NEW OR IMPROVED INSTRUMENTE OR MACHINES FOR EFFECTING OR FACILITATING CERTAIN ARITHMETICAL PROCESSES OR COMPUTATIONS
Year: 1846

page_text: TO ALL TO WHOM THESE PRESENTS SHALL COME, I, DAVID
BARNETT, of Birmingham, in the County of Warwick, Merchant, send
greeting.
WHEREAS Her present most Excellent Majesty Queen Victoria, by Her
Royal Letters Patent under the Great Seal of the United Kingdom of Great
Britain and Ireland. bearing date at Westminster. the Fifth day of November,
in the tenth year of Her reign. did. for Herself. Her heirs and successors,
give and grant unto me. the said David Barnett. my exors, admors, and
assigns. Her especial licence, full power. sole privilege and authority: that I,
the said David Barnett. my exors. admors. and assigns, or such others as
I, the said David Barnett. my exors, admors, or assigns, should at any
time agree with, and no others, from time to time and at all times during
the term of years therein expressed. should and lawfully might make. use,
exercise, and vend. within England. Wales. and the Town of Berwick-upon-
Tweed, the Invention of "NEW OR IMPROVED INSTRUMENTE OR MACHINES FOR
EFFECTING OR FACILITATING CERTAIN ARITHMETICAL PROCESSES OR COMPUTATIONS,"
being a communication from a certain foreigner residing abroad; in which
said Letters Patent is contained a proviso. that I, the said David Barnett.
shall cause a particnlar description of the nature of the said Invention, and
in what manner the same is to be performed, by an instrument in writing
under my hand and seal, to be inrolled in Her said Majesty's High Court
of Chancery within six calendar months next and immediately after the date
ED Q.77

page_text: of the said in part recited Letters Patent, as in and by the same, reference
being thereunto had, will more fully and at large appear.
NOW KNOW YE, that in compliance with the said proviso, I, the said
David Barnett, do hereby declare that the nature of the said Invention,
and the manner in which the same is to be performed, are fully described and
ascertained in and by the following statement thereof, reference being had to
the Drawings hereunto annexed, and to the figures and letters marked thereon,
that is to say:-
My Invention consists, firstly, of an instrument or apparatus for effecting the
arithmetical processes of addition and subtraction; and, secondly, of an instru-
ment for effecting the arithmetical processes of multiplication and division.
Figure 1 is a plan of the external front of the machine for effecting addition
and subtraction, and Figure 2 is. a plan of the interior of the same. A, B, is
a metal plate, which constitutes the front of the flat box in which the working
parts of the instrument are contained; C, D, E, F, G, H, &c. are curved
slots cut in the said plate A, B. The right-hand end of each of these
slots is marked with the plus sign (+), and the left-hand end of each
of the said slots is marked with the minus sign (-). At the points
a, b, c, d, which said points are the centres of the curved or circular slots
C, D, E, F, G, H, &c., are situated four axes perpendicular to the plate A, B,
A dentated or toothed wheel turns upon each of these axes. The teeth only
of the said wheels are seen through the circular slots C, D, E, F, G, H, &c.
on the plate A, B, in Figure 1, but in Figure 2 the said wheels are fully
represented.
It will be observed, by reference to the said Figure 2, that each of
the wheels a, b, c, d, has thirty teeth, and that the said wheels are so
situated with regard to each other that a portion of the teeth of each of the
said wheels are situated either above or below a portion of the teeth of the
adjoining wheel; the said wheels consequently are not situated in the same
plane, but alternately at a higher and lower level; that is to say, the axes of the
said wheels are situated so near each other, that were the wheels in the same
plane the teeth of each of the said wheels would engage in the teeth of the
adjoining one; but as the wheels are not situated in the same plane, the teeth
of the said wheels do not engage in the teeth of the adjoining ones, but simply
overhang the same. Each of the wheels a, b, c, d, may rotate upon its
own axis without its motion affecting or being affected by the adjoining wheel.
e, f, g, h, Figure 2, are springs of the form represented, one end of each of
which is fixed to the plate A, B. of the instrument, and the other end engages
between the teeth of the wheel to which it belongs, and holds the wheel in

