A METHOD OF AND APPARATUS FOR SETTING SUMS FOR THE PURPOSE OF TEACHING SOME OF THE RULES OF ARITHMETIC
Year: 1830

page_text: TO ALL TO WHOM THESE PRESENTS SHALL COME, I, JOHN
TYRRELL, of Saint Leonard's, in the County of Devon, Esquire, Barrister-at-
Law, send greeting.
WHEREAS IIis present most Excellent Majesty King William the Fourth,
by His Letters Patent under the Great Seal of Great Britain, bearing date at
Westminster, the Thirteenth day of November, in the first year of Ilis reign,
did, for Himself, IIis heirs and successors, givo and grant unto me, the said
John Tyrrell, His special licence, sole privilege and and authority, that I, the
said John Tyrrell, my exors, adñiors, and assigns, or such others as I, the said
John Tyrrell, my exors, adñiors, 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 mentioned, should and lawfully might make, use, exercise, and vend,
within England, Wales, and the Town of Berwick-upon-Tweed, my Invention
of "A METHOD OF AND APPARATUS FOR SETTING SUMS FOR THE PURPOSE OF
TEACHING SOME OF THE RULES OF ARITHMETIC ;" in which said Letters Patent
is contained a proviso, that I, the said John Tyrrell, shall cause a particular
description of the nature of my said Invention, and in what manner the same
is to be performed, to be inrolled in His said Majesty's High Court of
Chancery within six calendar months next and immediately after the dato
of the said in part recited Letters Patent, as in and by the same, referenco
being thereunto had, will more fully and at large appear.
NOW KNOW YE, that in compliance with the said proviso, I, the said
John Tyrrell, do hereby declare that the nature of my said Invention, and in

page_text: what manner the same is to be performed, is particularly described and
ascertained by the following description thereof, (reference being had to the
Drawings hereunto annexed, and to the Figures and letters marked thereon
(that is to say).
:-
My method of setting sums is this:-On a long strip of parchment or of
thick paper I place several rows of figures, each figure of the second row
being directly under a figure in the first, and so with the third and other rows;
the figures of the top row I number by the numbers one, two, three, &c.,
placed at some little distance above them. The principle of my apparatus is
to let only those figures be seen which will form a sum in the particular rule
which I wish to teach. To effect this I have found it convenient to prepare a
box or frame with a roller at each end, and I attach my strip of paper or
parchment to each roller, so that as it is rolled up on one it is rolled off the
other, leaving a portion of the rows of figures to be seen between them. Over
the face of that portion I place a card, with apertures cut in it to let the figures
forming the sum be seen, and to let one of the numbers 1, 2, 3, &c. at the
top be seen. Then if the suni to be set is common addition I cut a small
aperture for the number at the top, and I cut a larger rectangular aperture
to let several of the figures in each row appear. For subtraction I allow
a portion of two contiguous rows to be seen by cutting a long aperture in
another card, and taking care that the under row is the shorter by one figure
or more figures at the left-hand to insure its being always the lesser. For
multiplication I let several figures in one row be seen, and one, two, three, or
more figures in the row immediately under it, according as I wish to teach
multiplication by one, two, three, or more figures. For division I let a portion
of one row be seen, and at a little distance to the left hand of that portion I let
one, two, three, or more figures of the same row be seen, according as I wish
to set a sum in division by one, two, three, or more figures.
To understand this the better, refer to the accompanying paper marked
Plate A; there you will see the rows of figures with the numbers at the top
I have found five a convenient number of rows, but there may be more or
less. The accompanying paper marked Plate B is an impression from the
copper plate which I have to print five of the cards for the common rules
of arithmetic upon a large piece of card paper; the parts to be cut out are
marked round with lines and coloured blue.
My mode of setting sums in the compound elementary rules of arithmetic
is not so easily explained without referring to the accompanying paper marked
Plate C, which is an impression taken from a copper plate intended to print
six cards for these rules. By reference to this plate it will be obvious what

