ARITHMETIC.
_The arithmeticon--How applied--Numeration--Addition--Subtraction--
Multiplication--Division--Fraction--Arithmetical tables--Arithmetical
Songs--Observations_.
* * * * *
"In arithmetic, as in every other branch of education, the principal
object should be to preserve the understanding from implicit belief,
to invigorate its powers, and to induce the laudable ambition of
progressive improvement."--_Edgeworth_
* * * * *
The advantage of a knowledge of arithmetic has never been disputed.
Its universal application to the business of life renders it an
important acquisition to all ranks and conditions of men. The
practicability of imparting the rudiments of arithmetic to very young
children has been satisfactorily shewn by the Infant-school System;
and it has been found, likewise, that it is the readiest and surest
way of developing the thinking faculties of the infant mind. Since the
most complicated and difficult questions of arithmetic, as well as
the most simple, are all solvable by the same rules, and on the same
principles, it is of the utmost importance to give children a clear
insight into the primary principles of number. For this purpose we
take care to shew them, by visible objects, that all numbers are
combinations of unity; and that all changes of number must arise
either from adding to or taking from a certain stated number. After
this, or rather, perhaps I should say, in conjunction with this
instruction, we exhibit to the children the _signs_ of number, and
make them acquainted with their various combinations; and lastly, we
bring them to the abstract consideration of number; or what may be
termed _mental arithmetic_. If you reverse this, which has generally
been the system of instruction pursued--if you set a child to learn
its multiplication, pence, and other tables, before you have shewn it
by _realities_, the combinations of unity which these tables express
in words--you are rendering the whole abstruse, difficult, and
uninteresting; and, in short, are giving it knowledge which it is
unable to apply.
As far as regards the general principles of numerical tuition, it may
be sufficient to state, that we should begin with unity, and proceed
very gradually, by slow and sure steps, through the simplest forms of
combinations to the more comprehensive. Trace and retrace your first
steps--the children can never be too thoroughly familiar with the
first principles or facts of number.
We have various ways of teaching arithmetic, in use in the schools;
I shall speak of them all, beginning with a description of the
arithmeticon, which is of great utility.
[Illustration]
I have thought it necessary in this edition to give the original
woodcut of the arithmeticon, which it will be seen contains twelve
wires, with one ball on the first wire, two on the second, and so
progressing up to twelve. The improvement is, that each wire should
contain twelve balls, so that the whole of the multiplication table
may be done by it, up to 12 times 12 are 144. The next step was having
the balls painted black and white alternately, to assist the sense of
seeing, it being certain that an uneducated eye cannot distinguish
the combinations of colour, any more than an uneducated ear can
distinguish the combinations of sounds. So far the thing succeeded
with respect to the sense of seeing; but there was yet another thing
to be legislated for, and that was to prevent the children's attention
being drawn off from the objects to which it was to be directed, viz.
the smaller number of balls as separated from the greater. This object
could only be attained by inventing a board to slide in and hide the
greater number from their view, and so far we succeeded in gaining
their undivided attention to the balls we thought necessary to move
out. Time and experience only could shew that there was another thing
wanting, and that was a tablet, as represented in the second woodcut,
which had a tendency to teach the children the difference between real
numbers and representative characters, therefore the necessity of
brass figures, as represented on the tablet; hence the children would
call figure seven No. 1, it being but one object, and each figure they
would only count as one, thus making 937, which are the representative
characters, only three, which is the real fact, there being only three
objects. It was therefore found necessary to teach the children
that the figure seven would represent 7 ones, 7 tens, 7 hundreds, 7
thousands, or 7 millions, according to where it might be placed in
connection with the other figures; and as this has already been
described, I feel it unnecessary to enlarge upon the subject.
[Illustration]
THE ARITHMETICON.
