1895-96.] Lord Kelvin on the Motion of a Liquid, 
121 
every particle of the liquid is brought to rest at the same instant. 
But it is not so with a heterogeneous liquid. Of the following 
conclusions Nos. (1), (2), (3) need no proof. To prove No. (4) 
remark that as long as there is any motion of the heterogeneous 
liquid within the imperfectly elastic vessel the liquid must he 
losing energy ; and the energy cannot become infinitely small with 
any finite spherical portion of the liquid homogeneous. 
(1) The initial motion of a heterogeneous liquid is irrotational 
only at the first instant after being quite suddenly started from 
rest by motion of its boundary. Whatever motion be subsequently 
given to the boundary the motion of the liquid is never again 
irrotational. Hence 
(2) If the boundary be suddenly brought to rest at any time, the 
liquid, unless homogeneous throughout, is not thereby brought 
to rest ; and it would go on for ever with undiminished energy 
if the liquid were perfectly inviscid and the boundary absolutely 
fixed. The ultimate condition of the liquid, if there is no 
positive surface tension in the interfaces between heterogeneous 
portions, is an infinitely fine mixture of the heterogeneous parts.* 
And, if there were no gravity or other bodily force acting on 
the liquid, the density would ultimately become uniform through- 
out. Take, for example, a corked bottle half full of water or 
other liquid with air above it given at rest. Move the bottle 
and bring it to rest again : the liquid wall remain shaking for 
some time. An ordinary non-scientific person will scarcely thank 
us for this result of our mathematical theory. But, when we 
tell him that if air and the liquid were both perfectly fluid (that 
is to say perfectly free from viscosity), the well-known shak- 
ing of the liquid surface would, after a little time, give rise to 
spherules tossed up from the main body of the liquid ; and that 
the shaking of the liquid, left to itself in the bottle supposed 
perfectly rigid, will end in spindrift of spherules which would be 
infinitely fine if the capillary tension of the interface between 
* Popular Lectures and Addresses, by Lord Kelvin, vol. i. pp. 19, 20, 
and 53, 54. See also Philosophical Magazine, 1887, second half-year: “On 
the formation of corelees vortices by the motion of a solid through an inviscid 
incompressible fluid”; “On the stability of steady and of periodic fluid 
motion ” ; “On maximum and minimum energy in vortex motion.” 
