Year: 1886

page_text: I, JULES VICTOR CHARPANTIER of No G Carondelet Street New Orleans Parish
of Orleans State of Louisiana United States of America Notary Public, do hereby
declare the nature of this invention and in what manner the same is to be
performed, to be particularly described and ascertained in and by the following
statement:
The object of my Invention is to provide devices whereby to arrive at the
results of the multiplication of any numbers by the numerals from two to nine
without mental labor on the part of the operator.
The Invention consists in a novel construction, combination, and arrangement of
parts as will be hereinafter explained.
In the accompanying drawings forming part of this specification; figure 1 is a
perspective view of my improved apparatus, parts being broken away and others
shown in section, figure 2 is a plan view of the apparatus, the lid being removed;
figure 3 is a representation of the first or unit section of the table; figure 4 shows
a part of the second or tens section of the table; figure 5 represents a part of the
third or hundreds section of the table. Figure 6 shows reference tables; figures 7.
8. 9. and 10. show examples illustrating the operation of my Invention. The same
letters of reference indicate the same parts in all the figures.
The box or case A may be of any suitable construction, opening at one side as
shown, which opening may be covered with glass where so desired. In the front
of the box I secure parallel to each other a series of guides B, preferably journaled
rollers as shown. These guides are placed in close relation usually a distance apart
equal to the thickness of two sheets of paper about as shown. Manifestly, the
number of these guides may be varied. In the box in rear of these guides I arrange
carrying rolls C C two for each of the guides and having knobs c by which they
may be turned. It is preferred to arrange the rolls of each pair one in rear of the
other in order that a larger number of rolls may be arranged in a given width of
box, as will be understood from figure 2. The table-sections D, D', 'D', D³, D',
D, D, and D' being sheets usually of paper inscribed as will be described, are
supported alike so that the description of one will answer for all. The figures and
other marks forming the table may be printed or written upon linen, paper, or
other suitable material. Such section or sheet, it will bo seen, is passed around
one of the guides B and bas its ends passed through between such guide and those

page_text: on opposite sides thereof and such ends are then carried to and wound on the
rolls C of the paper used in connection with the particular guide B, as will be seen
in figure 2. By thus disposing the inscribed sheets it will be seen I am able to
bring the registered portions of the several sheets in close relation and also expose
but a single longitudinal row of figures of each of said sheets at the same time.
Thus, I prevent the possibility of misreading the several sheets, or of reading from
one row of figures of one sheet when another should be considered, as but a single
row is exposed at a time. Belts E are disposed around the rolls C and guide B of
each set, and serve to communicate positively to each member of the set the motion
given to any one thereof by the operator, enabling a rapid and easy movement of
the inscribed section, and serving to prevent any slipping thereof.
I will now proceed to describe the several sections, and the manner of using the
apparatus for the desired purpose. On the box, at the front, is fixed a vertical
row of numerals from 1. to 9 as shown at d. These are to be used as the
multiplying numerals, as will be explained hereinafter. Upon the rollers and guide
at the right of the box, a section D of the table representing units is placed. This
section is shown in figure 3 of the drawings. On the remaining sets of rollers,
sections D', D', D³, etc of the table, representing tens, hundreds, thousands, etc are
respectively arranged. The numbers to be multiplied by any of the numerals
fixed to the side of the box, occupy a position on the table in line with the
numeral 1 on the side of the box, as shown; and they are registered or set up as a
multiplicand by being brought to the front of the respective guides.
The first section of the table, figure 3, has upon it, as seen at a, figure 3. a row
of numerals from 0 to 9 arranged from right to left (when placed in proper position
upon the rollers within the box this line of figures will be opposite the figure 1
fixed to the margin of the box). Under these numerals are arranged the multiples
of each from 2 to 9 in line respectively with the multiplying numerals on the sides
of the box. The tens, or the number to be carried, are to be marked in red to the
left of the figure set down, or designated by smaller type, or in some other suitable
manner. In all the operations on the tables, if a cipher is registered to the left of
the last number to be multiplied it will not be necessary to use or pay attention to
the figures representing the amount to be carried to the next number to be
multiplied. If any one of the ten figures in the registration or multiplicand line
of the unit section of the table be registered or brought to the front of the box by
moving the rollers on which this table is placed, the products of the multiplication
of the said figure by any of the numerals from 2 to 9 appear on the table under
the number registered and in line with the respective multipliers on the margin of
the box, the unit of the product being in black or shown by large figure, the tena
if there should be any being in rod or shown by smaller type. If there is only one
number to be multiplied the tens, if any, are of course set down; but if more than
one number be registered for multiplication, no attention is paid to the carrying
figure, it being carried in the other sections of the table.
