended spectrum the angle of refraction of the prism must be of 1100 gives a very good result. Moreover, it is evidently faces of the prism should be perfectly plane, which is obtained ully made frame; by establishing exact equilibrium between e liquids; and, lastly, by arresting the action of the syringe roper point.

ture at every point; we know that one of these ure of the meridional line, and that the other is 3 line which is included between the point under revolution. We shall now endeavor to obtain

ur solid system be composed of two rings of iron parallel, and placed opposite to each other. One s rests upon the base of the vessel by three feet iron wire; the other is attached, by means of an piece, to the axis traversing the central stopper, y be approximated to or removed from the former ig or elevating this axis. The system formed o rings is represented in Plate VII, Fig. 20 bis; of those which I employed was 7 centimeters. ing raised the upper ring as much as possible, of oil, of a slightly larger diameter than that of e formed, and conducted towards the lower ring anner as to make it adhere to the entire circumhe latter; then depress the upper ring until it uid mass, and the latter is uniformly attached to become adherent to the system of the two rings, er ring be slowly raised; when the two rings are distance apart, the liquid will then assume the ertical projection of which is represented in Fig. h the lines a b and c d are the projections of the e two portions of the surface which are respected to each of the rings are convex spherical segthe portion included between the two rings congure of revolution, the meridional curve of which, ily. We shall recur, in the following series, to If we now continue gradually to raise the upper extremities and the meridional curvature of the iminished; and if there is exact equilibrium bensity of the oil and the surrounding liquid, the ed between the two rings will be seen to assume lindrical form, (Fig. 22.) The two bases of the re still convex spherical segments, but their curthan in the preceding figure. If the interval ngs be still further increased, it is evident that cluded between them would lose the cylindrical at a new figure would result. This is what of the figure thus produced must be deferred.

ly increasing the distance between the rings, let tain quantity of oil to the mass, which will again

are now about to describe, the short axis represented in and which has hitherto answered our purpose, must be timeters in length.

the first. If we repeat the sam
shall ultimately obtain the cylin
permits. I have in this manne
timeters in diameter, and about
of the cylinder of this consideral
fect equality be established betv
liquid. As a very slight differe
ascend or descend, the latter ass
the two forms represented in Fig
obtained by the proper addition
sien may require, (§ 24 of the p
ture are sufficient to alter and rep

39. Let us now examine the
point of view. First, it is evident
condition of equilibrium of liqui
same at every point. Moreover,
except in that of the meridional
corresponding to it ought to be g
face. The same conclusions are
(3) of paragraphs 4 and 5. In fa
one of the quantities R and R' is
and the other is the portion of t
point under consideration and the
cylinder, the meridional line bein
where infinitely great; and, on
parallel to the axis of revolution,
the second radius of curvature

cylinder. Hence it follows that

appears, and that the other is co stant, and consequently the condi denote by the radius of the cy this surface would become

Now being positive because it
(4) the above value is greater t

repeat the same manipulation a suitable number of times, we obtain the cylinder of the greatest height which our apparatus e in this manner obtained a perfectly cylindrical mass 7 ceneter, and about 14 centimeters in height, (Fig. 23.) To allow -f this considerable height being perfect, it is requisite that perestablished between the densities of the oil and the alcoholic ery slight difference in either direction tends to make the mass and, the latter assumes, to a more or less marked extent, one of epresented in Fig. 24. Even when the cylindric form has been proper addition of alcohol of 16°, or absolute alcohol, as occare, (§ 24 of the preceding memoir,) slight changes in temperaent to alter and reproduce one of the above two forms. now examine the results of these experiments in a theoretical First, it is evident that a cylindrical surface satisfies the general quilibrium of liquid figures, because the curvatures in it are the point. Moreover, such a surface being convex in every direction of the meridional line, where there is no curvature, the pressure to it ought to be greater than that corresponding to a plane surme conclusions are deducible from the general formulæ (2) and phs 4 and 5. In fact, as we have already stated in paragraph 37, antities R and R' is the radius of curvature of the meridional line, r is the portion of the normal to this line included between the consideration and the axis of revolution. Now, in the case of the meridional line being a right line, its radius of curvature is everytely great; and, on the other hand, this same right line being he axis of revolution, that portion of the normal which constitutes radius of curvature is nothing more than the radius itself of the

1 1

Hence it follows that one of the terms of the quantity + dis-
Ꭱ R'

that the other is constant; this same quantity is, therefore, conconsequently the condition of equilibrium is satisfied. Now, if we the radius of the cylinder, the general value of the pressure for = would become

A 1 P+ 1'7'

ng positive because it is directed towards the interior of the liquid, above value is greater than P, i. c., than that which would correspond

