Written for Moore’s Rural New-Yorker. 
SUCCESSFUL TEACHING. 
ONE STEP AT A TIME. 
Teaching is hcird wnrlc, I do not mean 
that it is hard work to assign a given number of 
pages for a lesson, and on the day following ask 
a routine of questions respecting it, ami if the 
answers as contained in the book are correctly 
repeated, assign another lesson, and so on; or if 
the lessen is not “learned,” put, down a “ black 
mark” for each delinquent, on the book or back, 
and “give the lesson over again.” The only 
hard work about such teaching is its wearisome 
monotony: in other respects it is comparatively 
easy and quite in harmony with indolence and 
the want of proper qualifications on the part of 
the teacher. 
But to develop properly the mental faculties— 
to discipline the mind to think closely, to judge, 
to compare, to investigate, and to enable it to 
acquire new ideas, is an arduous task, requiring 
great skill and much patient labor; and only in 
proportion to the accomplishment of it, can the 
teacher be said to be successful. Many teachers 
do not accomplish this end, doubtless, not from 
indolence, nor want of proper qualification, but 
because they do not aim to accomplish it; the 
thought never having occurred to them to teach 
otherwise than according to the established 
method of “giving out” lessons and hearing 
them recited. 
Successful teaching depends upon taking one. 
step at a time. To illustrate, let us take Addi¬ 
tion of Eructions, or what is preparatory to it— 
Reduction of Fractions to a Common Denomi¬ 
nator. As stated in a previous article, on 
Teaching Fractions, the first step is to render 
the minds of the pupils familiar with the idea of 
a fraction—that it originates from dividing a 
unit into a number of equal parts and using one 
or more of the parts, or from dividing several 
units (taken as a whole) into a certain number of 
equal parts, and using but one of the parts. 
This done, the pupils will be prepared for the 
next step—the multiplication, or division, of the 
numerator, or denominator, or both, by any 
given number, and the corresponding effect 
■ upon the value of the fraction. For instance, 
holding the minds of the pupils to the idea that 
the numerator is the dividend, and the denomi¬ 
nator the divisor, or that the numerator indi¬ 
cates the number of parts, and the denominator 
their size, and then asking them the effect of 
multiplying both numerator and denominator 
by the same number, they will readily see that 
while the terms of the fraction are changed, its 
valve remains the same. 
Having taken these two steps, each of which, 
as they include several distinct ideas, should be 
carefully dwelt upon till thoroughly understood, 
the pupils are prepared to ascertain how to 
change fractions whose denominators are unlike 
so as to make them alike, ami yet not change the 
value of the fractions; in other words, Low to 
reduce fractions to a common denominator. The 
usual method tijirst to require the pupils to repeat 
the rule. “ Multiply the terms ef each fraction 
by the denominators of all the other fractions;” 
or if the least common denominator be required, 
then the corresponding rule —and then if they 
can not work the examples and get the right 
answers, show them how. Though the pupils 
will doubtless In this way soon become familiar 
with the method of solving the examples, they 
will understand little or nothing of the princi¬ 
ples involved, and hence they will almost 
entirely fail of the two important ends to be 
attained — discipline of mind and practical 
knowledge. If the teacher would have his 
pupils acquire a practical knowledge ol' the sub¬ 
ject—the acquirement of which also involves 
discipline of mind—he must advance them but 
one step at a lime. 
In the examples before us, the course pur¬ 
sued might he something as follows: — First 
step. State to the pupil that a given number 
may be changed to any other number of which 
it is a factor, by multiplying it by the other 
factor, that is, by the factor arising from divid¬ 
ing the required number by the given number; 
or, what is better, (list ask such questions as to 
wliut number will five bo changed if multiplied 
by two? by three? by lour? by nine? and so 
on. IIow caii four be changed to eight? to 
twelve? to sixteen? to thirty-two? mid so on; 
varying the questions sufficiently to render the 
idea familiar, (as every teacher, whose aim is to 
convey an idea fully, will always do,) and then 
make the general statement above, which the 
pupil will readily comprehend. Second step. 
