The
machine consists of four essentially distinct parts. The first,
second and third exhibit the multiplicand, multiplier and product,
or quotient, divisor and dividend, according as the question to
be worked is one of multiplication or division. The fourth is a
carrying apparatus, which though at present detached, and employed
to reduce the result to its simplest form after the main operation
has been performed, might without much difficulty be attached to
the multiplier or divisor, and work with it.
Let
us now suppose a question of multiplication, both multiplier and
multiplicand being exhibited in the ternary system. The multiplicand
consists of nothing but a number of rods, each bearing an index,
and each movable backwards and forwards. When the indices are all
arranged in line, and in one particular line, this multiplicand
is 000.... But if any one of the rods be advanced by a certain
space forwards, the digit +1 is indicated as occupying the numeral
column which that rod represents, and if it be moved the same space
backwards, -1 is the digit indicated. This, which we may call the
frame of the multiplicand, is thus a collection of rods, not itself
connected with any machinery, but only useful as indicating the
manner in which the frame of the multiplier is to act.
The
multiplier is a frame movable in the direction perpendicular to
the rods of the multiplicand and product, and situated between
the planes of the two, in such manner that its extremity can be
brought by a sliding motion over each rod of the multiplicand in
succession. This multiplier consists of a number of rods in a common
system, each furnished with two teeth, one at each extremity, the
tooth by which it is acted on being a continuation of the rod,
that by which it acts being perpendicular to the axis of the rod.
The first set of teeth are dispersed/disposed so as to rest in
a frame which has a slight motion round an axis; and each rod can
be moved so that its teeth shall touch the frame above, on or below
the axis. Those rods, then, which have their teeth on the axis
do not receive motion from the frame, while the others receive
motion in one direction or another, according as the teeth touch
the frame above or below the axis. The perpendicular teeth at the
other extremities may thus be made to move in either direction,
or to remain stationery: and these last mentioned teeth act upon
the rods which make up the frame of the product. This last frame
precisely resembles the frame of the multiplicand, with the addition
of the connecting part by which the multiplier acts upon it.
The
process of multiplication is then as follows; the frame of the
multiplier having been set, and also that of the multiplicand,
the extremity of the multiplier frame is brought over the first
rod of the multiplicand. To this extremity is attached a tooth
which acts upon the rod of the multiplicand over which it comes,
giving it a motion in one or the other direction, according as
the slightly revolving frame of the multiplier is made to move
in one or the other direction. The rule is, to move the revolving
frame in such a way as to bring the rod of the multiplicand to
its zero position; and this one motion multiplies the figure of
the multiplicand by the whole of the multiplier, and by the action
of the perpendicular teeth, exhibits the result upon the product
frame. The lateral motion is then given to the whole of the multiplier
apparatus, until the tooth comes upon the next figure rod of the
multiplicand, and the revolving frame being then made to bring
the new multiplicand rod to zero, the effect upon the product frame
is that the new figure of the multiplicand is multiplied by the
whole of the multiplier, and the result added to that of the preceding
figure. This process is continued until the whole of the figures
of the multiplicand are exhausted.
The
result is then completely exhibited on the frame of the product,
but not in its simplest form, For, whereas +1 or -1 should be the
only digits in the final result, this intermediate result may exhibit
+2 or -2, +3 or -3 etc on any rod. The carrying frame is a simple
apparatus which, like the multiplier, has a lateral motion, and
can be brought on any pair of consecutive rods. By one motion of
the hand, it advances the left of two rods by a unit, and throws
back the right hand rod by 3 units, or vice versa. Some little
expertness is here necessary in making the carriages properly,
with reference to the simplicity of the result: but there is no
possibility of absolute error being introduced, since each process
can only consist in altering a lower column by 3 units while the
next column is altered in the contrary way by one unit.
The
method of performing division is precisely the reverse of the preceding,
and will hardly need description. |