page_text: such a position that the teeth of the said wheel cover or correspond with the
teeth of the adjoining wheel, and not with the interstices .between the said
teeth, as shewn in the Drawing. On those wheels b", ", which lie beneath
the others. circular discs. corresponding in size to the circular or untoothed
part of the said wheels, are attached. so that although the teeth and backs or
under surfaces of the said wheels are situated in different planes the faces or
upper parts of the said wheels on which the Figures are inscribed, as herein-
after explained, are on the same level. On the face of each wheel, and near
its periphery, the series of signs or numbers 0, 1. 2. 3. 4. 5. 6. 7. 8. 9 are
inscribed. the said signs or numbers being placed opposite ten consecutive
teeth, as shewn in the Drawing: one series, which I will call the upper series,
is commenced on the right hand and continued to the left hand; and on the
opposite side of the face of each wheel a second series of signs or numbers
0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is inscribed, which series I will call the lower series.
cach number of the lower series being placed at a point on the wheel exactly
opposite that at which the same number is placed in the upper series, as seen
in the Drawing: the lower series consequently commences on the left hand
and is continued to the right hand. The space in the circle between the 9 of
the upper series and the 0 of the lower series is filled with repetitions of the
plus sign (+). the said sign being inscribed opposite each tooth; and the space
in the circle between the 9 of the lower series and the 0 of the upper series is
filled by repetitions of the minus sign (-). the said sign being inscribed
opposite each tooth. All the teeth on each of the wheels between the number
6 of the upper series and the number 3 of the lower series, including the teeth
opposite the said 6 and 3, are painted black. The length of each of the circular
slots is such that only ten of the teeth of the wheel beneath it can be seen at
each of the said slots at once. On the convex side of each of the said slots the
series of signs and numbers + 1, 2, 3, 4, 5, 6, 7, 8, 9 are inscribed, the said
series commencing at the right-hand side of the said slot and terminating at
the left-hand end of the same, the sign and numbers of the said series being
placed opposite the interstices between the teeth of the wheels as seen in the
Drawing, Figure 1. That portion of the plate A, B, which is situated between
the upper and lower circular slot, and which is marked i in Figure 1, covers
two of the four teeth, which in each wheel overlap four of the next wheel. The
two overlapping teeth of each wheel which are not hidden are situated between
the sign (-), and the number 9 inscribed on the convex side of the upper and
lower circular slots; a', b', c', d', are circular openings in the plate A, B, one
such opening being placed on the concave side both of the upper and lower
circular slots C, D, E, F, &c.; one of the signs or numbers inscribed on the

page_text: reckoning from the right hand of the
resulting quantity, the openings over
forth. The peg or stile, Figure 3,
wheels and working the instrument.
wheels a, b, &c. is always visible at the openings a¹, b¹, &c.; and in the
process of using the instrument the result of any addition is exhibited at the
upper row of apertures, and the result of any subtraction is exhibited at the
lower row of apertures. The numbers exhibited at the openings over the wheel
on the extreme right-hand of the instrument are the units, numbers of the
sum, or difference of any process of addition or subtraction. (the upper aperture
being for addition and the lower for subtraction, as herein-before explained);
the openings over the second wheel,
instrument, exhibit the tens of the
the third wheel the hundreds and so
is used for the purpose of moving the
By an examination of Figure 2 it will be seen that if any of the wheels
be so placed that the sign (0) is visible through the upper and lower aper-
tures, all the teeth that are visible through the upper slot, excepting the one
on the extreme left hand, are white; and all those visible through the lower
slot are black. But if instead of the sign (0) any number be visible
through the said upper apertures, then a number of black teeth will be
visible in the upper slot, greater by one than the number so visible at the
opening. Thus, if the number 3 be exhibited at any upper opening, four black
teeth will be seen at the upper slot, and a number of white teeth will be seen
at the lower slot equal to the number (3) visible at the lower aperture.
Before commencing any process of addition or subtraction it is necessary to
adjust each of the wheels, so that the sign (0) shall be seen at each of the
circular apertures both of the upper and lower rows. In order to arrange the
wheels in this manner it is only necessary to introduce the stile, Figure 3, into
the interstice between the last black tooth seen at the lower slot and the white
tooth on its right, and move the wheel towards the plus sign (+) on the right
hand, until, by contact of the stile with the end of the slot, further motion is
prevented; the sign (0) will then be visible both at the upper and lower
apertures. The instrument having been thus adjusted, I will illustrate the
method of using it by adding together the sum 3976 and 5053. I first set
down or register the 3 (thousands) by placing the stile in the interstice imme-
diately opposite the number 3 in the slot O, P, of the thousands wheel d
By moving the stile to the right hand, or towards the plus sign (+), until it
strikes against the end of the slot O, P, the number 3 is made to appear
at the upper aperture of the said thousands wheel. I next register the 9
(hundreds) by placing the stile in the interstice opposite the number 9 in
the slot. K, L, of the next or hundreds wheel c", and again move the stile
to the right as far as possible. The number 9 is thereby brought to the

