But the shortest way for any one to convince himself of this relation of the magnetic power would be, in one and the same experiment, to interpose the same piece of iron between the magnet and the compass needle first _breadthways_; and in this case it will be found that the needle, which had been previously deflected by the magnet from its natural position at one of its poles, will instantly resume the same, either wholly or very nearly so--then to interpose the same piece of iron _lengthways_; in which case the position of the compass needle will be scarcely or not at all affected.
The assertion of Bernoulli and others, that the absolute force of the artificial magnet increases in the ratio of its superficies, stands corrected in the far more accurate experiments of Coulomb (published in his Treatise on Magnetism), which proves that the increase takes place (in a far greater degree) in the ratio of its length. The same naturalist even found means to determine that the directing powers of the needle, which he had measured by help of his _balance de tortion_, stand to the length of the needle in such a ratio as that, provided only the length of the needle is from forty to fifty times its diameter, the momenta of these directing powers will increase in the very same direct proportion as the length is increased. Nor is this all that may be deduced from the experiment last mentioned. If only the magnet be strong enough, it will show likewise that magnetism _seeks_ the length. The proof is contained in the remarkable fact, that the iron interposed between the magnet and the magnetic needle _breadthways_ constantly acquires its two opposite poles at both ends _lengthways_. Though the preceding experiments are abundantly sufficient to prove the position, yet the following deserves mention for the beautiful clearness of its evidence. If the magnetic power is determined exclusively by length, it is to be expected that it will manifest no force, where the piece of iron is of such a shape that no one dimension predominates. Bring a _cube_ of iron near the magnetic needle and it will not exert the slightest degree of power beyond what belongs to it as mere iron. By the perfect equality of the dimensions, the magnetism of the earth appears, as it were, perplexed and doubtful. Now, then attach a second cube of iron to the first, and the instantaneous act of the iron on the magnetic needle will make it manifest that with the length thus given, the magnetic influence is given at the same moment.