Fuly 29, 1886 | 
NATURE 291 
by the amount of the force per lineal centimetre. In any 
place where the surface is concave the effect of the sur- 
face tension is to suck outwards—that is to say, in 
mathematical language, to exert negative pressure inwards. 
Now, suppose in an instant the rigidity to be annulled, 
and the piece of glass which you see, still undisturbed by 
gravity, to become water. The instantaneous effect of 
these unequal pressures over its surface will be to set it 
in motion. If it were a perfect fluid it would go on 
vibrating for ever with wildly-irregular vibrations, start- 
ing from so rude an initial shape as this which I hold in 
my hand. Water, as any other liquid, is in reality vis- 
cous, and therefore the vibrations will gradually subside, 
and the piece of matter will come to rest in a spherical 
figure, slightly warmed as the result of the work done by 
the forces of mutual attraction by which it was set in 
motion from the initial shape. The work done by these 
forces during the change of the body from any one shape 
to any other is in simple proportion to the diminution of 
the whole surface area; and the configuration of equili- 
brium, when there is no disturbance from gravity, or from 
any other solid or liquid body, is the figure in which the 
surface area is the smallest possible that can enclose the 
given bulk of matter. 
Fic. 3. 
I have calculated the period of vibration of a sphere of 
water! (a dew-drop !) and find it to be $a’, where ais 
the radius measured in centimetres ; thus— 
For a radius of 4 cm. the period is ;4: second 
1 
” I ” ” cs ” 
” 2°54 55 LB] I ” 
” 4 22 29 2 ” 
3 16 29 ” 16 9 
” 30) Fs ys 36! ss 
” 1407 a7 ” 13,200 ” 
The dynamics of the subject, so far as a single liquid is 
concerned, is absolutely comprised in the mathematics 
‘without symbols which I have put before you. Twenty 
pages covered with sextuple integrals could tell us no 
more, 
Hitherto we have only considered mutual attraction 
between the parts of two portions of one and the same 
liquid—water for instance. Consider, now, two different 
kinds of liquid: forinstance, water and carbon disulphide 
(which, for brevity, I shall call sulphide). Deal with them 
* See paper by Lord Rayleigh in Prec. Roy. Soc., No. 196, May 5s, 1879. 
" 
exactly as we dealt with the two pieces of water. I need 
not go through the whole process again; the result is 
obvious. Thirty times the excess of the sum of the surface- 
tensions of the two liquids separately, above the tension 
of the interface between them, is equal to the work done 
in letting the two bodies come together directly over the 
Bicwds 
supposed area of thirty square centimetres. Hence the 
interfacial tension per unit area of the interface ts equal to 
the excess of the sum of the surface-tenstons of the two 
liquids separately, above the work done in letting the two 
bodies come together directly so as to meetin a untt area 
of each. >In the particular case of two similar bodies 
————— 
ge 
————— ee 
A 
~, 
. 
= 
Fic. 5. 
coming together into perfect contact, the interfacial tension 
must be zero, and therefore the work done in letting them 
come together over a unit area must be exactly equal to 
twice the surface-tension ; which is the case we first con- 
sidered. 
If the work done between two different liquids in letting 