The second section of the table, the first part of which is shown in figure 4, is to
be arranged on the second pair of rollers C from the right of the box and is
divided by vertical lines into ten parts, each of which has at its top the numerals
from 0 to 9 arranged from right to left, as shown at b. Under these numerals in
the first part of this section is arranged a horizontal row of ciphers e; in the second
part, which is partly shown in figure 4. a row of ones f; in the third (not shown)
a row of twos, etc; the tenth part having a row of nines. The horizontal row
formed of ciphers, ones, twos, etc is the registration row of the tens, and when the
table is placed on the roller is to be in line with the registration row on the first
roller. Under each figure of the rows of ciphers, ones, etc forming the multiplicand
or registration row are arranged in vertical lines the results produced by adding to
its different multiples (by the figures 2 to 9) the amount carried in the multiplication
of the figure placed above it in the line of figures at the top of the sheet, these
figures at the top representing the units that may be registered on the first roller,
the amount carried, if any, from the multiplication of the figures of the unit

page_text: column being added in the table. It will be noticed that the registration line in
the first part of this section of the table is formed of a series of ciphers, either one
of which can be brought to the front of the roller or registered, the registration
line in the second part (shown partly at f, figure 4) being formed of a series of
ones either of which can be registered. The table is so calculated and arranged
that in order to get the true result when we register a figure for multiplication
that one of the series must be registered which is beneath the figure corresponding
to the one registered for multiplication in the unit column. If we desire to
multiply 2 by 9 we turn the first roller until the figure 2 in the registration line
is brought to the front, and the result is seen opposite the multiplier 9 at the sides
of the box. If we want to multiply 92 by 9, the 2.is registered in the manner
described, and then the second roller is turned until the part having the series of
nines in the registration line appears, and the figure 9 in this line which is found
under 2 in the line above is brought to the front and the result is correctly shown
by the table.
On the third pair of rollers is to be placed another section of the table, the first
part of which is shown in figure 5. This section of the table, like the second
section, is divided into ten parts the first part of which is shown completely in
figure 5, and a portion of the second part being seen to the left of the vertical
line h figure 5. Each of these ten parts corresponds in the registration line to one of
the figures 0 to 9. In the first part as shown in the drawings at c the registration
row is composed of a series of ciphers; in the second part a portion of which is
shown at i figure 5 it will be formed of a series of ones; in the third of twos etc;
Above each of the ciphers are arranged in vertical rows, double figures from 00
to 99, which represent all of the combinations that can be registered in the
preceding operations. These double figures are arranged in vertical rows the first
rows containing the figures 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 10 and 11. the
second. containing the figures 12; the third figures 13 and 14 the fourth figures 15
and 16; the fifth figures 17 to 19 inclusive; the sixth figures 20 to 22 inclusive
the seventh figures 23 and 24; the eighth figures 25 to 28 inclusive; the ninth
figures 29 to 33 inclusive; the tenth figures 34 to 37 inclusive the eleventh
figures 38 and 39; the twelfth figures 40 to 42 inclusive; the thirteenth figures 43
and 44; the fourteenth figures 45 to 49 inclusive; the fifteenth figures 50 to 55
inclusive; the sixteenth figures 56 and 57; the seventeenth figures 58 and 59; the
eighteenth figures 60 to 62 inclusive; the nineteenth figures 63 to 66 inclusive ;
the twentieth figures 67 to 71 inclusive the twenty first figures 72 to 74 inclusive;
the twenty second figures 75 to 77 inclusive; the twenty-third figures 78
and 79; the twenty fourth figures 80 to 83 inclusive; the twenty-fifth figures 84
and 85; the twenty-sixth figures 86 and 87, the twenty seventh figures 88; and
the twenty eighth row figures 89 to 99 inclusive. It will be seen upon examination
that these double figures are so arranged in the several vertical columns, that the
amount to be carried in their multiplication (if any) is the same for all the figures
arranged in any particular column. These double figures are arranged in the
manner shown, on account of the changes that occur in multiplying.
The figures 00 to 11. in the first colump if multiplied by any of the numerals
from 2 to 9 have nothing to carry in the horizontal lines of results. Under 12
there is a change in the result given in the ninth horizontal line, for 12 multiplied
by 9 gives 108 or 1 to carry. Under 13 and 14 there is a change in the eighth
horizontal line, 1 to carry under 15 and 16, a change in the seventh line of result
1 to carry; under 17 a change in the sixth line 1 to carry; under the column
headed by 20 a change in the fifth line 1 to carry. Under 23 we have a change in
the ninth line 23 × 9=207 or 2 to carry. Under 25 there are two changes, in the
fourth line we have 1 to carry and in the eighth line 2 to carry. Under 29 we
have 2 to carry in the seventh line. Under the column headed by 34 there are
three changes, in the third line 1 to carry, in the sixth line 2 to carry, and in the
ninth line 3 to carry. Under 38 there is a change in the eighth line 3 to carry ;
under 40 a change in the fifth line 2 to carry; under 43 a change in the seventh

page_text: line 3 to carry. Under the column headed by. 45 we have 4 to carry in the
ninth line. Under 50 there are four changes, 1 to carry in the second line, 2 to
carry in the fourth line, 3 to carry in the sixth line, and 4 to carry in the
eighth line. The next change occurs under 56 where we have 5 to carry in the
ninth line. Under 58 we have 4 to carry in the seventh line. Under 60 we
have a change in the fifth line 3 to carry; under 63 a change in the eighth
line 5 to carry; under the column headed by 67 there are three changes, 2 to
carry in the third line, 4 to carry in the sixth line, and 6 to carry in the ninth
line. Under 72 we have a change in the seventh line 5 to carry. Under 75 there
are two changes, 3 to carry in the fourth line, 6 to carry in the eighth line.
