A gradual introduction would lessen the inconveniences which
might attend too sudden a substitution, even of an easier for a more
difficult system. After a given term, for instance, it might begin
in the custom-houses, where the merchants would become familiarized
to it. After a further term, it might be introduced into all legal
proceedings, and merchants and traders in foreign commodities might
be required to use it in their dealings with one another. After a
still further term, all other descriptions of people might receive it
into common use. Too long a postponement, on the other hand, would
increase the difficulties of its reception with the increase of our
population.
_Appendix, containing illustrations and developments of some
passages of the preceding report._
(1.) In the second pendulum with a spherical bob, call the
distance between the centres of suspension and of the bob, 2x19.575,
or 2d, and the radius of the bob = r; then 2d:r::r:rr/2d and 2/5 of
this last proportional expresses the displacement of the centre of
oscillation, to wit: 2rr/5x2d=rr/5d. Two inches have been proposed
as a proper diameter for such a bob. In that case _r_ will be = 1.
inch, and rr/5d = 1/9787 inches.
In the cylindrical second rod, call the length of the rod,
3x19.
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