Pursuing the same course, tile pupils will soon 
be enabled to understand the general statement 
that two or more numbers may always be i 
changed to the number represented by their 
product by multiplying each number by the 
product of the other numbers; and hence, also, 
they may be changed to any multiple of that 
product. Third step. Let the teacher now 
state to the pupils that numbers which do not : 
contain any factor common to two or moro of i 
them can not he changed to any number smaller / 
than their product, while numbers containing i 
one or more factors common to two or more of • 
them, can be changed to a number smaller than < 
their products, namely, to the number repre- I 
seated by the product of the common factors, and I 
the numbers remaining after eliminating the 1 
common factors from the given numbers. A t 
few examples will make this statement plain. ( 
1 Ims, any number containing the factors 2 and 1 
3 is divisible by their product, ti; ami any mini- 4 
ber containing the factors 5 and 7 is divisible by t 
tlu ir product, 35; hence, any number (and such 1 
a number only) containing the factors 2 and 3, 6 ^ 
and 7, can be exactly divided by the numbers ti and I 
36; the smallest number containing the factors 2, f 
MORNING IN SPRING. 
Llvelj 
Music by O. A. Arches. 
0_^_ 
im- 
-CfS-- 
-^v-f 
1. From the valleys to the hills, See the tnominij mists .-wise; 
* * 
And die ear - !y dew distils Balmy incense to the skies. Tra la la la 
la la La, 
Tra la la la 
&- 
VS-i 
- 
i i i._i 
00 
fi r 
-0 4 , J=i±=t: 
Purple clouds with vapory grace, Round the sun their soft veil fling 
XT , Beams the newborn bliss of spring:. Tra !a La la la la la. 
Now they fade, and from his face 
__a —— ■? 
_' > i _ 
itti 
la la l«, tala la; Tra la la la la la 
la la la la 
^ f —0 & -pp*—p— 
3. From die cool grass glitter origin Myriad drops of diamond dew: 
tJi: 
Bending ’nealh their pressure fight, 
Waves the green corn springing new. Tra la la la la 
u 
Tra la la la 
—4 
-0- 0-0-0- 0-q—srr 
4. Dewv mayfiower* to die sun Ope their buds of varied hue: Fragrant shades—ins beams to shun—Hide the violet’s heavenly blue 
Tra la la la la 1a 
la la la, la la la; Tra la la la la la 
la la la la 
3, (6,)5, 7, (36,) is their product, 210; therefore, 
the product of G and 35 is the smallest number to 
which they can be changed. Again : — Any 
number containing the factors 2 and 6 is divisible 
by their product, 10; and any number containing 
the factors 2 and 7 is divisible by their product, 
14— hmcc, any number containing the factors 2, 
5, 7. (one of the factors, 2,2, being omitted) is di¬ 
visible by 2 times 5 (10) and by 2 times 7, (14,) 
(bold the minds of the pupils to this point,) and 
hence 70, the product of the factors 2, 5, 7, is di¬ 
visible by the numbers 10 and 14. 
The three successive steps, just taken, prepare 
the pupils for the fourth and last step. Taking 
some examples, as three-fourths (f) and five- 
sixths, (5-6,) the teacher states to the pupils that 
he desires these fractions to be changed to frac¬ 
tions, such that the denominators shall be 
alike, and yet the fractions themselves equal in 
value to the fractions given. The pupils ascertain 
at once that the denominators 4 and G can each, 
be changed to 12, or to 24, 36,48, &c.,—12 being 
preferred, it being the smallest number. By 
now reminding them of what they learned at 
the outset, namely, that the value of a fraction 
will remain unchanged, if in changing the de¬ 
nominator there also he made a corresponding 
change of the numerator, they readily perceive 
that if the denominators 4 and 6 be multiplied 
successively by 3 and 2, the numerators 3 and 4 
must also be multiplied by the same numbers— 
the denominators being multiplied by 3 and 2 in 
order to obtain the desired result, namely, to 
change them to like denominators, and the nu¬ 
merators being multiplied by the same numbers 
(2 and 3) simply to preserve the value of the frac¬ 
tions unchanged. 