Under 78 there is a change in the ninth line 7 to carry. Under 80 in the fifth
line, there is four to carry. Under 84 in the sixth line we have 5 to carry;
under 86 a change in the seventh line 6 to carry; under 88 a change in the
eighth line 7 to carry; and under the column headed by 89 a change in the ninth
line, 8 to carry.
In all the succeeding parts of the third section of the table, the same double
figures are arranged in the same manner over the series of ones, twos, threes, etc
which form the registration row of the succeeding parts. Under each figure of
the rows of ciphers, ones etc forming the multiplicand line, are arranged the
results produced by adding to its different multiples the amount carried in the
multiplication of the figures placed above it This section of the table is used in
the same manner as the second, except that two numbers corresponding to the two
numbers previously registered are taken into consideration. Thus, if we have the
numbers 765 to multiply, we first register the 5 on the section of the table on
the first roller, then on the second roller we register the figure 6 that has the
figure 5 above it, and then we turn the third roller until the series of sevens
appears, and bring that one to the front which is under the figures 6 and 5.
sections of the table to be arranged on the fourth, and all succeeding rollers, to the
left, are similar in construction to the third section just described.
.
The
In the inultiplication of any number of more than three figures we meet with
a difficulty. If we have four figures to multiply and we register the fourth figure
under the row of double figures containing the two figures that we have just
registered to the right, the answer will not always be correct because the first
figure registered may be such that the amount to be carried in the multiplication
of the fourth figure will be changed. If, for example, the sum to be multiplied
was 1112, and we register the figure 1 in the fourth section of the table, that is,
underneath the figures 11-representing those just registered to the right, if we
use 9 as the multiplier the answer given by the table will be 9008 which will
be wrong, the correct answer being 10008. This difficulty is obviated in the fourth,
and all succeeding sections of the table, by proper references which prevent any
trouble on the part of the operator in arriving at the correct result of the multipli-
cation of any sum from four to any number of figures by the numerals from 2 to 9.
Under the vertical columns of double figures in the fourth and succeeding sections
of the table when any changes are to be made letters of reference are placed as
shown in the examples at d figure 7. and also in figure 9. These letters refer the
operator to a small book or table accompanying the apparatus, the letter A being
placed under the column ending with 11; the letter B under that.ending with 12;
the letter C under 14 etc. The first two pages of this book or table referring
respectively to the fourth and fifth sections are shown in figure 6 of the accom-
panying drawings.
The reference letter A under the column ending with 11 shows, by referring to
the book or reference sheet, that if 11 is registered and the number preceding it
in the registration line is any number from 2 up we must register the next number
under 12, because if 11 is preceding by any number from 2 up, the ninth horizontal
line of results is changed, and this change will correspond to the, results given
under 12. The reference letter B under 12 shows that if the 12 be preceded, to
the right by any number from 5. up we must register under 13 because the eighth

page_text: line of results is changed. Reference letter C shows that when 14 registered
and is preceded by any number from 3 up, we must register under 15 because the
seventh line is changed. Reference letter D shows that when 10 representing
the two numbers just registered to the right is preceded by any number from
7 up we must register under 17 because the result in such case will correspond to
the results given under 17, the sixth horizontal line being changed. E shows
that when 22 is preceded by any figure from 3 up we must register under 23 the
ninth line being changed. F shows that when 28 is preceded by any of the figures
from 6 up we should register under 29 the seventh horizontal line being changed.
G under 33 shows that if 33 is preceded by any figure from 4 up we should register
under 34 the third, sixth, and ninth horizontal lines being changed. H under 37
shows that when 37 is preceded by any figure from 5 up we must register under 38
the eighth horizontal line being changed I shows that when 42 is preceded by
figure we must register under 43 the seventh line being changed. J under 44
shows by the reference sheet that when 44 is preceded by any figure from 5 up we
must register under 45 because the ninth line is changed. K. under 55 shows that
when 55 has or a higher number to the right we must register under 56 because
the ninth line of results is changed. L shows that when 57 has 2 or a higher
figure to the right we must register under 58 the seventh line being changed.
