know the reason of things; but he would do it, without aid from this rigid, syllogistic, measuring, calculating science. He seeks indeed, no "royal road to geometry," but, he seeks one not less difficult to find, in which geometry is not needed.

3. He begins with the mechanical powers. He takes the lever and readily understands that it will move a weight. But the principle upon which different weights at different distances are moved, he is forbidden to know; for they depend upon ratios and proportions. He passes to the inclined plane; but quits it in disgust, when he finds its action depends upon the relations of angles and triangles. The screw is still worse, and when he comes to the wheel and axle, he gives them up forever; they are all mathematical !

4. He would investigate the laws of falling bodies, and moving fluids, and would know why their motion is accelerated at different periods, and upon what their momentum depends. But, roots and squares, lines, angles, and curves, float before him in the mazy dance of a disturbed intellect. The very first proposition is a mystery and he soon discovers, that mechanical philosophy is little better than mathematics itself.

5. But he still has his senses; he will, at least, not be indebted to diagrams and equations for their enjoyment. He gazes with admiration upon the phenomena of light; the many-colored rainbow upon the bosom of the clouds; the clouds themselves reflected with all their changing shades from the surface of the quiet waters. Whence comes this beautiful imagery? He investigates and finds that every hue in the rainbow is made by a different angle of refraction, and that each ray reflected from the mirror, has its angle of incidence equal to its angle of reflection; and, as he pursues the subject further, in the construction of lenses and +telescopes, the whole family of triangles, ratios, proportions, and conclusions arise to alarm his excited vision.

6. He turns to the heavens, and is charmed with its shining host, moving in solemn procession, "through the halls of the sky," each star, as it rises and sets, marking time on the records of nature. He would know the structure of this beautiful system, and search out, if possible, the laws which regulate those distant lights. But astronomy forever banishes him from her presence; she will have none near her to whom mathematics is not a familiar friend. What can he know of her parallaxes, anomalies, and precessions, who has never studied the conic sections, or the higher order of analysis? She sends him to some wooden orrery, from which he may gather as much knowledge of the heavenly bodies, as a child does of armies from the gilded troopers of the toy shop.

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7. But if he can have no companionship with optics, nor as tronomy, nor mechanical philosophy, there are sciences, he thinks, which have better taste and less austerity of manners. He flies to chemistry, and her garments float loosely around him. For a while, he goes gloriously on, illuminated by the red lights and blue lights of crucibles and retorts. But, soon he comes to compourd bodies, to the composition of the elements around him, and finds them all in fixed relations. He finds that gases and fluids will combine with each other, and with solids only in a certain ratio, and that all possible compounds are formed by nature in immutable proportion. Then starts up the whole doctrine of chemical equivalents, and mathematics again stares him in the face.

8. Affrighted, he flies to mineralogy; stones he may pick up, jewels he may draw from the bosom of the earth, and be no longer alarmed at the stern visage of this terrible science. But, even here, he is not safe. The first stone that he finds, quartz, contains a crystal, and that crystal assumes the dreaded form of geometry. Crystallization allures him on; but, as he goes, cubes and hexagons, pyramids and dodecagons arise before him in beautiful array. He would understand more about them, but must wait at the portal of the temple, till introduced within by that honored of time and science, our friendly Euclid.

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9. And now, where shall this student of nature, without the aid of mathematics, go for his knowledge, or his enjoyments? Is it to natural history? The very birds cleave the air in the form of the cycloid, and mathematics prove it the best. Their feathers are formed upon calculated mechanical principles; the muscles of their frame are moved by them. The little bee has constructed his +cell in the very geometrical figure, and with the precise angles, which mathematicians, after ages of investigation, have demonstrated to be that which contains the greatest economy of space and strength. Yes! he, who would shun mathematics, must fly the bounds of "flaming space," and in the realms of chaos, that

where Milton's Satan wandered from the wrath of heaven, he may possibly find some spot visited by no figure of geometry, and no harmony of proportion. But nature, this beautiful creation of God, has no resting place for him. All its construction is mathematical; all its uses, reasonable; all its ends, harmonious. It has no elements mixed without regulated law; no broken chord to make a false note in the music of the spheres.

E. D. MANSFIELD.

QUESTIONS.-What is it the object of this lesson to illust? If a student, unacquainted with mathematics, attempts to investigate the subject of mechanics, what will be the result? What, if he trusts to his senses? If he attempts to learn chemistry, what obstacles does he find here? How is it with mineralogy? With natural history? Point out the inflections in the 8th and 9th paragraphs.

LESSON LXXXVIII.

REMARK.-Observe the commas, and stop at each long enough to take breath.

PRONOUNCE Correctly.-Prog-ress, not pro-gress, (the noun is pronounced progress and the verb, pro-gress'): post-u-lates, not pos-tylates: en-gin-eer-ing, not in-gi-neer-ing: ves-ti-bule, not ves-tib-u-le : vol-ume (pro. vol-yum), not vol-lum: fract-ur'd (pro. fract-yur'd), not frac-ter'd.