It will be seen that on the twelve parallel wires there are 144 balls,
alternately black and white. By these the elements of arithmetic may
be taught as follows:--
_Numeration_.--Take one ball from the lowest wire, and say units,
_one_, two from the next, and say tens, _two_; three from the third,
and say hundreds, _three_; four from the fourth, and say thousands,
_four_; five from the fifth, and say tens of thousands, _five_; six
from the sixth, and say hundreds of thousands, _six_; seven from the
seventh, and say millions, _seven_; eight from the eighth, and say
tens of millions, _eight_; nine from the ninth, and say hundreds of
millions, _nine_; ten from the tenth, and say thousands of millions,
_ten_; eleven from the eleventh, and say tens of thousands of
millions, _eleven_; twelve from the twelfth, and say hundreds of
thousands of millions, _twelve_.
The tablet beneath the balls has six spaces for the insertion of brass
letters and figures, a box of which accompanies the frame. Suppose
then the only figure inserted is the 7 in the second space from the
top: now were the children asked what it was, they would all say,
without instruction, "It is one." If, however, you tell them that an
object of such a form stands instead of seven ones, and place seven
balls together on a wire, they will at once see the use and power of
the number. Place a 3 next the seven, merely ask what it is, and they
will reply, "We don't know;" but if you put out three balls on a wire,
they will say instantly, "O it is three ones, or three;" and that they
may have the proper name they may be told that they have before
them _figure 7_ and _figure 3_. Put a 9 to these figures, and their
attention will be arrested: say, Do you think you can tell me what
this is? and, while you are speaking, move the balls gently out, and,
as soon as they see them, they will immediately cry out "Nine;" and in
this way they may acquire a knowledge of all the figures separately.
Then you may proceed thus: Units 7, tens 3; place three balls on the
top wire and seven on the second, and say, Thirty-seven, as you point
to the figures, and thirty-seven as you point to the balls. Then go
on, units 7, tens, 3, hundreds 9, place nine balls on the top wire,
three on the second, and seven on the third, and say, pointing to
each, Nine hundred and thirty-seven. And so onwards.
To assist the understanding and exercise the judgment, slide a figure
in the frame, and say, Figure 8. Q. What is this? A. No. 8. Q. If No.
1 be put on the left side of the 8, what will it be? A. 81. Q. If the
1 be put on the right side, then what will it be? A. 18. Q. If the
figure 4 be put before the 1, then what will the number be? A. 418. Q.
Shift the figure 4, and put it on the left side of the 8, then ask the
children to tell the number, the answer is 184. The teacher can keep
adding and shifting as he pleases, according to the capacity of his
pupils, taking care to explain as he goes on, and to satisfy himself
that his little flock perfectly understand him. Suppose figures
5476953821 are in the frame; then let the children begin at the left
hand, saying, units, tens, hundreds, thousands, tens of thousands,
hundreds of thousands, millions, tens of millions, hundreds of
millions, thousands of millions. After which, begin at the right side,
and they will say, Five thousand four hundred and seventy-six million,
nine hundred and fifty-three thousand, eight hundred and twenty-one.
If the children are practised in this way, they will soon learn
numeration.
The frame was employed for this purpose long before its application to
others was perceived; but at length I found we might proceed to
_Addition_.--We proceed as follows:--1 and 2 are 3, and 3 are 6, and 4
are 10, and 5 are 15, and 6 are 21, and 7 are 28, and 8 are 36, and 9
are 45, and 10 are 55, and 11 are 66, and 12 are 78.
Then the master may exercise them backwards, saying, 12 and 11 are 23,
and 10 are 33, and 9 are 42, and 8 are 50, and 7 are 57, and 6 are 63,
and 5 are 68, and 4 are 72, and 3 are 75, and 2 are 77, and 1 is 78,
and so on in great variety.
Again: place seven balls on one wire, and two on the next, and ask
them how many 7 and 2 are; to this they will soon answer, Nine: then
put the brass figure 9 on the tablet beneath, and they will see how
the amount is marked: then take eight balls and three, when they will
see that eight and three are eleven. Explain to them that they cannot
put underneath two figure ones which mean 11, but they must put 1
under the 8, and carry 1 to the 4, when you must place one ball under
the four, and, asking them what that makes, they will say, Five.
Proceed by saying, How much are five and nine? put out the proper
number of balls, and they will say, Five and nine are fourteen. Put
a four underneath, and tell them, as there is no figure to put the 1
under, it must be placed next to it: hence they see that 937 added to
482, make a total of 1419.
