§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, etc., 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, etc., is a decreasing Geometrical Progression: while Vindex rightly identifies the fallacy as that of “Achilles and the Tortoise.” + 

Old King Cole. + 

Vindex. + 