1. Hu'-man-i-zes, v. renders kind and | 3. Civ'-il En-gin-eer'-ing, n. the science humane. of the construction of extensive works, such as canals, aqueducts, &c. Hy-draul'-ics, n. the science which treats of fluids in motion.

De-vel'-op-ment, n. an unfolding. 2. Im-preg'-na-ble, a. that can not be defeated. [taken as self evident. Pos'-tu-late, n, a position which is Syl'-lo-gism, n. an argument of three propositions, the first two of which are premises, the third, the inference.

VALUE OF MATHEMATICS.-(CONTINUED.)

1. LET us take another student, with whom mathematics is acither despised nor neglected. He sees in it the means of past success, to others; he reads in its history the progress of universal improvement; and he believes, that what has contributed so much to the civilization of the world; what is even now contributing so much to all that humanizes society; and what the experience of all mankind has sanctioned, may, perchance, be useful to his own intellectual development.

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2. He opens a volume of geometry, and steadily pursues its abstractions from the definition of a right line, through the elegant properties of the right-angled triangle, the relations of similar figures and the laws of curved surfaces. He finds a chain of unbroken and impregnable reasoning, and is at once possessed of all the knowledge of postulates, syllogisms, and conclusions, which the most accomplished school of rhetoric could have taught him.

3. He looks upon society, and wherever he turns, arts, sciences, and their results, from carpentry to civil engineering, from *archi tecture to hydraulics, from the ingenious lock upon a canal, to the useful mill upon its sides, disclose their operations, no longer mysterious to his enlightened understanding. Many an interesting repository of knowledge this key has opened to his vision, and as he thus walks through the vestibule of science, he longs to penetrate those deep aisles, and ascend that magnificent stairway, which lead up to the structure of the universe.

4. With the properties of the ellipsis, the laws of motion demonstrated by mathematics, and two facts drawn from observation, the one that bodies fall toward the earth, and the other, the regular motion of the planets, he demonstrates, beyond the power of refutation, the laws of the celestial system. He traces star after star, however eccentric their course, through the unseen immensity of space, and calculates with unfailing certainty, the hour of its return, after ages have passed away.

5. He does more, he weighs matter in the balances of creation, and finds that, to complete the harmony of the system, a planet is wanting in some distant corner of its wide domain; no mortal eye has ever seen it, no tradition tells of its existence. Yet with the confidence and zeal of prophecy, he announces that it must exist, for demonstration has proved it. The prediction is recorded in the volume of science.

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6. Long after, astronomy, by the aid of mathematics, discovers the long-lost tenant of the skies; and fractured though it be, while its members perform their revolution, no living soul can be permitted to doubt the worth of mathematics, or the powers of his own immortal mind.

7. And what were the glorious contemplations of that pupil of mathematical philosophy, as he passed behind the clouds of earth to investigate the machinery of celestial spheres! Alone, yet not solitary, amid the glowing lights of heaven, he sends his spirit forth through the works of God. He has risen by the force of cultivated intellect to hights which mortal fancy had never reached.

8. He has taken line, and figure, and measure, and from proposition to proposition, and from conclusion to conclusion, riveting link after link, he has bound the universe to the throne of its Creator, by that

Whose strong embrace holds heaven, and earth, and main."

9. And is there no moral instruction in this? Does he learn no lesson of wisdom? Do no strong emotions of love and gratitude arise toward that being who thus delights him with the charms of intellectual enjoyment, and blesses him with the multiplied means of happiness? Harder than the adamant of his own reasoning, colder than the abstractions in which he is falsely supposed to move, must be he, who, thus conducted by the handmaid of the arts and sciences, through whatever humanizes. man; through whatever is sublime in his progress to a higher state; through all the vast machinery, which the Almighty has made tributary to his comfort, and his happiness, yet feels no livelier sentiment of duty toward him; no kinder or more peaceful spirit toward his fellow

man.

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E. D. MANSFIELD.

QUESTIONS.-In what light does the student, referred to in this lesson, regard mathematics? What does he find in geometry? In what particulars, does he observe the influence of mathematical science upon society? Through what source, are the laws of the heavenly bodies discovered? What is said of a planet predicted to exist, before any discovery authorized such opinion? What is said of the moral instruction to be derived from all this?

Let the pupil point out each subject of a verb in the 5th paragraph. Let him point out also, each object of a verb or of a preposition. Which are the prepositions? Which are the adjectives? How many simple sentences?

TO TEACHERS.

In the grammatical questions it is not intended to prescribe any particular form of examination, but rather to draw attention to the subject. Each teacher will determine for himself how many and what questions to ask. But, it is believed that he will derive great advantage from connecting this study with the reading lesson.