_Subtraction_ may be taught in as many ways by this instrument. Thus:
take 1 from 1, nothing remains; moving the first ball at the same time
to the other end of the frame. Then remove one from the second wire,
and say, take one from 2, the children will instantly perceive that
only 1 remains; then 1 from 3, and 2 remain; 1 from 4, 3 remain; 1
from 5, 4 remain; 1 from 6, 5 remain; 1 from 7, 6 remain; 1 from 8, 7
remain; 1 from 9, 8 remain; 1 from 10, 9 remain; 1 from 11, 10 remain;
1 from 12, 11 remain.
Then the balls may be worked backwards, beginning at the wire
containing 12 balls, saying, take 2 from 12, 10 remain; 2 from 11, 9
remain; 2 from 10, 8 remain; 2 from 9, 7 remain; 2 from 8, 6 remain; 2
from 7, 5 remain; 2 from 6, 4 remain; 2 from 5, 3 remain; 2 from 4, 2
remain; 2 from 3, 1 remains.
The brass figure should be used for the remainder in each case. Say,
then, can you take 8 from 3 as you point to the figures, and they will
say "Yes;" but skew them 3 balls on a wire and ask them to deduct 8
from them, when they will perceive their error. Explain that in such a
case they must _borrow_ one; then say take 8 from 13, placing 12 balls
on the top wire, borrow one from the second, and take away eight and
they will see the remainder is five; and so on through the sum, and
others of the same kind.
In _Multiplication_, the lessons are performed as follows. The teacher
moves the first ball, and immediately after the two balls on the
second wire, placing them underneath the first, saying at the same
time, twice one are two, which the children will readily perceive. We
next remove the two balls on the second wire for a multiplier, and
then remove two balls from the third wire, placing them exactly under
the first two, which forms a square, and then say twice two are four,
which every child will discern for himself, as he plainly perceives
there are no more. We then move three on the third wire, and place
three from the fourth wire underneath them saying, twice three are
six. Remove the four on the fourth wire, and four on the fifth, place
them as before and say, twice four are eight. Remove five from the
fifth wire, and five from the sixth wire underneath them, saying twice
five are ten. Remove six from the sixth wire, and six from the seventh
wire underneath them and say, twice six are twelve. Remove seven from
the seventh wire, and seven from the eighth wire underneath them,
saying, twice seven are fourteen. Remove eight from the eighth wire,
and eight from the ninth, saying, twice eight are sixteen. Remove nine
on the ninth wire, and nine on the tenth wire, saying twice nine
are eighteen. Remove ten on the tenth wire, and ten on the eleventh
underneath them, saying, twice ten are twenty. Remove eleven on the
eleventh wire, and eleven on the twelfth, saying, twice eleven are
twenty-two. Remove one from the tenth wire to add to the eleven on
the eleventh wire, afterwards the remaining ball on the twelfth wire,
saying, twice twelve are twenty-four.
Next proceed backwards, saying, 12 times 2 are 24, 11 times 2 are 22,
10 times 2 are 20, &c.
For _Division_, suppose you take from the 144 balls gathered together
at one end, one from each row, and place the 12 at the other end, thus
making a perpendicular row of ones: then make four perpendicular rows
of three each and the children will see there are 4 3's in 12. Divide
the 12 into six parcels, and they will see there are. 6 2's in 12.
Leave only two out, and they will see, at your direction, that 2 is
the sixth part of 12. Take away one of these and they will see one is
the twelfth part of 12, and that 12 1's are twelve.
To explain the state of the frame as it appears in the cut, we must
first suppose that the twenty-four balls which appear in four lots,
are gathered together at the _figured side_: when the children will
see there are three perpendicular 8's, and as easily that there are 8
horizontal 3's. If then the teacher wishes them to tell how many 6's
there are in twenty-four, he moves them out as they appear in the
cut, and they see there are four; and the same principle is acted on
throughout.
The only remaining branch of numerical knowledge, which consists in an
ability to comprehend the powers of numbers, without either visible
objects or signs--is imparted as follows:
_Addition_.
