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Natural Science.

COMMUNICATIONS for this Department should be addressed to I. F. CADY, Warren.

For the Schoolmaster.

A Peep into the Dock.

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alive, there's an eel walloping among it "like mad"! And now he is out with his head in sight, and really is swallowing a monstrous worm. Eels and worms among the kelp? Yes; and there's a crab, and there another, larger and of different shape; this looks like a huge spider, that has claws like a lobster; and there goes another in a snail's shell that's a hermit; and there scramPROBABLY the first announcement of my sub- bles another, larger than all the rest together! ject, to some minds, will prove suggestive of little Yes, there is a pair of them; they are king crabs; else than dead cats and broken china. And there they are said lately to have been considered palatmight be a philosophic spirit sufficiently peculiar able when served upon the table. They are curito awaken interest in objects such as these. To ous fellows, and are generally called the "horsemost minds, however, the pleasantest thought re- foot," from their similarity in shape to the foot of specting the defunct felines will be, that the brine, a horse. And out yonder, where the tide has left in its semi-diurnal ebb and flow, will speedily re- the bottom out of water, what means that squirtmove whatever is disgusting to the senses to some ing? Ah! the clams. Funny, that they should place where the ocean scavengers will bid it wel- live all their lives on their beam ends, down in the come to their banquet. In regard to the broken mud there. What makes folks say, "As happy china, although thereto "may hang a tale,"

as a clam"? We may answer this question some other time, perhaps, for, unquestionably, there is more philosophy in a clam than even the wise are wont to dream of.

Let's spare our tears till all the tale is told. But what is there in the dock? Well, first of all, there is a ladder- at least the lower end of But here we are, on the ladder. Let us pluck one-well driven into the mud, and securely an- from it a single leaf of this green kelp. Stop! chored with a stone. It is well fastened both at there's a shoal of shrimps. They are clustering top and bottom, and at low tide and high tide it on the ladder, from the bottom to the very surface furnishes a tolerably convenient passage on board of the water. By the way, I have one of these a nice row-boat, which, when not in use, hangs by creatures that I have been keeping about three pullies from two wooden cranes, ready to be launch- weeks, as a subject for an aquarium that I have ed at the bidding of its owner's pleasure. Now, in progress. When this is completed I intend to there is much that is suggestive in both the ladder cultivate a more intimate acquaintance with a few and the boat. They serve as excellent illustrations of the "thousand and one" living creatures that of the old, familiar "Fast bind, fast find." By find their "Wide Wide World" in a dock, in exday and by night, through sunshine and storm, tent, some eight rods by ten. Meanwhile, as we they remain secure. The boat is not marred and are about to take a sail, perhaps I might as well bruised like those that careless boys sometimes recount some of the facts, interesting to me, which leave battering the wharves. Besides, both care- I have discovered by a few occasional observations less boys and other boys seem to understand that of the movements of two or three specimens of it is by no means common property. It is never life from the sea, which, for want of a better place, treated as some folks treat umbrellas. In fact I have kept, for a few days, in a common washthe boat and the ladder are both types of their bowl. One of these is the shrimp mentioned owner's character. They are staunch and reliable. They promise well, and are good for all they pro- It may be a more familiar fact to others than it mise. They are well cared for, and for this rca has been to me, that the shrimp is exceedingly son are always the more inviting and comfortable. tidy in its habits. No pet grimalkin was ever more Were we to proceed no farther, we might, by re- scrupulously attentive to personal neatness. Upflection, derive several lessons of practical value. on the under part of its body, toward the front, it But forbearing these, we will continue our search. has five pairs of legs, each consisting of three careHaving obtained the permission of the owner- fully articulated portions, and terminated with a for the property, by the way, belongs to another double claw capable of opening and closing like Child than ourself-let us lower the boat for a forceps. Of these pairs of legs the second is longsail. It is about five or six feet to the water from er and stouter than the others, and can be used the top of the wharf. The tide is rather low; still with such flexibility as to be brought in contact there is sufficient water to float our craft, so lower with any part of the animal. It is curious to away. Now we'll try the ladder. But stop. What observe the dexterity with which he performs the have we here? The ladder is very slippery, and operation of removing from himself whatever is toward the bottom the rounds and side's are cover-disagreeable. If anything has lodged upon his ed with leaves that look like lettuce. And see! antennae, of which he has three pairs, one pair The bottom of the dock is green with it;-in fact very long in proportion to the size of the animalcovered with it for several rods. And, as you are he passes them through his forcep-like feet with

above.