page_text: circular aperture of the said hundreds wheel. and by operating in a like
manner upon the tens and units wheels the 76 may be registered. The wholo
sum 3976 is thus presented at the upper row of circular apertures. the
thousands at the aperture d', the hundreds at c', the tens at b'. and the
units at a. In adding the quantity 5053 to the 3976 just registered, I
proceed in the same way as in registering the said 3976, that is to say, I place
the stile in the upper slot of each wheel under the figure which is to be added,
but in moving the said stile or wheel the following rule must be observed:-
If, in selecting the proper number to be added, the stile be introduced between
any two white teeth, or between a black and white tooth, the wheel must be
moved to the right hand, as before; but if the said stile be introduced between
any two black teeth. then the wheel must be turned to the left hand, the
motion of the wheel being continued in either case until the stile is arrested by
coming in contact with the end of the slot. If by any inadvertence the wheel
has been turned in the wrong direction, the instrument immediately points out
that such an error has been committed; for instance, if the wheel has been
turned to the right hand when it should have been turned. to the left hand,
there will be presented at the aperture the plus sign (+), and whenever that
sign appears it indicates that the stile must be inserted immediately beneath
the plus sign (+). inscribed over the circular slot, and the wheel carried round
to the left hand until the stile is brought under the minus sign (-), and the
further motion of the stile prevented. So also, if the wheel has been turned to
the left hand when it should have been turned to the right hand, the minus
sign (-) will be presented at the circular aperture, and the stile must then be
introduced under the minus sign (-), and the wheel carried to the right hand
until the stile comes in contact with the end of the slot under the plus sign
(+). It will sometimes happen that the plus sign (+) will be presented when
the instrument is properly worked, but in such cases the said sign is never
presented at the aperture of the wheel between the teeth of which the stile is
inserted, but after the motion of the said wheel the said sign sometimes
presents itself at the aperture of the wheel on the left of that which has been
moved. In such cases the same rule must be observed, that is to say, the stile
must be introduced at the plus sign (+) on the extreme right hand of the
wheel at the aperture of which the said sign is presented, and the said wheel
moved to the left. Suppose, for example, the quantity 999 has been registered
on the instrument, the addition of 1 in the units' place should produce 1000,
but on adding one to the units' place it will produce 0 in the aperture of that
place and the plus sign (+) at the aperture of the tens' place; but by moving
the tens' wheel, in accordance with the directions herein-before given, 0 will

page_text: be produced at the aperture of the tens' place and plus (+) at the aperture of
the hundreds' place, and by next moving the wheel of the hundreds' place in
the manner herein-before directed, the 0 will be brought to the aperture of the
hundreds' place and 1 at the aperture of the thousands' place, that is to say, the
proper quantity will be presented. The process of subtraction is performed
on the lower circular slots and apertures in precisely the same way as addition
is performed on the upper part of the instrument, that is to say, a number being
registered, any quantity may be taken from it by inserting the stile at the proper
number, and moving it to the right hand if it be inserted between white teeth
or between a black and white tooth and to the left if it be inserted among black
teeth. The same rules must also be observed with regard to the plus and
minus signs (+), (-), whether they be presented in the wheel moved by the
said wheel having been turned in the wrong direction, or presented at the aper-
ture of a wheel next to the one moved, as will occur in the proper working of
the instrument. From the representation of the parts of the instrument in the
accompanying Drawing, and the description herein-before given of the method
of using the said instrument, it will be seen that the action of the instrument
depends upon the peculiar arrangement of the numbers on the wheels with
regard to the black and white teeth; for example, (in addition) if the number 2
be visible at the circular aperture of the units' wheel and it is desired to add 1
thereto, by inserting the stile in the curved slot at the number 1 and turning
the wheel to the right hand (the teeth being white) the wheel will be moved
round one tooth, and in place of the number 2 the number 3 will be presented;
if it is now wished to add 7, by inserting the stile in the proper place in the
slot and on turning it to the left (the teeth being black) 10 will be presented,
the number in the units' place having been diminished by 3, and the wheel
of the tens' place having been advanced a tooth by the stile during its motion.
in the units' slot, having carried forward the overhanging tooth of the said tens'
wheel. Instead of arranging the several wheels according to the decimal
system of notation, it is evident that by altering the lengths of the slots and the
number of the teeth they may be arranged according to any other; for example,
the wheel on the extreme right hand may be arranged for farthings, the next
on the left hand for pence, the third for shillings, and the next for pounds; but
these modifications are so obvious that I deem a particular description of them
unnecessary.
Figure 4 represents a perspective view of my apparatus or instrument for
effecting the processes of multiplication or division. It consists of a shallow
rectangular box S, T, in the interior of which a series of cylinders turning in
their axes are situated, the number of which said cylinders depends upon the

