This resistance increases much more rapidly than is represented by increase of distance between the carbon points. Hence the electric power with Werdermann's lamp is economized to the utmost in this respect, and it becomes possible—as in the recent experiment—to make use of an electric current large in quantity but of low intensity. The tension being small, there is the less difficulty with regard to insulation. If one lamp or more should be accidentally extinguished, the rest will continue to burn. The whole of the lamps can also be extinguished and relit by merely stopping the current and then sending it on again. No nice and troublesome adjustment with reference to the length of the electric arc is requisite, and simple contact between the point of the rod and the surface of the disk is sufficient for the manifestation of the light.
In respect to duration, a carbon rod 5⁄32 in. in diameter, and a yard long, obtained from Paris, costs a franc. This, placed in a large lamp, having an estimated lighting power of 320 candles, will last from 12 to 15 hours. The smaller lamps take a carbon of ⅛ in. diameter.
Mr. Werdermann endeavors to make the resistance of the external portion of the circuit equal to the internal resistance, in order to obtain the greatest effect. It is well known that the best results are obtained when the internal and external resistances are equal. The method adopted is that known to electricians as the divided arc, and will easily be understood from Fig. 2. Let B represent the source of the electric current, and A a copper wire connected to the positive and negative poles of the source as in the diagram. The wire, A, has a certain resistance. Suppose, now, we arrange for the current to pass as in the diagram, Fig. 3. By the insertion of the new wire, C, we have lessened the total external resistance and increased the current, as will be seen by reference to Ohm's law.
| C = | E (R+r) |
where C = current; E = electromotive force; R = resistance external; r = resistance internal.
The fraction
| E (R+r) |
increases as its denominator is lessened.
The current passes along the two branches in equal quantities if the resistances of the wires are equal, but inversely as the resistances if they are unequal. Thus, if the branch, A, has a resistance, 9, and C has a resistance, 1, 9⁄10 of the current will pass through C, and 1⁄10 through A. Similarly, for any number of branches the current will divide itself according to the resistances. If, then, we have a number of branches, as indicated in Fig. 4, the current will divide itself equally among the branches when the resistances of the branches are equal. This is the arrangement adopted by Mr. Werdermann, as will be seen from the annexed diagram, Fig. 5, in which N and P represent the negative and positive poles of the machine, and L L the electric lamps.
When any one lamp is put out the inventor arranges that an equivalent resistance shall be put into the circuit, so that as a whole the circuit is unaltered, and the other lamps unaffected.