_W = 1/2Kh²_ and _W = Q²/2K_.
[Illustration: Fig. 38.]
[Illustration: Fig. 39.]
As a special case let us consider our jar. Its capacity is _C_ =
3700, its potential _V_ = 110; accordingly, its quantity _Q = CV_ =
407,000 electrostatic units and its energy _W = 1/2QV_ = 22,385,000
C. G. S. units of work.
The unit of work of the C. G. S. system is not readily appreciable
by the senses, nor does it well admit of representation, as we are
accustomed to work with weights. Let us adopt, therefore, as our
unit of work the gramme-centimetre, or the gravitational pressure of
a gramme-weight through the distance of a centimetre, which in round
numbers is 1000 times greater than the unit assumed above; in this
case, our numerical result will be approximately 1000 times smaller.
Again, if we pass, as more familiar in practice, to the
kilogramme-metre as our unit of work, our unit, the distance being
increased a hundred fold, and the weight a thousand fold, will be
100,000 times larger. The numerical result expressing the work done
is in this case 100,000 times less, being in round numbers 0.22
kilogramme-metre. We can obtain a clear idea of the work done here
by letting a kilogramme-weight fall 22 centimetres.
This amount of work, accordingly, is performed on the charging of
the jar, and on its discharge appears again, according to the
circumstances, partly as sound, partly as a mechanical disruption of
insulators, partly as light and heat, and so forth.
The large battery of the Prague physical laboratory, with its
sixteen jars charged to equal potentials, furnishes, although the
effect of the discharge is imposing, a total amount of work of only
three kilogramme-metres.
In the development of the ideas above laid down we are not
restricted to the method there pursued; in fact, that method was
selected only as one especially fitted to familiarise us with the
phenomena. On the contrary, the connexion of the physical processes
is so multifarious that we can come at the same event from very
different directions. Particularly are electrical phenomena
connected with all other physical events; and so intimate is this
connexion that we might justly call the study of electricity the
theory of the general connexion of physical processes.
With respect to the principle of the conservation of energy which
unites electrical with mechanical phenomena, I should like to point
out briefly two ways of following up the study of this connexion.
A few years ago Professor Rosetti, taking an influence-machine,
which he set in motion by means of weights alternately in the
electrical and non-electrical condition with the same velocities,
determined the mechanical work expended in the two cases and was
thus enabled, after deducting the work of friction, to ascertain the
mechanical work consumed in the development of the electricity.
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