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.
I myself have made this experiment in a modified, and, as I think, more advantageous form. Instead of determining the work of friction by special trial, I arranged my apparatus so that it was eliminated of itself in the measurement and could consequently be neglected. The so-called fixed disk of the machine, the axis of which is placed vertically, is suspended somewhat like a chandelier by three vertical threads of equal lengths l at a distance r from the axis. Only when the machine is excited does this fixed disk, which represents a Prony's brake, receive, through its reciprocal action with the rotating disk, a deflexion α and a moment of torsion which is expressed by D = (Pr2/l)α, where P is the weight of the disk.[37] The angle α is determined by a mirror set in the disk. The work expended in n rotations is given by 2nπD.