ds below the original level of the water can
be properly said to be immersed, and only an equal bulk of water is
displaced." Hence, according to HECLA, a solid, whose weight was equal
to that of an equal bulk of water, would not float till the whole of it
was below "the original level" of the water: but, as a matter of fact,
it would float as soon as it was all under water. MAGPIE says the
fallacy is "the assumption that one body can displace another from a
place where it isn't," and that Lardner's assertion is incorrect, except
when the containing vessel "was originally full to the brim." But the
question of floating depends on the present state of things, not on past
history. OLD KING COLE takes the same view as HECLA. TYMPANUM and VINDEX
assume that "displaced" means "raised above its original level," and
merely explain how it comes to pass that the water, so raised, is less
in bulk than the immersed portion of bucket, and thus land
themselves--or rather set themselves floating--in the same boat as
HECLA.

I regret that there is no Class-list to publish for this Problem.

* * * * *

Sec. 2. BALBUS' ESSAY.

_Problem._--Balbus states that if a certain solid be immersed in a
certain vessel of water, the water will rise through a series of
distances, two inches, one inch, half an inch, &c., which series has no
end. He concludes that the water will rise without limit. Is this true?

_Solution._--No. This series can never reach 4 inches, since, however
many terms we take, we are always short of 4 inches by an amount equal
to the last term taken.

* * * * *

Three answers have been received--but only two seem to me worthy of
honours.

TYMPANUM says that the statement about the stick "is merely a blind, to
which the old answer may well be applied, _solvitur ambulando_, or
rather _mergendo_." I trust TYMPANUM will not test this in his own
person, by taking the place of the man in Balbus' Essay! He would
infallibly be drowned.

OLD KING COLE rightly points out that the series, 2, 1, &c., is a
decreasing Geometrical Progression: while VINDEX rightly identifies the
fallacy as that of "Achilles and the Tortoise."

CLASS LIST.

I.

OLD KING COLE.
VINDEX.

* * * * *

Sec. 3. THE GARDEN.

_Problem._--An oblong garden, half a yard longer than wide, consists
entirely of a gravel-walk, spirally arranged, a yard