!

e of the spherical segments constituting the the cylinder.

eter, which is the same as that of the solid ht of the spherical segments; and if by any his height in the liquid figure, we shall thus en as regards the numbers. We shall now

figure to be intersected by a meridional plane, ents will be an arc belonging to a circle, the 24, according to what we have already stated, arc will be the height of the segment. If we orming the rings to be infinitely small, so that the exact circumference of the cylinder, the be equal to 22; and if we denote the height of

of my rings, or the value of 21, correspond1.4 millimeters, which gives h - 9.57 millimehave a certain thickness, and the segments do ference of the rings, it follows that the chord less than 22, and that, consequently, the true ts is a little less than that given by the preexactly, let us denote the chord by 2c, which

= 2λ — √/ 4λ2 — c2.

ridional plane intersects each of the rings in eridional arc of the spherical segment is tanthe chord of this arc intercepts a small circular eing tangential to the sections of the wire, it ular segments are similar to that of the spheriof the latter differs but very slightly from the e are belongs, the chords of the small circular equal to the radius of the small sections, which

is moreover evident that the excess of the exf the chord c is nothing more than the excess

Bere, which gives as the true theore

crcumstances,

h=9.46

I may remark that it is difficult to d
mit of the segments, i. e., the circum
bee of the rings. To get rid of this
the segments, commencing only at the
of each segment, commencing at a
tion, and resting upon the surface of
the summit of the segment. The quan
the total height minus the versed sine
have considered above; consequently t
lar to that of the spherical segment,

versed sine, which we shall denote by

case of our liquid figure gives ƒ=0.05
h-f=9.41

This, then, is definitively the theoretical
be measured.

41. Before pointing out the process w
Communicating the result of the operat
arks. If the densities of the alcoholi
sly equal, the mass has a slight tende
of one of the segments is then a little to
little too small; but we can understand th
exact result may still be obtained by tal
We thus avoid part of those preliminary
of perfect equality between the two densi
hich requires the greatest attention is the
Two liquids. If this condition be not fulfil
ture, i. e., if the upper part of this mixture
proportion of alcohol than the lower por
regular and present equal segments; all
mean density of that part of the mixture,
mass, must be equal to the density of the
the level of the two segments is too low.
Begment is then in contact with a less de
quently, has a tendency to descend, whilst
ing the inferior segment. Heterogeneity
effect, i. e., it renders the height of the segu
dense portions rising to the upper part of th
most dense portions descend to the lower pa

By intentionally producing very great heterogen preceding memoir,) and employing suitable precauti formed, the bases of which are absolutely plane.

as the true theoretical height of the segments under these

h9.46 millimeters.

it is difficult to distinguish in the liquid figure the precise ats, i. e., the circumferences of contact of their surfaces with To get rid of this inconvenience, I measured the height of mencing only at the external planes of the rings; i. e., in the ent, commencing at a plane perpendicular to the axis of revoupon the surface of the ring on that side which is opposite segment. The quantity thus measured is evidently equal to inus the versed sine of the small circular segments which we bove; consequently these small circular segments being simie spherical segment, we obtain for the determination of this

h we shall denote by f, the proportion

h

figure gives ƒ=0.05 millimeters, whence

h-f 9.41 millimeters.

f

с 1

which in the

nitively the theoretical value of the quantity which was required

nting out the process which I employed for this purpose, and he result of the operation, I must preface a few important - densities of the alcoholic mixture and of the oil are not rigormass has a slight tendency to rise or descend, and the height gments is then a little too great, whilst that of the other is a but we can understand that if their difference is very small, an y still be obtained by taking the mean of these two heights. part of those preliminary experiments which the establishment lity between the two densities requires. But one circumstance the greatest attention is the perfect homogeneity of each of the f this condition be not fulfilled with regard to the alcoholic mixupper part of this mixture be left containing a slightly greater alcohol than the lower portion, the liquid figure may appear esent equal segments; all that is required for this is, that the of that part of the mixture, which is at the same level as the equal to the density of the oil; but under these circumstances e two segments is too low. In fact, the oil forming the upper en in contact with a less dense liquid than itself, and, consetendency to descend, whilst the opposite applies to the oil formr segment.* Heterogeneity of the liquid produces an opposite renders the height of the segments too great. In fact, the least rising to the upper part of the mass tend to lift it up, whilst the rtions descend to the lower part, and tend to depress it. Now,

ally producing very great heterogeneity in the alcoholic mixture, (§ 9 of the ir,) and employing suitable precautions, a perfectly regular cylinder may be es of which are absolutely plane.