One of the children is placed before the gallery, and repeats aloud,
in a kind of chaunt, the whole of the school repeating after him; One
and one are two; two and one are three; three and one are four, &c. up
to twelve.
Two and two are four; four and two are six; six and two are eight, &c.
to twenty-four.
Three and three are six; six and three are nine; nine and three are
twelve, &c. to thirty-six.
_Subtraction_.
One from twelve leaves eleven; one from eleven leaves ten, &c.
Two from twenty-four leave twenty-two; two from twenty-two leave
twenty, &c.
_Multiplication_.
Twice one are two; twice two are four, &c. &c. Three times three are
nine, three times four are twelve, &c. &c.
Twelve times two are twenty-four; eleven times two are twenty-two, &c.
&c.
Twelve times three are thirty-six; eleven times three are
thirty-three, &c. &c. until the whole of the multiplication table is
gone through.
_Division_.
There are twelve twos in twenty-four.--There are
eleven twos in twenty-two, &c. &c.
There are twelve threes in thirty-six, &c.
There are twelve fours in forty-eight, &c. &c.
_Fractions_.
Two are the half (1/2) of four.
" " " third (1/3) of six.
" " " fourth (1/2) of eight.
" " " fifth (1/5) of ten.
" " " sixth (1/6) of twelve.
" " " seventh (1/7) of fourteen.
" " " twelfth (1/12) of twenty-four; two are the
eleventh (1/11) of twenty-two, &c. &c.
Three are the half (1/2) of six.
" " " third (1/3) of nine.
" " " fourth (1/4) of twelve.
Three are the twelfth (1/12) of thirty-six; three are
the eleventh (1/11) of thirty-three, &c. &c.
Four are the half (1/2) of eight, &c.
In twenty-three are four times five, and three-fifths
(3/5) of five; in thirty-five are four times eight, and three-eighths
(3/8) of eight.
In twenty-two are seven times three, and one-third
(1/3) of three.
In thirty-four are four times eight, and one-fourth
(1/4) of eight.
The tables subjoined are repeated by the same method, each section
being a distinct lesson. To give an idea to the reader, the boy in the
rostrum says ten shillings the half (1/2) of a pound; six shillings
and eightpence one-third (1/3) of a pound, &c.
Sixpence the half (1/2) of a shilling, &c. Always remembering, that
whatever the boy says in the rostrum, the other children must repeat
after him, but not till the monitor has ended his sentence; and before
the monitor delivers the second sentence, he waits till the children
have concluded the first, they waiting for him, and he for them; this
prevents confusion, and is the means of enabling persons to understand
perfectly what is going on in the school.
In a book lately published, which is a compilation by two London
masters, it is stated, in the preface, that they were at a loss
for proper lessons: had they used those in existence I cannot help
thinking they were enough for the capacity of children under six years
of age.
254 ARITHMETICAL TABLES.
Numeration, Addition, Subtraction, Multiplication, Division, and Pence
Tables.