M shows that when 62 has 5 or a higher figure to the right the eighth line is
changed and we must register under 63. When 66 is preceded by any number
from 7 up the reference letter N informs us that we must register under 67 third,
sixth, and ninth lines being changed When 71 is preceded by any figure from
5 up the letter O informs us that we must register under 72, the seventh horizontal
line being changed. If. 77 has 8 or a higher figure to the right the letter P informs
us that we must register under 78 the ninth line being changed. When 83 is
preceded by any figure from 4 up the sixth line changes and the letter Q informs
us that we must register under 84. When 85 is preceded by 8 or a higher
figure, the reference letter R directs us to register under 86, the seventh line
being changed. When 87 has 5 or a higher figure to the right, the letter S shows
that we must register under 88 the eighth line being changed. The reference
letter T under 88, indicates by reference to the corresponding letter on the table,
that if 88 is preceded by 9 we must register 89 the ninth line being changed.
Thus in registering the fourth figure to be multiplied if the second and third
figures just registered are 11 when the fourth roller is turned so as to bring the .
fourth figure to be registered under the vertical column of figures containing 11
the letter A under that column will refer the operator to the table or page corre-
sponding to the section of the table on the fourth roller and there he will see that
if the figure preceding the 11 in the line to be multiplied be any number from 2 up
he must register the fourth figure which is under the vertical column headed
by 12.
This is done by simply moving the roller one turn to the right. The
letters of reference on the fourth section of the table refer to the reference leaf
marked 1 in the drawings. If a fifth section is used, the references would refer
to the leaf marked 2. Any desired number of sections may be used in the table,
and the apparatus so arranged as to multiply any number of figures.
The following are examples of the manner in which the device is to be used for
multiplying To multiply 5,632 by 492 we first register 2 on the first roller, then
on the second roller under 2 at the top we register 3, on the third roller under 32
at the top we register 6, and on the fourth roller under 63 at the top we register 5,
attention being called to letter N. We refer to this letter in the reference
table or book. As we find no reference made to 63 the column stands correct.
The figures on the several rollers will then appear as in figure 7. The horizontal
rows in line with the desired. multipliers being set down as shown at figure 8 the
operation is completed by one addition. To multiply 4,667 by 3412 we register 7
in the multiplicand line on the first roller, 6 on the second roller under 7, 6 on the
third roller under 67 and, noticing that letter O has no reference to the present
case, we turn the fourth roller until the 4 under 66 comes to the front which would

page_text: give the column A as shown in figure 9. The reference N will show that the 4
must be registered under 67. We turn the register one number to the right, and
obtain 4 in column containing 67 and have the correct answer as shown by line B
figure 9. The amounts opposite the multipliers 3, 4, 1, and 2, having been set
down as shown in figure 10 the result will be found by adding them together.
From the above description, it will be seen that any given number can be
multiplied by any one of the numerals from 2 to 9 without requiring any addition
or carrying of figures and that when we desire to multiply by 2 or more numbers
it is only necessary to register the multiplicand in the manner directed, and
the result of the multiplication by each of the numerals is found in line with the
multipliers on the side of the box. We have only to set down the products of the
multiplication found in line with the multipliers as in ordinary multiplication, and
one addition will give the result.
As suggested, a difficulty arises in the multiplication by the apparatus described
of any number of more than three figures, which difficulty is met by reference
tables before described. To avoid the possibility of error in referring to such
tables I provide an index F numbering 1. 2. 3. etc ranging from the fourth section
out, 1 referring to fourth, 2 to fifth, 3 to sixth section, and so on. By this means
there is at once indicated to the operator the page or section of the reference table
to which he should refer in registering a figure in any given one of the inscribed
sections. By these constructions I secure an apparatus by which the several parts
to be read in order are held in close relation, and the tables of reference to which
the operator should refer is clearly indicated in each case, thus avoiding, or reducing
the liability to error.
Having now particularly described and ascertained the nature of the said
Invention and in what manner the same is to be performed, I declare that what
I claim is;
-
1. The combination of the support or case, the movable sections inscribed sub-
stantially as shown, and an index F arranged relatively to the rolls and beginning
at 1 with a predetermined one of said sections, and continuing in proper numerical
relation with the succeeding sections, substantially as set forth.
2. The improved apparatus for facilitating the multiplication of numbers, con-
sisting of the support or case, the series of carrying rolls arranged in pairs; the
series of guides arranged close together and provided one for each pair of carrying
rolls, the table or sections wound on the carrying rolls and directed between
their ends around the guides, the belts connecting the carrying rolls and guides,
and the index arranged relative to the rolls and beginning at with a predetermined
one of the tables or sections and continuing in proper numerical order in relation
with the succeeding sections substantially as set forth.
Dated thia 15th day of June 1886