1 − 2 + 4 − 8 + ⋯ 1 − 2 + 4 − 8 + ⋯ In mathematics, is the infinite series whose terms are the successive powers of two with alternating signs. As a geometric series, it is characterized by its first term, 1, and its common ratio, −2. As a series of real numbers it diverges, so in the usual sense it has no sum. In a much broader sense, the series has a generalized sum of . Gottfried Leibniz considered the divergent alternating series as early as 1673. He argued that by subtracting either on the left or on the right, one could produce
Minim (unit) size of a drop can vary considerably depending upon the viscosity and specific gravity of the liquid. (At the time, the phenomenon of surface tension was not well understood.) The minim, on the other hand, was measured with a graduated glass tube known as a "minimometer", later known as the minim-tube. The minim-tube was a type of graduated pipette, a device invented in 1791 by François-Antoine-Henri Descroizilles. Apothecaries' measures are fully defined in the United Kingdom's Weights and Measures Act of 1878, but the UK's 1963 Weights and Measures Act provided for the abolition of the minim, fluid scruple, and