[Illustration:  FIG. 7.]

However, it must not be thought that these so interesting facts are the result of groping in the dark and the outcome of some fortunate experiment; for they have, on the contrary, been foreseen and predetermined.  Mr. Bjerknes is especially a mathematician, and it was a study, through calculation, of the vibratory motion of a body or system of bodies in a medium that led him to the results that he afterwards materialized.

After the production, by Mr. Lejeune, of his solutions, Mr. Bjerknes in 1865 entered upon a complete study of the subject, and recognized the fact that the result of such motions was the production of regular mechanical actions.  He calculated the directions of these, and, along about 1875, perceived the possibility of reproducing the effects of permanent magnetism.  More recently, in 1879, he saw that magnetism by derivation might likewise be explained by those hypotheses, and figured by actions of this kind.  It was not till then that he performed the experiments, and submitted a body to the results of calculation.

The same process has led him to the conclusion that the action of currents might be represented in the same manner; only, instead of bodies in vibration, it would require bodies in alternating rotation.  The effects are much more difficult to ascertain, since it is necessary to employ viscid liquids.

Meanwhile, the experiments have been performed.  Up to the present time attractions and repulsions have not been shown, and I do not know whether Mr. Bjerknes has obtained them.  But, by the process pointed out, the lines of action (electric phantoms, if I may so express myself) have been traced, and they are very curious.  By supposing the current perpendicular to the plate, and in the presence of the pole of a magnet, the influences produced around it are very well seen, and the figures are very striking, especially in the case of two currents.  Mr. Bjerknes does not appear as yet to have obtained from these experiments all that he expects from them.  And yet, such as they are, they have already led him to important conclusions.  Thus, calculation, confirmed by application, has led him to renounce the formula proposed by Ampere and to adopt that of Regnard as modified by Clausius.  Is he right?  This is what more prolonged experimentation will allow to be seen.

These researches, however, are beset with difficulties of a special nature, and the use of viscid liquids is a subject for discussion.  Mr. Bjerknes desired to employ them for reproducing the effects that he had obtained from water, but he found that the lines of force were no longer the same, and that the phenomena were modified.  It is necessary, then, to hold as much as possible to liquids that are perfect.  The experimenter is at present endeavoring to use these liquids by employing cylinders having a fluted surface; but it is clear that this, too, is not without its difficulties.