page_text: value of the quantity which the instrument is intended to multiply, that is to
say, if it is intended to multiply sums or quantities not exceeding thousands
then there must be a series of five cylinders, one for the units, one for the tens,
one for the hundreds, one for the thousands, and one for tens of thousands.
The instrument represented has eight cylinders, and is calculated to effect the
multiplication of quantities not exceeding millions. One end of the axis of
each of the said cylinders project through the front of the box and is termi-
nated by a knob (see i, j, k, l, m, n, o, p, in the Figure.) By means of these
knobs a rotatory motion may be communicated to the said cylinders. Besides
a rotatory motion of the whole cylinder, a portion of each of the cylinders,
excepting the one on the extreme right hand of the instrument, (the units'
cylinder marked p in the Drawing,) has a longitudinal motion, that is to say,
a motion along or parallel to its axis. This longitudinal motion is communi-
cated to the cylinders by the lower series of knobs i, j, k, l, m³, n', o¹, and
the manner in which the said longitudinal motion of the cylinders is effected
by the said knobs will be understood by reference to the representation of one
of the cylinders shown in a detached form in Figure 5. q is the square axis of
the cylinder, and r is the knob by which it may be made to rotate; that part
of the cylinder marked s is immovably fixed to the axis q; while that portion
marked is capable of a sliding motion on the said square axis q. u is a
groove formed near the end of the moveable portion of the cylinder ; and v
is a fork which engages or falls into the said groove u; through this fork
the screw w works, and by turning the knob x on the end of the said screw the
fork and with it the moveable portion of the cylinder may be made to
slide up and down its axis. The knob r in Figure 5 corresponds to the knobs
i, j, k, l, &c. in Figure 4, and the knob x in Figure 5 corresponds to the
knobs i, . k, l, &c. in Figure 4. 1, 2, 3, 4, 5, 6, 7, 8, Figure 4, are
a series of rows of apertures in the top of the box S, T, through which
apertures some of the figures inscribed on the cylinders immediately under
them, as herein-after described, are visible. There is a row of these aper-
Lures over each of the cylinders of the instrument, and the number of such
rows will consequently vary with the number of the cylinders which the instru-
ment contains; but if these apertures be regarded as rows in a transverse
direction, that is to say, across the cylinders (in which way they must be
regarded in using the instrument), then it will be observed that they constitute
eleven such rows, and that by altering the number of cylinders the number of
apertures in each row will be altered, but the number of rows, (that is to say)
(eleven) always remains the same. The table of numbers hereunto annexed,
marked A, is wound round and attached to the cylinder on the right hand of