Although the several steps, in the illustration 
just given, include the definition of a fraction, 
changing fractions to higher or lower terms, 
finding multiples, &c., yet no definite, allusion is 
made to such a division of the subject, the de¬ 
sign being to so connect the several parts that 
the pupils shall see the full force and bearing of 
each step upon the step following, and thus be 
led along step by stop till they attain to a clear 
and definite understanding of the subject in all 
its parts. 
Too great care can not be taken in the use of 
scientific terms and expressions. Should such 
terms and expressions reach the pupils’ ears be¬ 
fore the ideas they represent reach the pupils’ 
minds, there is great danger of their proving 
stumbling blocks to all further progress. 
As stated In the beginning, to teach according 
to the method illustrated above, is hard work. 
The skill and patience of the teacher will bo 
called into full exercise in holding the minds of 
the pupils to each idea (especially to those more 
dilficult of apprehension, like the one contained 
in the latter part of the third stop, above, till it 
is clearly and fully apprehended. But though 
hard work, it is, nevertheless, very pleasant 
work, because successful; for success in a great 
and noble work—and development and culture 
of intellect is truly a great and noble work — is 
attended with the highest pleasure, k. m. c. 
Rochester, Feb. 20, 1864. 
Itefiii, jimutifk &t. 
Written for Moore’s Rural New-Yorker. 
HOW TO BUY. 
There is a right time to purchase. That 
time is when goods are low. Goods are low, as 
a general rule, when there is the least demand 
for them. Winter goods are low in the spring 
anu summer. Summer goods are low in the 
fall and wiuter. The merchant will sell liis 
winter stock in the spring at first cost, liis 
summer stock in the fall at cost. Ho commonly 
sells his goods at least twenty-live per cent 
above first cost. If, then, you buy his winter 
goods in the spring, and his summer goods in 
the lull, you save the per eentage, and get your 
goods at wholesale, or just as low as the mer¬ 
chant bought them by the quantity. If your 
family requires one hundred dollars yearly in 
these goods, tho saving will be twenty-five dol¬ 
lars, by buying at the proper time. When w in¬ 
ter renders navigation and transportation diffi¬ 
cult, groceries and heavy goods are generally 
higher. Sugar is generally high in fruit and 
“ preserving time.” Watch the markets. When 
tho goods you need are below an average price 
lay in a supply for some time ahead. Buy your 
goods by the quantity. Let the market be what 
it will, you can generally buy a quantity at less 
figures, proportionately, than small amounts. 
Sugar will cost you a cent on a pound less; tea, 
ten cents or a shilling; heavy cloths one to two 
shillings per yard, and so on to the end of the 
catalogue. Another consideration is not to be 
forgotten. A good article is much cheaper in 
the long run, than a poor one at a much less 
price. Better pay more for a thoroughly 
made serviceable article, than buy an inferior 
one, poorly made, at any price. Ready cash is 
always better than any man’s credit A dealer, 
who understands his business, can and will sell 
cheaper for ready money than he will for the 
best man’s credit. A handsome yearly saving 
may be made, in any family, depending in 
amount on the number in the family and the 
quantity of goods used, by buying at tho right 
time — buying by the large quantity — buying 
“good goods,” and paying ready cash. If you 
have not got the cash, live a little closer, cut off 
all unnecessary expenses, until you get a little 
ready money ahead, and are tlui3 ready to take 
advantage of the markets. The saving that can 
um is but a representative of the great standard. 
Only the Hindoo has ever learned to test coin ac¬ 
curately by the hand. 
Of all gold coinage that of England is perhaps 
the most beautiful. A new, fresh gold sovereign 
is probably as graceful and attractive a coin as 
exists. Next to it, the American eagle is the 
most elegant gold coin. The twenty-franc pieces 
of the present kingdom of Italy are also very 
neat. Probably the smallest gold coin in use is 
the French five-frauc piece, although a few 
half-dollar gold pieces have been struck off in 
California. At present there are current in 
France in everyday traffic, coin bearing the noble 
The moderate tobacco monger will use a pound 
and a half of it per month, which at the price of 
fifty cents per pound, would be nine dollars a 
year, or two hundred and twenty-five dollars in 
a life-time. 