page_text: apertures are necessary to set sums in these rules; these apertures also are
marked round by lines and coloured blue. On the cards which set the sums
in addition of money, wherever I wish the shillings to amount to ten or more,
I put the figure 1 upon the card so as to stand immediately before the figure
on the strip of paper or parchment, which will come into the aperture for
shillings. If I wish to have halfpence or farthings in any of these sums, I mark
them upon the card in their proper place. In addition, &c. of avoirdupois weight,
I also mark the figure 1 upon the cards, so as to make the hundredweights
and pounds equal or exceed ten; and I also put the figure 1, or 2, or 3, or
a cypher, in the place which denotes quarters, because 3 is the highest number
which can stand in this place, and if I left an aperture, higher numbers would
appear. In compound multiplication or division, one row of figures on the
strip of paper or parchment must be so arranged (with the exception of a few
of the first figures on it) that cach contiguous two figures upon it will form'
a composite number; and another row must be so arranged, with the exception..
of a few of the first figures on it, that no contiguous two figures on it will
form a composite number.
The accompanying paper marked Plate D is an impression taken from the
copper plate intended to print two cards for reduction, and one for the rule of
three direct; a mere inspection of this paper will shew the apertures neces-
sary for setting sums in these rules. These apertures also aro marked round
and coloured blue. That I may explain my apparatus for setting sums still
more fully, supposing the figures to be of the size and number marked in
Plate A, I make a box about nine inches long and about five inches broad,
with a roller of about an inch in diameter at each end, so that the strip of
paper or parchment resembling Plate A shall pass from one roller to the other,
leaving about twelve or fourteen figures in each row not rolled up. There
should be a board or something stiff the greater part of the way between the
two rollers for the paper to lie flat upon, and to prevent the paper giving way
when one of the cards is pressed upon it. I then take the card belonging to
the rule I want to set a sum in, with the aperture cut in it, and I place it over
the face of the figures on the strip of paper or parchment. (The box or frame
may be so formed as to slide it over the strip of paper or parchment.) This
being done, the figures composing the sum which I wish to set remain visible;
all the others are hidden, except the number which appears through the aper-
ture at the top of the card. If I wish to set another sum in the same rule,
I turn one or other of the rollers so as to draw the strip of paper or parchment
with the rows of figures on it to the right or to the left, and another sum
appears. In order to change the rule, 1 must take away the card and put

page_text: another in its place. The use of the numbers at the top is this:-When my
apparatus is complete I put on the card for common addition, and draw the
strip of paper or parchment to the right or left till No. 1 appears through the
top aperture; I then work the sum that is visible, and put the answer down in
a book under the head "addition," and mark it No. 1. I then draw the strip
to No. 2 and work that sum, and put the answer of it down in my book under
the same head, and mark it No. 2; and so I proceed till I have worked the
sum under each number in that rule, and booked the answer of it. I then
work through each of the rules I have mentioned in the same way, and in the
same way book the results each under its proper head; so that afterwards,
when I set a sum in any rule, and I wish to know the answer, I have only to
refer to that rule in my book and look for the number which appears at the
top of the card & under that number in the book I find the answer. The
number which follows the word "page" on the cards is intended to refer to the
page in the book where the rule will be found. I have only prepared Plate A
for thirty sums, as I thought a greater number would make it unnecessarily
long. There may be apertures from one or more rules on each card, accord-
ing to the number of rows of figures on the strip of paper or parchment, and
according to the size I choose to make the apparatus.
By cutting apertures in their proper places in other cards, and writing on
the cards a few appropriate words in a similar manner to what is done on
Plate D, sums may be set in some other rules.
In witness whereof, I, the said John Tyrrell, have hereunto set my hand
and seal, this Ninth day of May, in the year of our Lord One thousand
eight hundred and thirty-one
Inrolled the Thirteenth day of May, in the year of our Lord One thousand
eight hundred and thirty-one.