all the facility of a fly or bee. If offensive matter finds it unwelcome. For amusement, I have seve has fallen upon his back, he gives them a reverse ral times fed my little pet with the intestines and motion, and neatly slides it from his polished sur- eggs of grasshoppers, which he receives from the face. He effects the work of freeing the hinder point of a pin with as much thankfulness as such part of his body and his curiously fashioned tail a personage as he can be expected to exhibit, and from foreign matter by curving them beneath his swallows them with evident relish. Moreover, his body within reach of his claws. But with all this perfect transparency allows one to observe prefacility for thorough ablution and the frequency cisely where he makes the temporary deposit of with which he employs it, his wants, in this par- his food for the purpose of digestion, and to trace ticular, are not thus sufficiently provided for. it in its onward course. He thus affords opportu Hence he has the power of periodically casting off nity for observation which has not been afforded to the garments which he has so often and so fastidi-physiologists even by the famous Alexis St. Marously cleansed. His coat,- including the cover- tin.

ing of his antenna and of his very eyes, pants, But some one may be ready to ask, "What of boots, and all his external gear, are all thrown all this?" The old utilitarian "cui bono"! Well, aside as worthless. The creature which I have I will tell you. I have performed the important been specially observing has performed this opera-work of cultivating and exercising the power of tion twice in less than three weeks. observation. I have found a source of perfect re

The mechanical structure, in general, of this laxation from hours of weariness, anxiety and toil. animal is not unworthy of attention. His body I have found a source of rational enjoyment in consists, essentially, of six articulating sections, studying the mechanism and functions of a little of which the anterior constitutes about one-third creature fashioned for its own peculiar mode of of his entire length. This terminates in front with life and its own species of enjoyment by the Divine two movable, shield-like projections, beneath the hand that has manifested thought, skill, benevobase of which are attached the three pairs of an- lence and wisdom no less in the construction of an tennae. This section also contains the eyes, which insect than in the erection of a world. Still furare movable, being situated at the extremity of ther. I think I am not mistaken, when I imagine two arm-like organs, as is common in the crusta- that my observations, simple as they are, have a ceans. The next five sections, which diminish in tendency to refine and ennoble my better nature, size toward the tail, thus imparting to the body a and to enkindle a higher admiration, and to awaktapering form, are each furnished beneath with en a more ardent love for that wonderful Being two jointed oars, which are quite thin and concave who, in creating a universe too vast for mortal on the posterior side, so as to cause a vigorous re- comprehension, omitted nothing essential to the action upon the water when in motion. These wants of the least of the creatures that he has enoars have just the position in respect to the entire dued with a sentient existence; who has given length of the animal which the boatman finds, by wings to the thistle's seed, a thousand microscopes experiment, to be most efficient for propelling his to the fly, as many telescopes to the bee, — to the boat. The structure of the tail is admirable. It brute, instinct, to man & reason like his own. If consists of four parts, which somewhat resemble we, as teachers, can guide the minds of our own the tail feathers of a bird, and which the animal pupils into channels of thought such as these, can unfold or close at pleasure, and turn in various none can say that we have altogether taught in directions so as to serve the purposes of a perfect vain. rudder. Each separate part appears to be bordered with delicate fringe; but under the microscope SONG OF THE SKYLARK. It is a curious fancy this fringe is found to consist of plumes of much which makes the skylark boast, in his song, of its finer and more delicate texture than those of a most striking physical peculiarity, which consists humming bird. The posterior segment of the in the length of the toe to facilitate its progress body has a backward projection, terminated by a in travelling on the grass, where it is wont to build small tuft of delicate bristles, which seem, at the its nest. The rule is that the hearer, in order to same time, to steady the tail in its movements and understand the song, must lie down on his back in to aid its general purposes. It is interesting to the fields, when he will hear it as follows: observe the ease and gracefulness with which the little animal effects its movements through the wa

ter.

66

Up in the lift we go,

Te-hee, te-hee, te-hee, te-hee!

1. F. C.

There's not a shoemaker on the earth
Can make a shoe to me!
Why so, why so, why so?