-------------------------------------------------------------------
| ADDITION AND SUBTRACTION TABLE |
| 1 & | 2 & | 3 & | 4 & | 5 & | 6 & |
| 1 are 2 | 1 are 3 | 1 are 4 | 1 are 5 | 1 are 6 | 1 are 7 |
| 2 -- 3 | 2 -- 4 | 2 -- 5 | 2 -- 6 | 2 -- 7 | 2 -- 8 |
| 3 -- 4 | 3 -- 5 | 3 -- 6 | 3 -- 7 | 3 -- 8 | 3 -- 9 |
| 4 -- 5 | 4 -- 6 | 4 -- 7 | 4 -- 8 | 4 -- 9 | 4 -- 10 |
| 5 -- 6 | 5 -- 7 | 5 -- 8 | 5 -- 9 | 5 -- 10 | 5 -- 11 |
| 6 -- 7 | 6 -- 8 | 6 -- 9 | 6 -- 10 | 6 -- 11 | 6 -- 12 |
| 7 -- 8 | 7 -- 9 | 7 -- l0 | 7 -- 11 | 7 -- 12 | 7 -- 13 |
| 8 -- 9 | 8 -- 10 | 8 -- 11 | 8 -- 12 | 8 -- 13 | 8 -- 14 |
| 9 -- 10 | 9 -- 11 | 9 -- 12 | 9 -- 13 | 9 -- 14 | 9 -- 15 |
| 10 -- 11 | 10 -- 12 | 10 -- 13 | 10 -- 14 | 10 -- 15 | 10 -- 16 |
| 11 -- l2 | 11 -- 13 | 11 -- 14 | 11 -- 15 | 11 -- 16 | 11 -- 17 |
| l2 -- 13 | 12 -- 14 | 12 -- 14 | 12 -- 16 | 12 -- 17 | l2 -- 18 |
-------------------------------------------------------------------
| 7 & | 8 & | 9 & | 10 & | 11 & | 12 & |
| 1 are 8 | 1 are 9 | 1 are 10 | 1 are 11 | 1 are 12 | 1 are 13 |
| 2 -- 9 | 2 -- 10 | 2 -- 11 | 2 -- 12 | 2 -- 13 | 2 -- 14 |
| 3 -- 10 | 3 -- 11 | 3 -- 12 | 3 -- 13 | 3 -- 14 | 3 -- 15 |
| 4 -- 11 | 4 -- 12 | 4 -- 13 | 4 -- 14 | 4 -- 15 | 4 -- 16 |
| 5 -- 12 | 5 -- 13 | 5 -- 14 | 5 -- 15 | 5 -- 16 | 5 -- 17 |
| 6 -- 13 | 6 -- 14 | 6 -- 15 | 6 -- 16 | 6 -- 17 | 6 -- 18 |
| 7 -- 14 | 7 -- 15 | 7 -- 16 | 7 -- 17 | 7 -- 18 | 7 -- 19 |
| 8 -- 15 | 8 -- 16 | 8 -- 17 | 8 -- 18 | 8 -- 19 | 8 -- 20 |
| 9 -- 16 | 9 -- 17 | 9 -- 18 | 9 -- 19 | 9 -- 20 | 9 -- 21 |
| 10 -- 17 | 10 -- 18 | 10 -- 19 | 10 -- 20 | 10 -- 21 | 10 -- 22 |
| 11 -- l8 | 11 -- 19 | 11 -- 20 | 11 -- 21 | 11 -- 22 | 11 -- 23 |
| 12 -- 19 | 12 -- 20 | 11 -- 21 | l2 -- 22 | 12 -- 23 | 12 -- 24 |
===================================================================
| MULTIPLICATION AND DIVISION TABLE. || NUMERATION TABLE. |
|------------------------------------||---------------------------|
|2--2 are 4|4--5 are 20| 6--12 are 72|| 1 Units. |
| 3 -- 6| 6 -- 24| 7-- 7 -- 49|| 21 Tens. |
| 4 -- 8| 7 -- 28| 8 -- 56|| 321 Hundreds |
| 5 -- 10| 8 -- 32| 9 -- 63|| 4,321 Thousands. |
| 6 -- 12| 9 -- 36| 10 -- 70|| 54,321 X of Thousands.|
| 7 -- 14| 10 -- 40| 11 -- 77|| 654,321 C of Thousands.|
| 8 -- 16| 11 -- 44| 12 -- 84|| 7,654,321 Millions. |
| 9 -- 18| 12 -- 48| 8-- 8 -- 64|| 87,654,321 X of Millions. |
| 10 -- 20|5--5 -- 25| 9 -- 72||987,654,321 C of Millions. |
| 11 -- 22| 6 -- 30| 10 -- 80||===========================|
| 12 -- 24| 7 -- 35| 11 -- 88|| |
|3--3 -- 9| 8 -- 40| 12 -- 96|| PENCE TABLE |
| 4 -- 12| 9 -- 45| 9-- 9 -- 81|| |
| 5 -- 15| 10 -- 50| 10 -- 90||---------------------------|
| 6 -- 18| 11 -- 55| 11 -- 99|| _d_. _s. d._|_d._ _s. d._|
| 7 -- 21| 12 -- 60| 12 -- 108|| 20 is 1 8 | 90 is 7 6 |
| 8 -- 24|6--6 -- 36|10--10 -- 100|| 30 -- 2 6 |100 -- 8 4 |
| 9 -- 27| 7 -- 42| 11 -- 110|| 40 -- 3 4 |110 -- 9 2 |
| 10 -- 30| 8 -- 48| 12 -- 120|| 50 -- 4 2 |120 --10 0 |
| 11 -- 33| 9 -- 54|11--11 -- 121|| 60 -- 5 0 |130 --10 10 |
| 12 -- 36| 10 -- 60| 12 -- 132|| 70 -- 5 10 |140 --11 8 |
|4--4 -- 16| 11 -- 66|12--12 -- 144|| 80 -- 6 8 |144 --12 0 |
-------------------------------------------------------------------
_Tables of Weights and Measures_.
