Suppose we take batteries which aren’t going to be injured by being made to work–storage batteries will do nicely–and connect them in series as in Fig. 13. When batteries are in series they act like a single stronger battery, one whose e. m. f. is the sum of the e. m. f.’s of the separate batteries. Connect these batteries to a long fine wire as in Fig. 14. There is a stream of electrons along this wire. Next connect the negative terminal of the standard cell to the negative terminal of the storage batteries, that is, brace their feet against each other. Then connect a wire to the positive terminal of the standard cell. This wire acts just like a long arm sticking out from the positive plate of this cell.
Touch the end of the wire, which is p of Fig. 14, 61 to some point as a on the fine wire. Now what do we have? Right at a, of course, there are some free electrons and they hear the calls of both batteries. If the standard battery, S of the figure, calls the stronger they go to it. In that case move the end p nearer the positive plate of the battery B, so that it will have a chance to exert a stronger pull. Suppose we try at c and find the battery B is there the stronger. Then we can move back to some point, say b, where the pulls are equal.
To make a test like this we put a sensitive current-measuring instrument in the wire which leads from the positive terminal of the standard cell. We also use a long fine wire so that there can never be much of an electron stream anyway. When the pulls are equal there will be no current through this instrument.
As soon as we find out where the proper setting is we can replace S by some other battery, say X, which we wish to compare with S. We find the setting for that battery in the same way as we just did for S. Suppose it is at d in Fig. 14 while the setting for S was at b. We can see at once that X is stronger than S. The question, however, is how much stronger.
Perhaps it would be better to try to answer this question by talking about e. m. f.’s. It isn’t fair to speak only of the positive plate which calls, we must speak also of the negative plate which is shooing electrons away from itself. The idea of e. m. f. takes care of both these actions. The steady stream of 62electrons in the fine wire is due to the e. m. f. of the battery B, that is to the pull of the positive terminal and the shove of the negative.
If the wire is uniform, that is the same throughout its length, then each inch of it requires just as much e. m. f. as any other inch. Two inches require twice the e. m. f. which one inch requires. We know how much e. m. f. it takes to keep the electron stream going in the part of the wire from n to b. It takes just the e. m. f. of the standard cell, S, because when that had its feet braced at n it pulled just as hard at b as did the big battery B.
Suppose the distance n to d (usually written nd) is twice as great as that from n to b (nb). That means that battery X has twice the e. m. f. of battery S. You remember that X could exert the same force through the length of wire nd, as could the large battery. That is twice what cell S can do. Therefore if we know how many volts to call the e. m. f. of the standard cell we can say that X has an e. m. f. of twice as many volts.
If we measured dry batteries this way we should find that they each had an e. m. f. of about 1.46 volts. A storage battery would be found to have about 2.4 volts when fully charged and perhaps as low as 2.1 volts when we had run it for a while.