Because my heel is as long as my toe."

Nor is the facility with which the shrimp takes his food inferior to that with which he effects his locomotion. On meeting with something which he thinks may serve for food, he takes it in his OIL OF TOBACCO A POISON.-Rees' Cyclopædia claws and brings it to his mouth with perfect ease; says that a drop or two of the oil of tobacco placed or, when he chooses, will pass it, as it were, from upon the tongue of a cat, produces convulsions hand to hand, or carelessly throw it away when he and death in the space of a minute.

Mathematics.

COMMUNICATIONS for this Department, if relating to the higher branches, should be addressed to J. M. Ross, Lonsdale; otherwise to N. W. DEMUNN, Providence.

For the Schoolmaster.

Fractions.

"Addition is vexation,
Division is as bad;

Rule of Three doth puzzle me,

And Fractions make me mad."

are) you certainly have not received studied attention. Excuse us, and we will endeavor to be a little more attentive, and in the outset we can do no better service than to introduce you to THE RHODE ISLAND SCHOOLMASTER, and to assign you a place in that ably conducted department of our friend Mr. Ross, whose modesty is only excelled by his real worth.

A fraction is any number of the equal parts of a unit considered together. The expression (usual means by which the parts are represented) is also called a fraction. Thus seven of the eight equal parts of an apple considered together form one fraction, and the expression (3) is also called a fraction; but considered separately they form seven fractions, and the expression for each (3) is also a fraction.

The above sentence, compounded of four sighs, though breathed in verse and oft repeated by parents and grand-parents, as their minds revert to the time when they "did sums on the slate," has lost none of its force of feeling upon the pupils of The fraction, one-fourth of an orange, was just to-day. It is true we can, in a practical sense, as much one-fourth of an orange before it was add numbers expressive of dollars receivable, well separated from the unit as afterward, but it was enough, and we can divide the same when payable, not a fraction, for it lacked its distinctive characand as for "Rule of Three," it is perfectly splen- ter as such. Then, in our study of fractions we did except when that fearful word, "double" is must consider them always in their distinctive charplaced before it, when even a Yankee boy has to acter, as being really the equal parts of a unit, guess three times before he can get the answer. and the unit must always be the basis of compariAnd here let me say to teachers, always require son; and in order to understand the comparative your pupils to give the answer in the right place; value of fractions they must be considered as parts that is, at the end of the demonstration. We not of the same or of equal units. unfrequently hear, "I know the answer, but I 1. Analyze the fraction 4-5. cannot explain the solution," Such a pupil has no right to claim, much less to say, I know the answer; he must have "climbed up some other way" than by the way of correct reasoning.

2. Multiply the terms of the fraction by 2 and explain the effect.

It is an expression for four of the five equal parts of a unit, or for one of the five equal parts from each of four units. The first, of course, is obtained by separating a unit into five equal parts and But Fractions! O Fractions! why do ye make expressing four of them; the other is obtained by the little ones mad? Ah, yes, I anticipate your separating each of four units into five equal parts reply. It is like this: -"We, poor little pieces and considering together one part from each of of a divided unit, have no desire to puzzle or to the units divided. vex, much less to madden, the little boys and girls. We claim to be a very social, interesting family, and when we are really understood and properly The result is 4-6, which is the same in value as dealt with we claim to excite no less interest and 3, because multiplying the denominator of any enthusiasm, even, in the mind of the child, than fraction by 2 makes it signify that the number of does Uncle Tom's Cabin' or Aunt Chloe's Map-original parts have been halved, hence each part puzzle of the United States. We have been slight- being only one-half as large as the former parts, ed; and some teachers, who, by the by, never made it will take twice their number to express an equal our thorough acquaintance themselves, have ad- value. vised their pupils to pass us by as unworthy their consideration. Deluded teachers, ye were willing to earn by very delicate application an imperfect The result is, which is the same in value as smattering of the first book in French, the rudi- 3-9, because dividing the denominator of a fracments of music, took delight in making flowers of tion by 3 makes it signify that the number of parts wax and raising worsted butterflies on broadcloth, is only the former number, hence each part being while ye openly declared your inability to compre- 3 times as large as the former parts it will take hend even the utility of studying that of which all only one-third their number to express an equal things are composed, viz., the parts of a thing. We value.

