MECHANICS. 
vein has a tendency to enlarge itfelf. Now in the widening 
cone the pipe admits of this augmentation, at the fame 
time that it increafes the velocity; but the cylindrical 
pipe, though it equally inoreaf'es the velocity, yet it does 
not permit the vein to enlarge itfelf 5 and, by thus con¬ 
fining it, the efflux is obltruCted, and the: quantity dif- 
charged in a given time is diminifhed. Accordingly, 
under the receiver of an air-pump, even in a moderate 
degree of exhauftion, there is no difference perceived 
between the velocities with which a fluid is difcharged 
through a conical or a cylindrical pipe.” 
Of Capillary Attraction, and the Cohesion of 
Fluids. 
We have already feen, when difcuffing the equilibrium 
of fluids, that, when water or any other-fluid is poured 
into a veffel, or any number of communicating veflels, its 
furface will be horizontal, or it will rile to the lame height 
in each veffel, whatever be its form or polition. This 
pfopofition, however, only holds true when the diameter 
of thefe veflels or tubes exceeds the fifteenth of an inch ; 
for, if a fyftem of communicating veflels be compofed of 
tubes of various diameters, the fluid will rife to a level 
furface in all the tubes which exceed one-fifteenth of an 
inch in diameter ; but, in the tubes of a fmaller bore, it 
will rife above that level, to altitudes inverfely propor¬ 
tional to the diameters of the tubes. The power by which 
the fluid is raifed above its natural level is called capillary 
attraction, and the glals tubes which are employed to exhibit 
its phenomena are named capillary tubes. Thefe appella¬ 
tions derive their origin from the Latin word capillus, fig- 
nifying a hair, either becaufe the bores of thefe tubes have 
almolt the finenefs of a hair, or becaufe that ftibftance is 
itfelf fuppofed to be of a tubular ftruCture. 
When we bring a piece of clean .glafs in contaCt with 
water or any other fluid, except mercury and fufed me¬ 
tals, and withdraw it gently from its furface, a portion of 
the fluid will not only adhere to the glafs, but a fmall 
force is neceffary to detach this glafs from the fluid mafs, 
which feems to refill: any feparation of its parts. Hence 
it is obvious that there is an attraElion of cohejion between 
glafs and water, and.that the conltituent particles of wa¬ 
ter have' alfo an attraction for each other. The fufpen- 
fion of a drop of water from the lower fide of a plate of 
glafs is a more palpable illuftraiion of the firft of thefe 
truths; and the following experiment will completely 
verify the fecond : Place two large drops of water on a 
fmooth metallic furface, their diitance being about the 
tenth of an inch ; with the point of a pin unite thefe 
drops by two parallel canals, and the drops will inftantly 
rulh to each other through thefe canals, and fill the dry 
fpace that intervenes. This experiment is exhibited in 
fig. 25. where A B is the metallic plate; C, D, the drops 
of water ; and m, n, the two canals. 
Upon thefe principles many attempts have been made 
to account for the rifing of water in capillary tubes; but 
all the explanations which Have hitherto been offered, 
are founded upon hypothelis, and are very far from being 
1 'atisfaCtory. Without prefuming to fubftitute a better 
explanation in the room of thofe which have been already 
given, and fo frequently repeated, we (hall endeavour to 
illuftrate that explanation of the phenomena of capillary 
attraction which feems liable to the feweft objections. 
For this purpofe let E, in the fame figure, be a drop of 
water laid upon a clean glafs furface A B. Every particle 
of the glafs immediately below the drop E exerts an at¬ 
tractive force upon the particles of water. This force 
will produce the fame effeCV upon the drop as a preifure 
in the oppolite direction; the pteffure of a column of air, 
for inflance, on the upper furface of the drop. The ef¬ 
fect of 1 he attractive force, therefore, tending to prefs the 
drop to the glals, will be an enlargement of its fize, and 
the water will occupy the fpace F G ; this increafe of its 
dimenlions will take place when the furface A B is held 
downwards 5 and that it does not arife from atmofpheric 
719' 
preffure may be fhown by performing the experiment in- 
vacuo. Now let A B, fig. 26, be a Section of the plate of 
glals held vertically; part of the water will defcend by 
its gravity, and form a drop B, while a fmall film of the 
fluid will be iupported at m by the attraction of the glafs. 
