reason, perhaps, that the considerations, which have remained general, have not at once permitted of obtaining forms what could be employed with perfect knowledge of the results.  This is what led Mr. Ulbricht, of Dresden, to make calculations for a few forms of conductors, and to test their approximate values.  The results of these researches are printed in the Elektrotechnischen Zeitschrift for 1883 (p. 18).

[Illustration]

The equations found show, in the first place, that there exist three means of obtaining a considerable effect, as regards the ground conductor, with a slight expenditure of material:  The cylindrical electrode may be drawn out into the form of a bar or wire; the plate may be rendered narrow, and elongated in the form of a ribbon; and, besides, the annular plate may be enlarged in lessening the metallic surface.

Finally, a short, open cylinder with a vertical axis may be formed by curving a narrow plate or ribbon.  It is not necessary to see the formula to recognize the fact that this cylinder must behave like a ribbon and a flat ring.  The radius increasing, and the surface remaining constant, the resistance of the earth here likewise approaches zero.

As the resistance of the earth is inversely proportional to the diameter of the plates, the zero resistance can also be reached by dividing a plate ad infinitum.  As the parts of the plate may be brought quite close to each other without perceptibly interfering with the action, a network has finally been reached by a division carried very far, yet limited, and by connecting the parts with one another by conducting cylinders.

If we seek to determine what forms of ground conductors are efficient and economical under given conditions, we shall have to begin by informing ourselves as to the choice of material to be used for the electrode, and shall then have to ascertain whether putting it in the ground will or will not necessitate much outlay.  The most suitable material is copper, which may be used with advantage, in that it lasts pretty well underground, and that the facility which it may be worked permits of easily giving it more appropriate forms than those that can be obtained with cast iron, which is of itself less costly.

If the burying in the ground requires little or no labor, as when there exist ponds, rivers, and wells, or subterranean strata of water near the surface of the earth, elongated forms of conductors will be employed, such as the solid or hollow cylinder, the wire, the ribbon, the narrow ring, and the network.  Plates approaching a square or circular shape are not advantageous.  But if the ground has to be dug deeply in order to sink the conductor, the form of the electrode must be more condensed, and selected in such a way that the necessary action may be obtained with a minimum output of copper and labor.  For great depths, and when the ground will permit of boring, an elongated