3. Divide the terms of the fraction 3-9 by 3 and explain the effect.

only ask to be placed in the hands of a skillful If the terms of a fraction be multiplied (No. 2) teacher, one who knows what we were, what we or divided by any number, the effect is not to are, how we became such, and what we may be, in change the value of the fraction but simply its deorder to exhibit our interesting properties." nomination.

Well done! Mr. Fractions. If one half your insinuations be true (and I am inclined to think they

4. Multiply the numerator of 3-16 by 4.
Result is 12-16, which expresses parts of the

same size but 4 times as many of them, hence the one of them being of 1-5 the apple, or 1-15 the fraction 3-16 has been multiplied by 4. entire apple.

Had it been required to get of 4-5 the apple,

5. Divide the denominator of 3-16 by 4. Result, which expresses the same number of it would be necessary to separate the apple as be

parts but each is 4 times as large, hence the fraction 3-16 has been multiplied by 4.

6. Divide the numerator of by 3. Result, which expresses parts of the same size but only as many of them, hence the fraction has been divided by 3.

7. Multiply the denominator of by 3. Result 3-12, which expresses the same number of parts each as large, hence the fraction been divided by 3.

8. 10-12 5.6.

fore, but instead of one, four of the parts must be dealt with, each one of which is to be separated into 3 equal parts and one of these parts taken from each division, giving of 4-5 the apple or 4-15 the entire appie. Abstractly, if | of 1-5 = 1-15, of 4-5 must equal 4-15.

Had it been required to get of 4-5 the apple, it would be necessary to separate the apple as last has divided, but instead of taking 1 part from the division of each of the four-fifths, 2 would be taken, giving from each of the 4-5 or 3 of 4-5 the apple, or 8-15 the entire apple. Abstractly, if † of 4-5 = of 4-5 must equal 8-15.

10-12 expresses 10 of 12 equal parts of a unit, each part being as large as those of the fraction 4-15, 5-6, hence a given number of twelfths must be equal to that number of sixths.

Or, by No. 3, dividing the terms of 10-12 by 2 equals 5-6.

In like manner show what 7-9 may equal. 7-9 expresses 7 of 9 equal parts of a unit, and if each one of the 9 parts be separated into 8 equal parts the unit would be divided in 72 parts, and 7 parts of the first size would be equal to 56 of the last, hence 7-9 56-72. Or, since it takes 8 of 72 equal parts of a unit to equal 1 of 9 equal parts, 7 times 8 or 56 of 72 equal parts must equal 7 times 1 or 7 of 9 equal parts, hence 56-72 = 7-9.

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The solution of such examples as the above, if expressed like the accompanying form, can be seen and judged of at a glance. It consists of three parts, (1) factoring the denominators; (2) getting the product of those factors that enter into the L. C. D.; (3) multiplying each numerator by the factors of the L. C. D. excepting those of its own de nominator, and placing the sum of the products over the common denominator.

ft. ft.
ft. ft.
ft. ft.
14. 616, 618, 69.
Of course a foot-measure is contained in a dis-
tance of 6 feet, 6 times; that is, the measure must
be applied or put upon that distance 6 times. A
in 6 times the distance it must be contained 6 times
measure ft. long is contained in 1 ft. 3 times, and
would be contained in a given distance one-half as
as many times, or 18 times. A measure ft. long
many times as ft. long; hence it must be con-
tained in 6 ft. 9 times.

15.4-3 }+4=4-9
is contained in 1 four times, in
be contained of 4 times = 4-3.

Looking at the numerators alone the first fraction } ÷ 1 = 8-9. is 3-7 the value of the second; looking at the deof 1 it must nominators alone the first fraction is 13-10 the valmust be conue of the second; looking at both numerators and tained in only as many times as is, or of 4-3 denominators the first fraction is 3-7 of 13-10 or 4-9. must be contained in twice as many 39-70 the value of the second. Proof, 39-70 of times as in, or 2 times of 4-3 = 8-9 (that is 8-9 7-133-10. The second fraction is 7-3 of 10-13 of, product of divisor and quotient, is contained or 70-39 the value of the first. Proof, 70-39 of once in the dividend, or is equal to it.) 3-107-13.

8-9 x 7-556-45.