The beer toper, of moderate appetite, will 
drink one glass of beer per day, costing at least 
five cents a glass, making thirty-five cent 3 a 
week, eighteen dollars and ten cents a year, or 
four hundred and fifty-two dollars and fifty cents 
in a life-time. 
If you arc in the habit of visiting billiard 
saloons, or places where any of the kindred 
games are practiced, you are led or by the ex¬ 
face of the first Napoleon, both as consul and era- citement of the game, until game after game has 
peror; the heavy round heads of Charles X and been played. Perhaps you are the unlucky one, 
Louis XV III; the shrewd countenance of Louis and have the “ rub ” to pay. MaybeyouhaTe 
1 hillippe, and the familiar features of the bet the segars, or beer, or the whisky for the 
present Emperor. Insome cases Napoleon III is party. If you visit them as moderately as once 
represented with, and in others without, a a week, that one visit will cost you at least fifty 
laurel wreath. cents, making the sum of twenty-six dollars a 
The most beautiful silver coinage is that of year, or six hundred and fifty dollars in the 
Russia, each piece being in itself a work of art, course of your life-time, 
so finely and elaborately is the die cut. On the In our calculations, one considerable item of 
other hand, the ugliest silver coinage is that of expense has been overlooked; that is, the trim- 
thus be made in providing for the household, if Russia, each piece being in itself a work of art, 
carefully husbanded, will provide for a “rainy so finely and elaborately is the die cut. On the 
day,” or a competence to make old age eomfortr other hand, the ugliest silver coinage is that of 
L. L. Fairchild. the city of Hamburg; each piece, adulterated and 
Rolling Prairie, Wis., January, 1861 poorly cut, is usually to be found encrusted with 
Remarks.— Tho above is very sensible advice dirt and filth, and looking like a refuse fragment 
and sound economical doctrine. of tin. The silver coinage of Germany is verv 
“THAWING OUT PUMPS." 
Eds. Rural New-Yoricer:— Your corres¬ 
pondent “ L. L. F.” has not given the proper 
system for “thawing out pumps.” He cannot, 
I think, thaw out a pump with eight feet of ice 
in it in two days; and, If he could, it must be 
considered a slow process, I can tell him how 
he can accomplish the work in a few minutes— 
certainly within half an honr—in the most sim¬ 
ple manner. 
Let him procure a tin pipe of any size that 
will pass freely into the pump along side of the 
rod, and set it in the pump, the lower end rest¬ 
ing on the ice. Then pour hot water into the 
top of the pipe, and he will see it immediately 
commence a journey downwards, which it will 
continue so long as lie continues to pour in hot 
water, until it has bored a hole through the ieo 
in the pump. Pouring hot water iuto the open 
pump can have no good effect. It will at the 
first dose melt u small bole In the ice, and 
become cold and remain there, and probably 
freeze again while you are pouring hot water in 
at the top which runs off at the spout. Tho 
object is to bring the hot water immediately and 
continuously in contact with the lee, which is 
fully accomplished by means of the tube. The 
hot water, by its greater height in the pipe, is 
forced to the bottom, and having done its work 
and become cold, is forced up outside and flows 
off. 
The pipe should be in two or more parts, fit¬ 
ting snugly into each other, so that when the 
first, pipe has descended its full length into 
the pump, you can add another link, and so 
on. It should also be secured with a small cord, 
to prevent its sinking down when it gets through 
the ice. Every person using a pump in the 
winter, exposed to the frost, should have such a 
pipe ready for use. The expense is quite tii fling. 
The application of “ hot iron,” or hot coals and 
ashes, which I have sometimes seen applied, 
is perfectly useless. j. l. 
Brampton, C. W., 186-1 
- »- — 
THE MONEY PHASES OF COIN AND PAPER. 
