[Illustration: FIG. 6.]

Mr. Bjerknes has carried the examination of these phenomena still
further in studying experimentally the actions that occur in the
depths of the liquid; and for this purpose he has made use of the
arrangement shown in Fig. 7. By the side of the vibrating body there
is placed a light body mounted on a very flexible spring. This assumes
the motion of that portion of the fluid in which it is immersed, and,
by the aid of a small pencil, its direction is inscribed upon a plate
located above it. By placing this registering apparatus in different
directions the entire liquid may be explored. We find by this means
figures that are perfectly identical with magnetic phantoms. All the
circumstances connected with these can be reproduced, the vibrating
sphere giving the phantom of a magnet with its two poles. We may even
exhibit the mutual action of two magnets. The figures show with
remarkable distinctness--much more distinct, perhaps, than those that
are obtained by true magnets.

[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