χχίν
INTRODUCTION
produced. You seem to have similar thoughts in your own mind.
However that may be, I should like you to feel free to make any
use of what I have mentioned above, for I have no time at present
to work at the subject. These ideas suggest themselves so readily
in reading your investigation that they must soon occur to you if
they have not already done so. -With kindest regards, yours,
H. HELMHOLTZ.
While still busily engaged in completing this investiga-
tion on the discharge Hertz began to reflect upon another
problem which seems to have been suggested to him by sheets
of ice floating upon water during the winter.
BERLIN, 24th February 1883.
From the date of my
My researches are going on all right.
last letter until to-day I have been wholly absorbed in a problem
which I cannot keep out of my head, viz. the equilibrium of a
floating sheet of ice upon which a man stands. Naturally the
sheet of ice will become somewhat bent, thus [follows a small
sketch of the bent sheet], but what form will it take, what will be
the exact amount of the depression, etc.? One arrives at quite
paradoxical results. In the first place a depression will certainly
be produced underneath the man; but at a certain distance there
will be a circular elevation of the ice; after this there follows
another depression, and so on, somewhat in this way [another
sketch]. As a matter of fact the elevations and depressions
decrease so rapidly that they can never be perceived: but to the
intellectual eye an endless series of them is visible.
Even more
paradoxical is the following result. Under certain circumstances
a disc heavier than water, and which would therefore sink when
laid upon water, can be made to float by putting a weight on it;
and as soon as the weight is taken away it sinks. The explana-
tion is that when the weight is put on, the disc takes the form of
a boat, and thus supports both the weight and itself. If the load
is gradually removed the disc becomes flatter and flatter; and
finally there comes an instant when the boat becomes too shallow
and so sinks with what is left of the load. This is the theoretical
result, and the way I explain it to myself, but meanwhile there
may be errors in the calculation. Such a subject has a peculiar
effect upon me.
For a whole week I have been struggling to have
done with it, because it is not of great importance, and I have
other things to do, e.g. I ought to be writing out the research
which is to serve for my induction at Kiel, which is all ready in
my mind but not a stroke of it on paper. Still it seems impos-
sible to finish it off properly; there always remains some contra-