Napier’s rods or bones consist of ten oblong pieces
of wood or other material with square ends. Each of
the four faces of each rod contains multiples of one
of the nine digits, and is similar to one of the
slips just described, the first rod containing the
multiples of 0, 1, 9, 8, the second of 0, 2, 9, 7,
the third of 0, 3, 9, 6, the fourth of 0, 4, 9, 5,
the fifth of 1, 2, 8, 7, the sixth of 1, 3, 8, 6,
the seventh of 1, 4, 8, 5, the eighth of 2, 3, 7,
6, the ninth of 2, 4, 7, 5, and the tenth of 3, 4,
6, 5. Each rod, therefore, contains on two of its
faces multiples of digits which are complementary to
those on the other two faces; and the multiples of a
digit and its complement are reversed in position.
The arrangements of the numbers on the rods will
be evident from fig. 2, which represents the four
faces of the fifth bar. The set of ten rods is thus
equivalent to four sets of slips as described above.
[Illustration]
[Illustration: From Drawings of Barbour Patent No. 130,404]
It is unnecessary to go into the history of the Hopkins Bookkeeping
Machine to show the evolution of the Art relative to this class of
machines, as the features that have made such a machine practical were
developed by Hopkins himself, and at the present date there is none to
dispute the title since his is the only machine having the required
combination referred to. The scheme used by Hopkins for multiplication
in his billing machine is, as stated, direct multiplication or that
of adding the multiples of digits directly to the accumulator numeral
wheels instead of pumping it into the accumulator wheels by repeated
addition of the digits as is more commonly used.
[Illustration: John Napier]
The direct method of multiplying is old, as a matter of fact, the first
mechanical means employed for multiplying worked by the direct method.
But its combination with recording and typewriter mechanism invented by
Hopkins was new.
[Sidenote: _Napier’s bones first direct multiplier_]
Napier, in 1620, laid the foundation of the mechanical method of direct
multiplication when he invented his multiplying bones. The scheme of
overlapping the ordinal places is shown in the diagonal lines used to
separate units from the tens in each multiple of the nine digits (see
illustration, page 179), thus providing a convenient means by which the
ordinal values may be added together.
[Sidenote: _First direct multiplying machine_]
The first attempt to set Napier’s scheme to mechanism that would add
and register the overlapping ordinal values was patented by E. D.
Barbour in 1872. See reproduction of patent drawings on opposite page.