After assuring himself, by experiments on a small scale, that calculation and observation gave concordant results for the flat ring, the author made an experiment on a larger scale with the annular network. For practical reasons he employed for this purpose a copper wire 2.5 mm. in diameter, which may be expected to last as long as one of iron plate 2 mm. in thickness. Calculation showed that in a ribbon 160 mm. wide, meshes 40 mm. in breadth were advantageous and favorable as regards rigidity. A reticulated ribbon like this, 4 meters in length, was made and formed into a flat ring having an external diameter of 1.42 m. and an internal one of 1.10 m. The resistance of this ring was found to be W = 0.3485 1/k, and that of a plate one meter square, W = 0.368 1/k.

As the conductivity of the earth is very variable, and as we cannot have an absolute guarantee that the ramming will be uniform, it seemed proper to make the measurements of the resistance by fixing the plate and the ring in succession to the lower surface of a small raft, in such a way that the contact with the water should correspond as well as possible to the suppositions made for the calculation. As a second ground conductor, a system of water pipes was used, and, after this, a lightning rod conductor, etc.

Repeated and varied experiments gave, for the calculation of the values of the resistances, equations so concordant that the following results may be considered very approximate.

The square plate had a resistance of 35.5 Siemens units, and the reticulated ring one of 32.5. From the first figure we deduce k = 1/91.12, that is to say, the specific conductivity of river-water is 1:91120000. Calculation, then, gives as the resistance of the earth in Siemens units:

These figures prove the accuracy of the calculations that had been made in an approximate way.

The experiments were performed upon the Elba, above Dresden. Other experiments still had reference to the influence of immersion. In order to diminish polarization, only instantaneous currents from the measuring pile were employed. It was to be supposed that the current of water through which the bubbles of gas were removed from the electrodes would not have permitted of a notable resistance of polarization. Later measurements, made upon a ribbon buried, like the plates, in the earth, gave likewise most favorable results.

As a result of these experiments, the State railways of Saxony have, in such cases as were practicable, introduced the annular network of copper. There are some manufacturers, too, who seem desirous of adopting this system, although it has hardly emerged from the period of experiment. The pecuniary advantages that will result from an application of it ought, it would seem, to dispel a large proportion of the criticisms directed against the erection of lightning rods, from the standpoint of expense, and contribute to extend an arrangement which may be considered as a very happy one.

If we compare the square plate with the equivalent annular network, constructed as above indicated, and which should possess, according to the author an external diameter of 1.26 m. and of 3.45 m., we find that:

The cost of reticulated ribbon per meter amounts to about 4.4 francs, supposing it to be arranged as shown in the cut.

As term of comparison, we may admit that the following forms are nearly the equivalent of a horizontal, unburied plate one meter square.

Horizontal flat ring 1.32 m. in external diameter, and 1.08 m. internal.

Horizontal network 1.01 m. square, and having meshes of the same size as those of the reticulated ribbon.

Horizontal reticulated ribbon 3 m. in length and of the structure described.

Horizontal annular ring 1.26 m. in external diameter, 0.94 m. internal.

In conclusion, let us meet an objection that might be made to the accuracy of the hypotheses that serve as a base to the preceding calculations, in cases where ground plates for lightning rods and not for telegraphs are concerned. Between the two ground plates of a telegraph line there is generally a distance such that the curves of the current undergo no deviation in the vicinity of one of the electrodes (the only part important for integrations) through the influence of the other. But it might be admitted that such would prove the case with a lightning rod in a storm, at the time of the passage of the fluid into the earth. The ground plate here is one of the electrodes, and the other is replaced by the surface of the earth strongly charged to a great distance under the storm clouds. If we suppose (what may be admitted in a good lightning rod) that there no longer occurs any spark from the point downward, the curves of the current, in starting perpendicularly from the ground plate, would be obliged to leave their rectilinear trajectory and strike the surface of the earth at right angles.

When the electricity flows through a plane surface into an infinite body, it is only when such surface presents a very great development that the respective potentials decrease very slowly in the vicinity of the said surface. No notable modification occurs, then, in the curves of equal potential, in the vicinity of the ground plate through the action of this extended charge, nor consequently any modification in the curves of the current; but the electricity which spreads has but a short distance to travel in order to overcome the most important resistances.

The calculations of resistances given above have, then, the same value for discharges of atmospheric electricity. - Bull. du Musee de l'Industrie.