[Footnote 35: The energy of a sphere of radius _r_ charged with the quantity _q_ is 1/2(_q_²/_r_). If the radius increase by the space _dr_ a loss of energy occurs, and the work done is 1/2(_q_²/_r_²)_dr_. Letting _p_ denote the uniform electrical pressure on unit of surface of the sphere, the work done is also 4_r_²[pi]_pdr_. Hence _p = (1/8r²[pi])(q²/r²)_. Subjected to the same superficial pressure on all sides, say in a fluid, our half sphere would be an equilibrium. Hence we must make the pressure _p_ act on the surface of the great circle to obtain the effect on the balance, which is _r²[pi]p = 1/8(q²/r²) = 1/8V²_.] [Footnote 36: The arrangement described is for several reasons not fitted for the actual measurement of potential. Thomson's absolute electrometer is based upon an ingenious modification of the electrical balance of Harris and Volta. Of two large plane parallel plates, one communicates with the earth, while the other is brought to the potential to be measured. A small movable superficial portion _f_ of this last hangs from the balance for the determination of the attraction _P_. The distance of the plates from each other being _D_ we get _V = D[sqrt](8[pi]P/f)_.] [Footnote 37: This moment of torsion needs a supplementary correction, on account of the vertical electric attraction of the excited disks. This is done by changing the weight of the disk by means of additional weights and by making a second reading of the angles of deflexion.] [Footnote 38: The jar in our experiment acts like an accumulator, being charged by a dynamo machine. The relation which obtains between the expended and the available work may be gathered from the following simple exposition. A Holtz machine _H_ (Fig. 40) is charging a unit jar _L_, which after _n_ discharges of quantity _q_ and potential _v_, charges the jar _F_ with the quantity _Q_ at the potential _V_. The energy of the unit-jar discharges is lost and that of the jar _F_ alone is left. Hence the ratio of the available work to the total work expended is _½QV/[½QV + (n/2)qv]_ and as _Q = nq_, also _V/(V + v)_. If, now, we interpose no unit jar, still the parts of the machine and the wires of conduction are themselves virtually such unit jars and the formula still subsists _V/(V + [sum]v)_, in which [sum]_v_ represents the sum of all the successively introduced differences of potential in the circuit of connexion.] ON THE PRINCIPLE OF THE CONSERVATION OF ENERGY.[39]