er = CE, and during the time, [tau], the number of
[tau]
discharges = -----, t being the fixed time between two discharges;
t
[tau] and t are here supposed to be expressed by the aid of an
arbitrary unit of time; the second circuit yields, therefore, a
[tau]
quantity of electricity equal to CE x -----. The condition of
t
E [tau]
equilibrium is then ---[tau] = CE x ----- ; or, more simply, t = CR.
R t
C and R are known in absolute values, i.e., we know that C is equal to
_p_ times the capacity of a sphere of the radius, _l_; we have,
therefore, C = _pl_; in the same manner we know that R is equal to _q_
times the resistance of a cube of mercury having l for its side. We
l [rho]
have, therefore, R = q[rho] --- = q ----- ; and consequently t = pq[rho].
l squared l

Such is the value of _t_ obtained on leaving all the units
undetermined. If we express [rho] as a function of the second, we have
_t_ in seconds. If we take [rho] = 1, we have the absolute value
[Theta] of the same interval of time as a function of this unit; we
have simply [Theta] = _pq_.

If we suppose that the commutator which produces the successive
charges and discharges of the condenser consists of a vibrating tuning
fork, we see that the duration of a vibration is equal to the product
of the two abstract numbers, _pq_.

It remains for us to ascertain to what degree of approximation we can
determine _p_ and _q_. To find _q_ we must first construct a column of
mercury of known dimensions; this problem was solved by the
International Bureau of Weights and Measures for the construction of
the legal ohm. The legal ohm is supposed to have a resistance equal to
106.00 times that of a cube of mercury of 0.01 meter, side
measurement. The approximation obtained is comprised between 1/50000
and 1/200000. To obtain _p_, we must be able to construct a plane
condenser of known capacity. The difficulty here consists in knowing
with a sufficient approximation the thickness of the stratum of air.
We may employ as armatures two surfaces of glass, ground optically,
silvered to render them conductive, but so slightly as to obtain by
transparence Fizeau's interference rings. Fizeau's method will then
permit us to arrive at a