Bring a fnnilar plate of glafs C D into a pofition parallel 
to AB, and make them approach nearer and nearer each 
other. When the drops B and D come in contact, they 
will rufh together from their mutual attraction, and will 
fill the fpace op. The gravity of the drops B and D being 
thus diminifhed, the film of water at m and n, which was 
prevented from rifing by their gravity, will move upwards. 
As the plates of glals continue to approximate, the fpace 
between them vs ill fill with water, and the films at m and 
n, being no longer prevented from yielding to the aCtion 
of the glafs immediately below them (by the gravity of 
the water at op, which is diminifhed by the mutual action 
of the fluid particles), will rife higher in proportion to 
the approach of the plates. Hence it may be eafily un¬ 
derflood how the water rifes in capillary tubes, and how 
its altitude is inverfely as their internal diameters. For, 
let A, a, be the altitudes of tfie fluid in two tube3 of dif¬ 
ferent diameters D, d\ and let C, c, be the two cylinders 
of fluid which are raifed by virtue of the attraction of the 
glafs. Now, as the force which rifes the fluid mull be as 
the number of attracting particles, that is, as the furface of 
the tube in contaCt with the water, that is, as the diameter 
of the tubes, and as this fame force muft be proportioned 
to its effeCts on the cylinder of water raifed, we (hall have 
D : d— C : c. But C : ca=D 2 A : d 2 a-, therefore D 2 A : 
1 d 2 aD 
d 2 a —D : d ; hence D 2 A d—d 2 aD, and DA:=—or 
DA —da, that is, D : d=.a : A, or the altitudes of the 
water are inverfely as the diameters of the tubes. Since 
D A—da, the product of the diameter by the altitude of 
the water will always be a conftant quantity. In a tube 
whofe diameter is 0 01, or of an inch, the water,has 
been found to reach the altitude of 5'3 inches; hence the 
conltant quantity 5^3 X o , oi=o o53 may fitly reprefent 
the attraction of glafs for water. According to the expe¬ 
riments of Mufchenbroek, the conltant quantity is 0'039 ; 
according to Weitbrecht o'o^S ; according to Monge 
o - o42, and according to Atwood o’o53. When a glafs 
tube was immerfed in melted lead, Geiiart found the de- 
preffion multiplied by the bore to be o - oo54. 
Having thus attempted to explain the caufes of capil¬ 
lary aCtion, we fnall now proceed to confider fome of its 
molt interefting phenomena. In fig. 27, M N is a veffel 
of water in which tubes of various forms are immerfed. 
The water will rife in the tubes A, B, C, to different al¬ 
titudes m, n,'0, inverfely proportioned to their diameters^ 
If the tube B is broken at a, the water w ill not rife to the 
very top of it at a, but will ftand at b, a little below tiis 
top, whatever be the length of the tube or the diameter 
of its bore. If the tube be taken from the fluid and laid 
in a horizontal pofition, the water will recede from the 
end that was immerfed. Thefe two faCts feem to coun¬ 
tenance ftie opinion of Dr. Jurin and other phiiofophers, 
(Phil. Tranf. N° 363. Art. 2.) that the water is elevated in 
the tube by the attraction of the annulus, or ring of glafs, 
immediately above the cylinder of water. This hypothelis 
is fofficiently plaufible"; but, fuppofing it to be true, the 
ring of glafs immediately below the furface of the cylin- 
derof fluid lhottld produce an equal and oppofite effect, and 
therefore the water inftead of rifing (hould be Itacionary, be¬ 
ing influenced by two forces of an equal and oppofite kind. 
If a tube D, cornpofed of two cylindrical tubes of dif¬ 
ferent bores, be immerfed in water with the widell pare 
downwards, the water will rife to the altitude p: ; and, if 
another tube E, of the fame fize and form, be plunged in 
the fluid with the Smaller end downwards, the water will 
rife to the fame height q as it did in the tube D. This 
experiment feems to be a complete refutation of the opi¬ 
nion of Dr. Jurin, that the water is raifed by the aCtion 
of the annulus of glafs above the fluid column 3 for, flnee 
the 