_Shilling Tables_
_s. l. s_.
20 are 1 0
30 ---- 1 10
40 ---- 2 0
50 ---- 2 10
60 ---- 3 0
70 ---- 3 10
80 ---- 4 0
90 ---- 4 10
100 are 5 0
110 --- 5 10
120 --- 6 0
130 --- 6 10
140 --- 7 0
150 --- 7 10
160 --- 8 0
170 --- 8 10
* * * * *
_Practice Tables_.
* * * * *
Of a Pound.
_s. d_.
10 0 are half
6 8 --- third
5 0 --- fourth
4 0 --- fifth
3 4 --- sixth
2 6 --- eighth
1 8 --- twelfth
1 0 --- twentieth
Of a shilling.
6_d_. are half
4 --- third
3 --- fourth
2 --- sixth
1 --- twelfth
* * * * *
_Time_.
60 seconds 1 minute
60 minutes 1 hour
24 hours 1 day
7 days 1 week
4 weeks 1 lunar month
12 cal. mon. 1 year
13 lunar months, 1 day, 6 hours, or 365 days, 6 hours, 1 year.
Thirty days hath September,
April, June, and November;
All the rest have thirty-one,
Save February, which alone
Hath twenty-eigth, except Leap year,
And twenty-nine is then its share.
* * * * *
_Troy Weight_.
24 grains 1 pennywt.
20 pennywhts. 1 ounce
12 ounces 1 pound
* * * * *
_Avoirdupoise Weight_.
16 drams 1 ounce
16 ounces 1 pound
28 pounds 1 quarter
4 quarters 1 hund. wt.
20 hund. wt. 1 ton
* * * * *
_ Apothecaries Weight._
20 grains 1 scruple
3 scruples 1 dram
8 drams 1 ounce
12 ounces 1 pound
* * * * *
_Wool Weight_.
7 pounds 1 clove
2 cloves 1 stone
2 stones 1 tod
6½ tods 1 wey
2 weys 1 sack
12 sacks 1 last
* * * * *
_Wine Measure_.
2 pints 1 quart
4 quarts 1 gallon
10 gallons 1 ank. brandy
42 gallons 1 tierce
63 gallons 1 hogshead
84 gallons 1 puncheon
2 hogsheads 1 pipe
2 pipes 1 ton
* * * * *
_Ale and Beer Measure_.
2 pints 1 quart
4 quarts 1 gallon
8 gallons 1 firkin of ale
9 gallons 1 firk. of beer
2 firkins 1 kilderkin
2 kilderkins 1 barrel
14 barrel 1 hogshead
2 barrels 1 puncheon
3 barrels 1 butt
* * * * *
_Coal Measure_.
4 pecks 1 bushel
9 bushels 1 vat or strike
3 bushels 1 sack
12 sacks 1 chaldron
91 chaldron 1 score
* * * * *
_Dry Measure_.
2 pints 1 quart
2 quarts 1 pottle
2 pottles 1 gallon
2 gallons 1 peck
4 pecks 1 bushel
2 bushels 1 strike
5 bushels 1 sack flour
8 bushels 1 quarter
5 quarters 1 wey or load
5 pecks 1 bushl. water measure
4 bushels 1 coom
10 cooms 1 wey
2 weys 1 last corn
* * * * *
_Solid or Cubic Measure_.
