575 or 3d, and its radius = r and rr/2x3d=rr/6d will express the
displacement of the centre of oscillation. It is thought the rod
will be sufficiently inflexible if it be 1/5 of an inch in diameter.
Then _r_ will be = .1 inch, and rr/6d=1/11745 inches, which is but
the 120th part of the displacement in the case of the pendulum with a
spherical bob, and but the 689,710th part of the whole length of the
rod. If the rod be even of half an inch diameter, the displacement
will be but 1/1879 of an inch, or 1/110356 of the length of the rod.
(2.) Sir Isaac Newton computes the pendulum for 45 degrees to
be 36 pouces 8.428 lignes. Picard made the English foot 11 pouces
2.6 lignes, and Dr. Maskelyne 11 pouces 3.11 lignes. D'Alembert
states it at 11 pouces 3 lignes, which has been used in these
calculations as a middle term, and gives us 36 pouces 8.428 lignes =
39.1491 inches. This length for the pendulum of 45 degrees had been
adopted in this report before the Bishop of Autun's proposition was
known here. He relies on Mairan's ratio for the length of the
pendulum in the latitude of Paris, to wit: 504:257::72 pouces to a
4th proportional, which will be 36.71428 pouces = 39.1619 inches, the
length of the pendulum for latitude 48 degrees 50'.
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