page_text: the instrument, that is to say, the units' cylinder and the table hereunto an-
nexed, marked B, is wound round and attached to the fixed portion of the
cylinder on the extreme left of the instrument. The table hereunto annexed,
marked C, is wound round and attached to the moveable part of the cylinder
on the extreme left hand of the instrument, and on the fixed part of each of
the other or intermediate cylinders the table hereunto annexed, and marked D,
is wound round and affixed. The table hereunto annexed, marked E, is wound
round and attached to the moveable part of each of the said intermediate.
cylinders. As the tables to be attached to the cylinders on the extreme right
hand and left hand of the instrument are less than those to be attached to the
intermediate cylinders, the said extreme cylinders are of less diameter than the
said intermediate cylinders, and in order to bring the figures on the said
extreme right-hand and left-hand cylinders as close to the top of the box as
those of the intermediate cylinders, the axes of the said extreme cylinders are
placed nearer the top of the box than those of the intermediate cylinders,
as seen by the position of the knobs on their ends at i, p, Figure 4.
Before describing the method of using the instrument, I wish it to be
particularly observed that the multiplicand, or quantity to be multiplied,
must be made to appear in the manner herein-after described in the lower
transverse row of apertures, marked 11; that is to say, the units of the
said multiplicand in the extreme right-hand aperture of the said row; the
tens of the said multiplicand in the second aperture, counting from the
right hand, the hundreds in the third aperture, and so forth; and when
the multiplicand has been made to appear in the said row 11, and the
other manipulations gone through, herein-after described, the product of the
said multiplicand by 2 is exhibited at the row of apertures marked 2; the
product by 3 at the row 3'; the product by 4 at the row 41; the product by
5 at the row 5'; the product by 6 at the row 6¹; the product by 7 at the
row 7; the product by 8 at the row 8'; the product by 9 at the row 9. By
consulting the table A, to be attached to the units' cylinder, it will be seen that
the bottom row of figures consists of the series 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and
that if the said cylinder be turned, so as to bring any one of these numbers to
the units' place of the multiplicand (I will suppose the number 2), there will
appear at the units' place of the row 3' (the product by 3) the number 6; at the
units place of the row 4' (the product by 4) the number 8; at the units' place
of the row 5 (the product by 5), the number 0; at the units' place of the
row 6' (the product by 6) the number 2; at the units' place of the row 71 (the
product by 7) the number 4; at the units' place of the row 8' (the product by 8)
the number 6; at the units' place of the row 9' (the product by 9) the number 8;

page_text: and since the said units' cylinder has but one motion (that of rotation) these
same numbers must always present themselves in the rows 2, 3¹, 4¹, 5¹,
6, 7, 8, 9, when the same number is brought to the units' place of the
multiplicand. But by consulting the tables D, E, which are attached to the
tens'. hundreds', &c. cylinders, it will be observed that each number in the
multiplicand row is repeated four times; so that if any number, 9 for example,
be brought to the tens' place of the multiplicand row since either of the
four numbers 9 may, by turning the knob be brought there, the numbers pre-
sented at the tens' places exhibiting the several products by 2, 3, 4, 5, 6, 7, 8, 9,
may vary: thus. if the first number 9, counting from the right hand. be brought
to the tens' place in the multiplicand row (the moveable portion of the cylinder
being brought as near as possible to the fixed portion of the said cylinder), the
numbers 9, 9. 9. 8. 8. 8, 8, 7 will appear at the tens' places of the several
rows 2, 4, 3, 5, 6, 7, 8, 91; if the second number 9 be brought to the tens'
place of the multiplicand, the numbers 9. 8. 8. 7. 7, 6, 6, 5 will appear at the
tens' places of the several rows 2¹, 41, 31, 51, 61, 71, 81, 91, and the series will
be varied each time a different number 9 is chosen, that is to say, the same
number (9) being presented at the tens' place of the multiplicand four different
numbers may be presented at each of the tens' places in the product rows, and
that by the rotatory motion of the cylinders; but since that part of each cylinder
which is presented at the rows exhibiting the products by 3, 5, 6, 7, 8, 9 has
a sliding motion, as herein-before described, and as the extent of that sliding
motion is such that seven different numbers in the vertical rows of the table
may be presented at pleasure, hence by the rotatory and sliding motion of each
cylinder there may be presented at the aperture of the tens' place in the rows
representing the products of the multiplicand by 3, 5, 6, 7, 8, 9, any one of the
twenty-eight figures constituting the several groups into which the table may
be divided, as shewn by the coloring in the Drawing. It is hence necessary to
select the proper one of the four numbers 9 which may be taken, and also
necessary that the position of the moveable portion of the cylinder be properly
adjusted, before the correct number can be presented at the product apertures.
By further consulting the tables D, E, it will be observed that the same applies
to every number in the multiplicand (excepting the number in the units' placo)
that is to say, for each such multiplicand number there is a series of twenty-
eight numbers, either of which may by adjustment of the cylinder appear at
the same aperture.
In order therefore to use this instrument it is necessary to possess some rule
whereby each of the cylinders may by its rotatory and longitudinal motions

