144
KINETIC ENERGY OF ELECTRICITY IN MOTION [II]
IV
=
density, measured electrostatically, divided by the velocity v;
hence m Mv/i and X = 4w.Mv2/i = 4iw. Mv²/i2. Now with-
out altering the equation we may use magnetic units on both
sides; if we do so, Mv2/i² = Mv2/3 is that quantity which in
the introduction is denoted by μ, and thus X = 4μiw. Here
we put for the current-density i the quotient of the total
current-strength J by q, the cross-section of the conductor, and
for the electromotive intensity X the quotient of 4, the differ-
ence of potential between the points C and D, by b, the breadth
of the plate; if we call its mean thickness d, then we get
$ = 4μJwb/q = 4μJw/d, or, as we require μ,
=
με
фя φα
4Jbw 4Jw
=
We may approximately calculate the cross-section q or
the thickness d from the amount of silver deposited; but it is
more rational, as well as more accurate, to determine it from
the electrical resistance of the plate, for this resistance depends
directly on the mean velocity with which the electricity flows
through the plate, and we are concerned with just this velocity
and only indirectly with the cross-section. As the conduction
was doubtless metallic we must take for the specific resistance
of the conducting material that of silver; from the length of
the plate 45 mm., and its mean resistance
= 5.1 Siemens
units, we get the required cross-section q = 0.00014 mm², and
the corresponding thickness d= 0.6 x 10-6 mm. It is true
this thickness is only about one-tenth of that deduced from
the amount of silver deposited; but this only shows what
was very probable before, namely, that the silver is very un-
equally distributed over the glass. Employing the value thus
obtained for the thickness, we put J=117 mg* mm* sec-¹,
∞ = 2π × 34 sec-1, p=1 scale division = 1/32 × 106 of a
Daniell = 3300 mg mm² sec-¹; and thus find μ= 0.0000185
mm². Thus μ appears as an area, namely, energy divided by
the unit of the square of a magnetic current-density and by
the unit of volume. Since the value 1 scale division was
found to be extremely improbable, the statement made in the
introduction is justified. Even if the assumptions made in
calculating the experiments were only very rough approxima-
w
=