1728 inches 1 foot
27 feet 1 yard or load
* * * * *
_Long Measure_.
3 barleycorns 1 inch
12 inches 1 foot
3 feet 1 yard
6 feet 1 fathom
5½ yards 1 pole or rod
40 poles 1 furlong
8 furlongs 1 mile
3 miles 1 league
20 leagues 1 degree
* * * * *
_Cloth Measure_.
24 inches 1 nail
4 nails 1 quarter
4 quarters 1 yard
5 quarters 1 English ell
3 quarters 1 Flemish ell
6 quarters 1 French ell
* * * * *
_Land or Square Measure_.
144 inches 1 foot
9 feet 1 yard
30¾ yards 1 pole
40 poles 1 rood
4 roods 1 acre
640 acres 1 mile
This includes length and breadth.
* * * * *
_Hay_.
36 pounds 1 truss of straw
56 pounds 1 do. of old hay
60 pounds 1 do. of new hey
36 trusses 1 load
MONEY.
Two farthings one halfpenny make,
A penny four of such will take;
And to allow I am most willing
That twelve pence always make a shilling;
And that five shillings make a crown,
Twenty a sovereign, the same as pound.
Some have no cash, some have to spare--
Some who have wealth for none will care.
Some through misfortune's hand brought low,
Their money gone, are filled with woe,
But I know better than to grieve;
If I have none I will not thieve;
I'll be content whate'er's my lot,
Nor for misfortunes care a _groat_.
There is a Providence whose care
And sovereign love I crave to share;
His love is _gold without alloy_;
Those who possess't have _endless joy_.
TIME OR CHRONOLOGY.
Sixty seconds make a minute;
Time enough to tie my shoe
Sixty minutes make an hour;
Shall it pass and nought to do?
Twenty-four hours will make a day
Too much time to spend in sleep,
Too much time to spend in play,
For seven days will end the week,
Fifty and two such weeks will put
Near an end to every year;
Days three hundred sixty-five
Are the whole that it can share.
Saving leap year, when one day
Added is to gain lost time;
May it not be spent in play,
Nor in any evil crime.
Time is short, we often say;
Let us, then, improve it well;
That eternally we may
Live where happy angels dwell.
AVOIRDUPOISE WEIGHT.
Sixteen drachms are just an ounce,
As you'll find at any shop;
Sixteen ounces make a pound,
Should you want a mutton chop.
Twenty-eight pounds are the fourth
Of an hundred weight call'd gross;
Four such quarters are the whole
Of an hundred weight at most.
Oh! how delightful,
Oh! how delightful,
Oh! how delightful,
_To sing this rule_.
Twenty hundreds make a ton;
By this rule all things are sold
That have any waste or dross
And are bought so, too, I'm told.
When we buy and when we sell,
May we always use just weight;
May we justice love so well
To do always what is right.
Oh! how delightful,
&c., &c., &c.
APOTHECARIES' WEIGHT.
Twenty grains make a scruple,--some scruple to take;
Though at times it is needful, just for our health's sake;
Three scruples one drachm, eight drachms make one ounce,
Twelve ounces one pound, for the pestle to pounce.
By this rule is all medicine mix'd, though I'm told
By Avoirdupoise weight 'tis bought and 'tis sold.
But the best of all physic, if I may advise,
Is temperate living and good exercise.
DRY MEASURE.
Two pints will make one quart
Of barley, oats, or rye;
Two quarts one pottle are, of wheat
Or any thing that's dry.
Two pottles do one gallon make,
Two gallons one peck fair,
Four pecks one bushel, heap or brim,
Eight bushels one quarter are.
If, when you sell, you give
Good measure shaken down,
Through motives good, you will receive
An everlasting crown.
ALE AND BEER MEASURE.
Two pints will make one quart,
Four quarts one gallon, strong:--
Some drink but little, some too much,--
To drink too much is wrong.
Eight gallons one firkin make,
Of liquor that's call'd ale
Nine gallons one firkin of beer,
Whether 'tis mild or stale.
With gallons fifty-four
A hogshead I can fill:
But hope I never shall drink much,
Drink much whoever will.