page_text: present the proper numbers at the several product apertures over it; and
I will next explain the rule to be observed to effect this object.
In order more clearly to illustrate the method to be pursued in using this
instrument, I will suppose that it is wished to obtain the products of the
quantity 1, 2, 3, 4 by 2, 3, 4, 5, 6, 7, 8, 9: the units number of the
multiplicand (4) must be brought to its plate in the right-hand aperture of
the row 1. When this is done the small number 2, see the (table A), will
immediately appear in the first or right-hand place of the row 10, which row
I will call the lower index row, to distinguish it from the other row of small
figures 11, which I will call the upper index row. The tens' number of the
multiplicand (that is to say the number 3) must be brought to the tens' place of
the multiplicand row; but since (see the table D) there are four numbers 3 it
must be determined which of these must be selected. In order to do this, the
knob 0 of the cylinder must be turned until that number 3 is presented, over
which in the second aperture of the lower index row there is presented the
small number 22; next bring the number 2 to the hundreds' place in the
multiplicand row, selecting that number 2, over which in the lower index row
the number 12 is situated; next bring the number 1 in the thousands' place of
the multiplicand row, selecting that number 1 which has over it in the lower
index row the number 11; to all the other places of the multiplicand row
that 0 must be brought which has over it in the lower index row the small
number 11. When this has been done there will be found in the row 2¹ the
sum 2468, which is the product of 1234 by the multiplier 2, and in the row 4'
there will be found the sum 4936, which is the product of 1234 by 4; in the
several rows 31, 51, 6, 7, 8, 9', however, the products of 1234 by 3, 5, 6,
7, 8, 9 will not be presented until another adjustment of the moveable parts
of the cylinders has been effected by the knobs o¹, n', m², l', k', j', . In order
to make this adjustment, regard must be had to the upper index row 11. In
the units' place of this row (the number 4 having been brought, as already
supposed, to the units' place of the multiplicand row, and the adjustments
herein-before described having been made, the number 5 will be found the
lower knob of the tens' place, (to which place in the multiplicand row the
number 3 has been brought, as herein-before described,) must be turned until
the number 35 has been brought to the tens' place of the upper index row, and
the lower knob of the hundreds' place (to which place in the multiplicand row
the number 2 has been brought must be turned until the number 73 has been
brought to the hundreds' place of the upper index row, and the lower knob of
the thousands' cylinder (the number 1 having been brought to the thousands'

page_text: place of the multiplicand row, as herein-before described,) must be turned until
the number 27 is presented at the thousands' place of the upper index row, and
the lower knobs of the other cylinders must be turned until the numbers
12, 11, 1, have been brought in succession to the other apertures in the
upper index row. When this has been done the several rows of apertures
31, 5, 6, 7, 8, 9¹, will exhibit the product of 1234 by 3, 5, 6, 7, 8, 9.
The rule by which these adjustments have been made is as follows:-
In registering the multiplicand in the proper row, observe after the units
number (4) has been brought to the units' place, the small number (2), which
is presented at the units' place of the lower index row, and in selecting the
number (3) for the tens' place in the multiplicand, that number (3) must be
selected, which will bring to the tens' place of the lower index row two small
numbers (22), the right-hand one of which is the same as that in the units
place of the lower index row. So also, in proceeding to select the numbers in
the other places of the multiplicand, it is necessary to select those which will
bring to the aperture in the lower index row two numbers, the right-hand one
of which is the same as the left-hand one, in the place of the lower index row
last adjusted. The same rule must also be observed in adjusting the upper
index row the number presented at the units' place of that row must be
observed, and the tens place cylinder must be so adjusted by the lower knob of
the said cylinder that the right-hand number of the two numbers presented at
the aperture of the upper index row shall be the same as that presented at the
units' place of the said upper index row; and in adjusting the other places,
proceeding from the units to the tens, hundreds, thousands, and so forth, the
two figures in the aperture of the index row must be selected, the right-hand
one of which is the same as the left-hand one in the aperture of the index row,
in the place last adjusted. When these adjustments have been made, the
several rows 2, 3, 4, 5, 6, 71, 81, 9' will exhibit the products of the quan-
tity 1234 by 2, 3, 4, 5, 6, 7, 8, 9. It is scarcely necessary to observe, that if
it is wished to perform a compound multiplication it is only necessary to select
the product of the multiplicand by the unit of the multiplier, and setting that
down, or registering it by the addition instrument, herein-before described,
proceed to set down or register the product by the tens figure of the multiplier,
taking care to place that product in its proper place, so that the units of that
quantity shall be under the tens of the previous one, as in the common method
of compound multiplication, and on adding them up (if set down on paper),
the result will be the product of the multiplicand by the compound multiplier.
The application of this instrument for effecting or facilitating the arith-
metical process of division is so obvious that I deem a particular description