It is a rather curious fact that the only coin 
now in current use on this continent which is 
not round, is the fifty dollar gold piece’ struck 
for California, which is octagonal in shape. All 
the eoius in Europe are round. In Japan they 
have oblong wedges of silver. It is curious, too, 
that for many years money has been made out 
of paper, when leather or doth would seem to 
be much more durable. Yot paper, w hen repre¬ 
senting coin: lasts a great while, and not unfre¬ 
quently the Bank of England receives a note of 
extraordinary age; and the Bank of Bengal, in 
India, recently was called upon to pay several 
thousand pounds of notes so old that ttoue of 
the present generation remembered the pattern. 
It is also worthy of remark that gems or pre¬ 
cious stone have never been used for money, nor 
lias platinum or any other metal taken the place 
of gold. In Africa a species of shell forms the. 
circulating medium, the value of which fluctu¬ 
ates sometimes twenty per cent, a week. But 
all civilized countries have gold as the standard 
of money value, and all other circulating rnedi- 
the city of Hamburg; each piece, adulterated and 
poorly cut, is usually to be found encrusted with 
dirt and filth, and looking like a refuse fragment 
of tin. The silver coinage of Germany is very 
bad also. In Italy—excepting portions sub¬ 
ject to the Pope and the Emperor of Austria— 
the franc piece is taking the place of former 
coins, though the local coinage of the duchies of 
Parma and Nodena still infests those portions of 
the country. Naples also retains in retail traffic 
the complicated coins in use under the Bourbon 
rule. 
Perhaps the neatest paper money in the world 
is that of Greece—which is manufactured by 
American engravers and workmen. The old bunk 
currency of this country is often very elegant. 
The worst and most wretched paper money iu the 
world is the fivc-kreutzer note of Austria, printed 
on a soft, thick, grayish paper, which has a fac¬ 
ulty of washing and rubbing away like ordinary 
b’otting paper. But nearly as bad is the postal 
currency with which, for our sins, we are now 
afflicted. He who steals a purse full of our five 
and ten oent notes— frayed, dirty, worn and il¬ 
legible, does indeed steal “trash.”—AT. Y. Even¬ 
ing Post. 
gkMi»$ fai iltf fjflinig. 
A TALK WITH THE BOYS. 
Eds. Rural New-Yorker: — With your 
permission I would like to talk a littfe with “ the 
boys." Some may ask. “how old are you?” 
That may be answered by saying—I am a few 
years beyond my “ teens.” But that does not 
matter. Let us set about our talk. Suppose 
wo converse of habits, especially bad ones, such 
as drinking tea and coffee, smoking and chewing 
tobacco, drinking beer, wine and rum, and visit¬ 
ing gaming houses. 
Don’t thiuk this a 44 lecture on morals,” for I 
am no great moralist. But I like to see men 
come up erect, without leaning upon broken 
reeds in the shape of "naughty habits.” It is 
not expected that you will disrespect your father, 
or any one else, but tho bad practices they have 
acquired. Make up your miuds to be men with¬ 
out the stain of tobacco juice on your face, or 
the smell of its smoke upon your clothes—men, 
without the smell of strong drink in your breath, 
without the appearance of being a red-faced 
beer keg, bloated to its utmost extremity, with 
blood-shot eyes, peering out from their swollen 
sockets, like suu-burned potatoes, as seen thro’ 
the cracks of an over-filled potato hill. 
We will consider the matter “financially,” 
Suppose you form the practice of drinking tea 
and coffee at twelve or fifteen years of age, ami 
you are permitted to live to tho age of forty, 
making twenty-five years of tea and coffee dilut¬ 
ing. Drinking coffee for breakfast, and tea for 
supper, you will require one-quarter ot a pound 
of tea, and one pound of coffee e»cry month, 
which at the price of one dollar per pound for 
the former, and twenty-five cents for the latter, 
we have the sum of six dollars a year, or the 
total of one hundred and fifty dollars in a life¬ 
time. 
mings to the tea and coffee, which will cost at 
least thirty-seven and a half cents per month, 
four dollars and a half a year, or one hundred 
and twelve dollars and fifty cents in the term of 
years mentioned. This makes a total of twenty- 
five hundred dollars in twenty-five years—all to no 
purpose, except to give a little fleeting enjoy¬ 
ment which tends only to make life shorter, and 
freight it with disease. 