WINE, OIL, AND SPIRIT MEASURE.
Two pints will make one quart
Of any wine, I'm told:
Four quarts one gallon are of port
Or claret, new or old.
Forty-two gallons will
A tierce fill to the bung:
And sixty-three's a hogshead full
Of brandy, oil, or rum.
Eighty-four gallons make
One puncheon fill'd to brim,
Two hogsheads make one pipe or butt,
Two pipes will make one tun.
A little wine within
Oft cheers the mind that's sad;
But too much brandy, rum, or gin,
No doubt is very bad.
From all excess beware,
Which sorrow must attend;
Drunkards a life of woe must share,--
When time with them shall end.
The arithmeticon, I would just remark, may be applied to _geometry_.
Round, square, oblong, &c. &c., may be easily taught. It may also be
used in teaching _geography_. The shape of the earth may be shewn by
a ball, the surface by the outside, its revolution on its axis by
turning it round, and the idea of day and night may be given by a ball
and a candle in a dark-room.
As the construction and application of this instrument is the result
of personal, long-continued, and anxious effort, and as I have rarely
seen a pirated one made properly or understood, I may express a
hope that whenever it is wanted either for schools or nurseries,
application will be made for it to my depot.
I have only to add, that a board is placed at the back to keep the
children from seeing the balls, except as they are put out; and that
the brass figures at the side are intended to assist the master when
he is called away, so that he may see, on returning to the frame,
where he left off.
The slightest glance at the wood-cut will shew how unjust the
observations of the writer of "Schools for the Industrious Classes, or
the Present State of Education amongst the Working People of England,"
published under the superintendance of the Central Society of
Education, are, where he says, "We are willing to assume that Mr.
Wilderspin has originated some improvements in the system of Infant
School education; but Mr. Wilderspin claims so much that many persons
have been led to refuse him that degree of credit to which he is
fairly entitled. For example, he claims a beneficial interest in
an instrument called the Arithmeticon, of which he says he was the
inventor. This instrument was described in a work on arithmetic,
published by Mr. Friend forty years ago. The instrument is, however,
of much older date; it is the same in principle as the Abacus of the
Romans, and in its form resembles as nearly as possible the Swanpan
of the Chinese, of which there is a drawing in the Encyclopaedia
Brittanica. Mr. Wilderspin merely invented the name." Now, I defy
the writer of this to prove that the Arithmeticon existed before I
invented it. I claim no more than what is my due. The Abacus of the
Romans is entirely different; still more so is the Chinese Swanpan;
if any person will take the trouble to look into the Encyclopaedia
Britannica, they will see the difference at once, although I never
heard of either until they were mentioned in the pamphlet referred to.
There are 144 balls on mine, and it is properly simplified for infants
with the addition of the tablet, which explains the representative
characters as well as the real ones, which are the balls.
I have not yet heard what the Central Society have invented; probably
we shall soon hear of the mighty wonders performed by them, from one
end of the three kingdoms to the other. Their whole account of the
origin of the Infant System is as partial and unjust as it possibly
can be. Mr. Simpson, whom they quote, can tell them so, as can
also some of the committee of management, whose names I see at the
commencement of the work. The Central Society seem to wish to pull me
down, as also does the other society to whom reference is made is the
same page of which I complain; and I distinctly charge both societies
with doing me great injustice; the society complains of my plans
without knowing them, the other adopts them without acknowledgment,
and both have sprung up fungus-like, after the Infant System had been
in existence many years, and I had served three apprenticeships to
extend and promote it, without receiving subscriptions or any public
aid whatever. It is hard, after a man has expended the essence of his
constitution, and spent his children's property for the public good,
in inducing people to establish schools in the principal towns in
the three kingdoms,--struck at the root of domestic happiness, by
personally visiting each town, doing the thing instead of writing
about it--that societies of his own countrymen should be so anxious to
give the credit to foreigners. Verily it is most true that a Prophet
has no honour in his own country. The first public honour I ever
received was at Inverness, in the Highlands of Scotland, the last was
by the Jews in London, and I think there was a space of about twenty
years between each.