Fuly 22, 1886] 
NAROKLE 
271 
matter in one body and any particle of matter in another 
continue to vary inversely as the square of the distance, 
when the distance between the nearest points of the two 
bodies is diminished to an inch (Cavendish’s experiment 
does not demonstrate this, but makes it very probable), 
or to a centimetre, or to the hundred-thousandth of a 
centimetre, or to the hundred-millionth of a centimetre ? 
Now I dip my finger into this basin of water; you see 
proved a force of attraction between the finger and the 
drop hanging from it, and between the matter on the two 
sides of any horizontal plane you like to imagine through 
the hanging water. These forces are millions of times 
greater than what you would calculate from the Newtonian 
law, on the supposition that water is perfectly homo- 
geneous. Hence either these forces of attraction must, at 
very small distances, increase enormously more rapidly 
than according to the Newtonian law, or the substance of 
water is not homogeneous. We now all know that it is 
not homogeneous. The Newtonian theory of gravitation 
is not surer to us now than is the atomic or molecular 
theory in chemistry and physics ; so far, at all events, as its 
assertion of heterogeneousness in the minute structure of 
matter apparently homogeneous to our senses and to our 
most delicate direct instrumental tests. Hence, unless we 
find heterogeneousness and the Newtonian law of attrac- 
tion incapable of explaining cohesion and capillary at- 
traction, we are not forced to seek the explanation in a 
deviation from Newton’s law of gravitational force. Ina 
little communication to the Royal Society of Edinburgh 
twenty-four years ago,' I showed that heterogeneousness 
does suffice to account for any force of cohesion, however 
great, provided only we give sufficiently great density to 
the molecules in the heterogeneous structure. 
Nothing satisfactory, however, or very interesting 
mechanically, seems attainable by any attempt to work out 
this theory without taking into account the molecular 
motions which we know to be inherent in matter, and to 
constitute its heat. But so far as the main phenomena of 
capillary attraction are concerned, it is satisfactory to 
know that the complete molecular theory could not but 
lead to the same resultant action in the aggregate as if 
water and the solids touching it were each utterly homo- 
geneous to infinite minuteness, and were acted on by 
mutual forces of attraction sufficiently strong between 
portions of matter which are exceedingly near one another, 
but utterly insensible between portions of matter at sen- 
sible distances. This idea of attraction insensible at 
sensible distances (whatever molecular view we may learn, 
or people not now born may learn after us, to account for 
the innate nature of the action), is indeed the key to the 
theory of capillary attraction, and it is to Hawksbee® that 
we owe it. Laplace took it up and thoroughly worked it 
out mathematically in a very admirable manner. One 
part of the theory which he left defective—the action of a 
solid upon a liquid, and the mutual action between two 
liquids—was made dynamically perfect by Gauss, and the 
finishing touch to the mathematical theory was given by 
Neumann in stating for liquids the rule corresponding to 
Gauss’s rule for angles of contact between liquids and 
solids. 
Gauss, expressing enthusiastic appreciation of Laplace’s 
work, adopts the same fundamental assumption of attrac- 
tion sensible only at insensible distances, and, while pro- 
posing as chief object to complete the part of the theory 
not worked out by his predecessor, treats the dynamical 
problem afresh in a remarkably improved manner, by 
founding it wholly upon the principle of what we now call 
potential energy. Thus, though the formulas in which he 
expresses mathematically his ideas are scarcely less 
alarming in appearance than those of Laplace, it is very 
easy to translate them into words by which the whole theory 
will be made perfectly intelligible to persons who imagine 
' Proceedings of the Royal Society of Edinburgh, April 21, 1862 (vol. iv.). 
* Royal Society 7rausactions, 1709-13. 
themselves incapable of understanding sextuple integrals. 
Let us place ourselves conyeniently at the centre of the 
earth so as not to be disturbed by gravity. Take now 
two portions of water, and let them be shaped over a 
certain area of each, call it A for the one, and B for the 
other, so that when put together they will fit perfectly 
throughout these areas. To save all trouble in manipu- 
lating the supposed pieces of water, let them become for 
a time perfectly rigid, without, however, any change in 
their mutual attraction. Bring them now together till the 
two surfaces Aand B come to be within the one-hundred- 
thousandth of an inch apart, that is, the forty-thousandth 
of a centimetre, or two hundred and fifty micro-millimetres 
(about half the wave-length of green light). At so great 
a distance the attraction is quite insensible; we may feel 
very confident that it differs, by but a small percentage, from 
the exceedingly small force of attraction which we should 
calculate for it according to the Newtonian law, on the 
supposition of perfect uniformity of density in each of the 
attracting bodies. Well known phenomena of bubbles, 
and of watery films wetting solids, make it quite certain 
that the molecular attraction does not become sensible 
until the distance is much less than 250 micro-millimetres. 
From the consideration of such phenomena Quincke 
(Pogg. Ann., 1869) came to the conclusion that the mole- 
cular attraction does become sensible at distances of 
about fifty micro-millimetres. His conclusion is strikingly 
confirmed by the very important discovery of Reinold and 
Riicker that the black film, always formed before an un- 
disturbed soap bubble breaks, has a uniform or nearly 
uniform thickness of about eleven or twelve micro-milli- 
metres. The abrupt commencement, and the permanent 
stability, of the black film demonstrate a proposition of 
fundamental importance in the molecular theory :—The 
tension of the film, which is sensibly constant when the 
thickness exceeds fifty micro-millimetres, diminishes to a 
minimum, and begins to increase again when the thickness 
is diminished to ten micro-millimetres. It seems not pos- 
sible to explain this fact by any imaginable law of force 
between the different portions of the film supposed homo- 
geneous, and we are forced to the conclusion that it 
depends upon molecular heterogeneousness. When the 
homogeneous molar theory is thus disproved by observa- 
tion, and its assumption of a law of attraction augmenting 
more rapidly than according to the Newtonian law when 
the distance becomes less than fifty micro-millimetres is 
proved to be insufficient, may we not go farther and say 
thet it is unnecessary to assume any deviation from the 
Newtonian law of force varying inversely as the square of 
the distance continuously from the millionth of a micro- 
millimetre to the remotest star or remotest piece of 
matter in the universe; and, until we see how gravity 
itself is to be explained, as Newton and Faraday thought 
it must be explained, by some continuous action of inter- 
vening or surrounding matter, may we not be temporarily 
satisfied to explain capillary attraction merely as New- 
tonian attraction intensified in virtue of intensely dense 
molecules movable among one another, of which the 
aggregate constitutes a mass of liquid or solid. 
But now for the present, and for the rest of this evening, 
let us dismiss all idea of molecular theory, and think of 
the molar theory pure and simple, of Laplace and Gauss. 
Returning to our two pieces of rigidified water left at a 
distance of 250 micro-millimetres from one another. 
Holding them in my two hands, I let them come nearer 
and neerer until they touch all along the surfaces A and 
B, They begin to attract one another with a force which 
may be scarcely sensible to my hands when their distance 
apart is fifty micro-millimetres, or even as little as ten 
micro-millimetres ; but which certainly becomes sensible 
when the distance becomes one micro-millimetre, or the 
fraction of a micro-millimetre ; and enormous, hundreds 
or thousands of kilogrammes’ weight, before they come 
into absolute contact. Iam supposing the area of each 