16. 8-9 5-7
+ -
1-7 is contained in 1 seven times, it must be con-

12. Get of 1-5 of an apple. I must first get 1-5 the apple by separating it in-tained in 8-9 of one 8-9 of 7 times, and 5-7 must to 5 equal parts. I then have to deal with only 1 be contained 1-5 as many times as 1-7 is, or 1-5 of of these parts, which I divide into 2 equal parts; 8-9 of 7 times 56-45. Or thus: 1-7 is contain

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The true answer to the oft-repeated question, "Why do you invert the terms of the divisor and

QUESTIONS FOR

Written Examinations.

COMMUNICATIONS for this Department should be addressed to A. J. MANCHESTER, Providence.

Questions Used in the Examination

proceed as in multiplication," is, evidently, because OF THE FIRST GRADE, GRAMMAR SCHOOLS, CHICAa process of correct reasoning requires it.

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GO, ILLINOIS, JUNE 18, 1861.

[The examples may be worked out first on slates, and then copied on the paper, if pupils prefer to do so; but all the copying must be completed within the time specified. THE SOLUTIONS SHOULD BE COPIED ON THE PAPER

2.78061 2.7806 2 78061000..0027806. IN FULL, so that the committee may see the process as 2.78062000. = of .0027806 = .0013903.

well as the answers. No books nor helps of any kind,

19. Divide 16 bushels into parts each contain- allowed on the desks, and none to be used during the exing 4-7 of a bushel. amination. Al communication to be avoided. Pupils to If 16 bushels be divided into parts each contain-receive no information from teachers, or others, respecting ing 17 bushel, the number of parts would be 112; and if these parcels be collected, placing 4 (4-7) bu.) of them together, there would be of 112, or 38 parts.

any of the questions. Every pupil to write at the top of each paper, his or her name, age in years and months, name of the school, and grade of the class. Each an

swer should be numbered to correspond with the number of the question. At the close of the time specified, every paper will be taken up, whether completed or not.]

ARITHMETIC.

[Fifty minutes allowed for this exercise.]
Define notation and numeration.

1.

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These isolations have been gathered here, not to throw new light upon the subject of Fractions, for the illustrations are homely, and are common enough in some schools, but we would impress upon the mind of the learner the fact that in studying fractions he is not dealing with abstractions, gotten up on purpose to perplex the mind, but that he has to do with real things just as much as when he deals with whole numbers. As $25 is the representation of a collection of 25 ones of dollars, so is $4-5 a representation of a collection of 4 fifths| 3. Give the rule for contractions in multiplicaof a dollar. Fractions is no more a book of ab- tion, when the multiplier is a composite number; stractions or imaginations than is the book of and illustrate by an example.

Banking.

2. Add the following numbers: Three hundred and one millions and ten; one billion, one hundred thousand and one; ten millions, ten thousand and ten; ten billions and one hundred millions; one billion, one thousand and one hundred.

4. Divide one hundred and ten millions, one In every graded school the beginner of the stu- thousand, one hundred and ten, by eleven millions, dy of fractions should use the head without any one thousand, one hundred and eleven. assistance from the hand for at least one term of 5. Define denominate numbers, and give examthree months;-mind-work, and not hand-work, ples. is the developing agent.

ZERO. QUESTION.-A gentleman making his addresses in a lady's family who had five daughters; she told him that their father had made a will, which imported that the first four of the girls' fortunes were, together, to make $50,000; the last four, $66,000; the last three with the first, $60,000; the first three with the last $56,000; and the first two with the last two, $64,000, which, if he would unravel, and make it appear what each was to have, as he appeared to have a partiality for Harriet, her third daughter, he should be welcome to her: pray what was Miss Harriet's fortune?

6. Reduce £18 7s. 8d. and 2 far. to farthings. Prove the work.

7. For what is cubic measure used? For what is Troy weight used?

8. What are the prime factors of 7684 ?

9. Reduce the fractions, 5-12, 7-18, and 11-24, to their least common denominator. 10. Divide .0101 by .001.

GRAMMAR.

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SOME read to think, these are rare; some to write, these are common; and some to talk, and these form the great majority. It has been said of the latter class that they treat books as some do lords and that? -inform themselves of their titles, and then boast | 6. Write a sentence containing a compound reof an intimate acquaintance. lative pronoun, and underscore the pronoun.

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