y large bore.

But although a complete solution of the dynamical problem is
impracticable, much interesting information may be obtained from the
principle of dynamical similarity. The argument has already been applied
by Dupre (_Theorie mecanique de la chaleur_, Paris, 1869, p. 328), but
his presentation of it is rather obscure. We will assume that when, as
in most cases, viscosity may be neglected, the mass (M) of a drop
depends only upon the density ([sigma]), the capillary tension (T), the
acceleration of gravity (g), and the linear dimension of the tube (a).
In order to justify this assumption, the formation of the drop must be
sufficiently slow, and certain restrictions must be imposed upon the
shape of the tube. For example, in the case of water delivered from a
glass tube, which is cut off square and held vertically, a will be the
external radius; and it will be necessary to suppose that the ratio of
the internal radius to a is constant, the cases of a ratio infinitely
small, or infinitely near unity, being included. But if the fluid be
mercury, the flat end of the tube remains unwetted, and the formation of
the drop depends upon the internal diameter only.

The "dimensions" of the quantities on which M depends are:--

[sigma] = (Mass)^1 (Length)^(-3),
T = (Force)^1 (Length)^(-1) = (Mass)^1 (Time)^(-2),
g = Acceleration = (Length)^1 (Time)^(-2),

of which M, a mass, is to be expressed as a function. If we assume

M [approximately equals] T^{x}.g^{y}.[sigma]^{z}.a^{u},

we have, considering in turn length, time and mass,

y - 3z + u = 0, 2x + 2y = 0, x + z = 1;

so that

y = -x, z = 1 - x, u = 3 - 2x.

Accordingly

Ta / T \x-1
M ~ --- ( ----------- ).
g \g[sigma]a^2/

Since x is undetermined, all that we can conclude is that M is of the
form

Ta / T \
M = ---.F( ----------- ), (1)
g \g[sigma]a^2/

where F denotes an arbitrary function.

Dynamical similarity requires that T/g[sigma]a^2 be constant; or, if g
be supposed to be so, that a^2 varies as T/[sigma]. If this condition be
satisfied, the mass (or weight) of the drop is proportional to T and to
a.

If Tate's law be true, that _ceteris paribus_ M varies as a, it follows
from (1) that F is constant. For all fluids and for all similar tubes
similarly wetted, the weight of a drop would then be proportional not
only to the diameter of the tube, but also to t