Counting the interest on the above amount at 
six per cent, and compounding it, which is not 
extravagant, we have the sum of about $6,700— 
perhaps more. Boys, some of you whose heads 
arc clear, look this over, and see if it is near 
correct. 
This seems almost unreasonable, yet it is no 
over estimation, but falls short of the cost of 
these habits to a great many. Drinking tea and 
coffee may not be considered so bad as some 
other habits. All allow that they are stimu¬ 
lants which do not strengthen nature perma¬ 
nently, but merely brings her faculties into 
more vigorous action — wastes vitality. For 
they expend that which they cannot replace. 
We need not look far to see this demonstrated. 
Perhaps your father, or mother, or some of your 
acquaintances use these “drugs.” Observe them 
when, by some mishap or other, they are de¬ 
prived of their drams. How low-spirited they 
are, and what 44 awful headaches” they have! 
And how eager they are to get a supply! 
The same may be said of these using tobacco, 
there being but little difference bet ween them. 
And also of those using beer and wine, “ onlv a 
little more so.” All of them are as nearlv rela¬ 
ted as second or third cousins to the 44 worm of 
the still,” whose liquid tire has burned and 
blasted the better natures of millions of human 
beings, turning them iuto intellectual “ brutes,” 
—sinking, in its owu conflagration, millions of 
its victims—making at least seventy-five thou¬ 
sand paupers annually for our country to sup¬ 
port—which, but for rum, might help support it. 
This is the “worm” who commits three- 
fourths of all the crimes—five-sixths of all the 
murders, and who is responsible for the de¬ 
stroyed happiness of multitudes in a future 
existence. 
Then be sure that you are laying the founda¬ 
tion sure upon which you are building your 
characters. Remember that "just as the t w ig 
is bent the tree’s inclined.” It is easier to keep 
from bad habits than to break off from them, 
when established. 
Better spend your money for books, or give it 
to the poor, and your time in reading those 
books, or in doing good. F. B! Me. 
Pontiac, Mich, 1864. 
Written for Moore's Rural New-Yorker. 
SHUN EVIL COMPANY. 
Vicious company is as dangerous as the 
infectious, contagious distomp- r—as smothering 
as the blasts of Sahara’s burning waste—as de¬ 
lusive as the mirage, which seems to the weary 
traveler us a placid, cooling lake; but as ho .ad¬ 
vances to cool his burning lips, it, too, advances 
with equal vapidity. Evil company will steal 
your noble intentions, and mould them into de¬ 
moniac designs. Its fruit ia vile and corrupting 
conversation, which tends to prostrate true 
excellence, subvert true modest), expunge true 
affability, and finally, it leads the young victim 
into the drifting mists of vice, w hich so deaden 
and benumb his once noble mind, that it even 
refuses to try to extricate itself, Then avoid evil 
company—tho instigator of evil thought—tho 
poisonous reef upon which hangs the hideous 
wrecks of multitudes of once noble miuds. 
time. Plajr with tho venomous coya, sport, in your 
I, you ,habit or u,i„ s tobacco „ 
^,11 s, us>ii)£ them moderately, say two each strum, carelessly bask befovo the sweeping tor- 
day, a segar fit for your dignity will cost at least 
tive ceuts, making seventy cents a week; thirty- 
six dollars and forty cents a year, or the sum of 
ine hundred and ten dollars duriug your life. 
sirom, earcie-siy uasx uetove the sweeping tor¬ 
rent of buruiug lava, but arise and flee from the 
soul-blackening curse —evil company. Its effects 
will last until the sun of eternity will set to rise 
no more. r s. a. g. 
Lexington, Ohio. 