page_text: unnecessary. It will suffice to remark, that in effecting any division, particu-
larly long division, if the division be brought to the multiplicand row, and all
the adjustments berein-before described, be made, the several products. of the
division by 2, 3, 4, 5, 6, 7, 8, 9 will be presented. and the product of the
division by the proper multiplier being selected and subtracted from the
dividend, the next number (in long division) being brought down, the next
product of the division by the proper multiplier may be selected.
Having now described the nature of my said Invention, and the manner in
which the same is to be performed, I wish it to be understood that I do not
limit myself to the precise method of carrying my Invention into effect, herein-
before described, and represented in the accompanying Drawing, as the same
may be varied without departing from the nature of my said Invention. For
example, I have herein-before explained. that my instrument or apparatus
for effecting multiplication consists of an arrangement of parts whereby the
proper one of a group of twenty-eight figures may be brought to each of the
apertures of the several rows (excepting in the case of the units' place, and the
place on the extreme left of the instrument, in which places individual num-
bers of other series, as herein-before described, must be brought); and in the
tables C and E, hereunto annexed, I have alternately coloured and left
uncoloured the said groups of figures. Now, although I consider the method
of grouping I have adopted, namely, four vertical columns of seven numbers
each, the most convenient, it is evident the same series may be grouped in a
different manner, and the like results produced as in seven rows of four num-
bers, two rows of fourteen numbers, or a single row of twenty-eight numbers,
and suitable arrangements may be made for bringing into view the proper
figure of the series by means of cylinders or continuous bands passing over
rollers, but all such arrangements of the series of numbers inscribed on the
tables C, E, as well as those on the tables A, B, D, I consider inferior to the
method or arrangement I have herein-before described.
I claim as my Invention, Firstly, the method of constructing an instrument
or apparatus for effecting the arithmetical processes of addition and subtrac-
tion, herein-before described, and represented in the accompanying Drawing,
that is to say, an instrument or apparatus consisting of a series of toothed
wheels, on each of which a series of numbers are inscribed, the said wheels
being wholly unconnected with each other, and moved by a stile introduced
between the teeth thereof, the said stile moving only the wheel between the
teeth of which it is introduced when the said wheel is turned in one direction,
but moving also the adjoining wheel, by engaging in its overhanging teeth,
when moved in the other direction whether the details of the said instrument

page_text: resemble or differ from those of the instrument herein-before described, and
whether the instrument is constructed according to the decimal or any other
system of notation.
Secondly, the method of constructing an instrument or apparatus for effect-
ing the arithmetical processes of multiplication and division, herein-before
described, and represented in the accompanying Drawing, that is to say, an
instrument whereby the proper individuals of series or groups of numbers are
presented at apertures, so as correctly to represent the product of any multi-
plicand by the multipliers 2, 3, 4, 5, 6, 7, 8, 9, whether the said series or
groups of numbers be arranged in the manner represented in the accompany-
ing tables, marked A, B, C, D, E, or in any other manner, and whether the
same mechanism be employed for bringing the proper number to the proper
aperture, or any other mechanism be used for that purpose.
In witness whereof, I, the said David Barnett, have hereunto set my
hand and seal, this Twenty-second day of March, in the year of our
Lord One thousand eight hundred and forty-seven.
DAVID (L.s.) BARNETT.
AND BE IT REMEMBERED, that on the Twenty-second day of March,
in the year of our Lord 1847, the aforesaid David Barnett came before our
said Lady the Queen in Her Chancery, and acknowledged the Specification