the achromatic* microscope to it. What do we see? A well! in which numerous animalcules, of different sizes, and of very different forms, are floating and diving! Each seems to be pursuing his own way, and enjoying, in the spacious area of our needle-hole, the unrestricted use of his powers of movement! How diversified the workings of those powers! Some appear crawling on the interior surface of the upper piece of glass; others, no sooner arrive at the surface of the water, than they quit it, again to make their way out of sight, through its depth-which, in this case is, of course, equal to the thickness of our paper! Whilst you are reading, a leech-like monster has attached himself by the tail to the circumference of our well; and, stretching, reaches nearly to the centre! What is that perturbation? a whirlpool!-it is caused by his wheels: he has two above his head; and their numerous exquisitely adjusted paddles, each of them much larger than many of the living individuals he is swallowing, are in eager and rapid revolution, and these are creating the vortex which is dragging towards him, in abundance, the prey which he would otherwise fail to reach. Now, having wrapped up and taken in his machinery, he has rolled himself into a ball, and all seems hushed; whilst from 60° distance from his station, there comes a globule! the bright specks I discover on him, show me that he is revolving as he steadily crosses the field of view! Has he 360° in his circlet too? How minute! Yet we may conceive each of those degrees to contain its 60 minutes, and each of those minutes to comprehend its 60 seconds! Is he rotating about his centre of gravity also! That it is impossible to tell its position would depend upon the distribution of the several parts of his interior if he were mere matter; but he is organized and sentient; he acts with purpose to fulfil his wants, and his Creator and mine, the Upholder of the sun, and of the myriads of the rolling stars, has given him the nervous and muscular powers which are peculiarly fitted, at least to sustain, and to direct his course; for see! he has changed it. N Thus, whilst "the Telescope indicates the insignifi* The application of the achromatic correction to the Microscope has admitted a ninefold quantity of light, and great distinctness. (See "Microsc. Cab.," by Mr. A. Pritchard, of Fleet Street, the coadjutor of Dr. Goring.) (See, also, H on p. 15.)

cance of the world I tread upon, the Microscope redeems it from all insignificance; for it tells me, that in the leaves of every forest, and in the flowers of every garden, and in the waters of every rivulet, there are worlds teeming with life, and numberless as are the glories of the firmament. The one has suggested, that beyond and above all that is visible to man, there may lie fields of creation, which sweep immeasurably along, and carry the impress of the Almighty's hand, to the remotest scenes of the universe: the other suggests, that within and beneath all that minuteness which the aided eye of man has been able to explore, there may lie a region of invisibles; and that, could we draw aside the mysterious curtain which shrouds it from our senses, we might then see a theatre of as many wonders as astronomy has unfolded, a universe within the compass of a point!"*

B A Globe or Sphere, is a body bounded by one uniform convex surface, every point on which surface is equally distant from a point within it, and which is therefore called its centre.

C If the globe or sphere rotate, the diameter about which it revolves, is called its Axis.

Every diameter of a sphere is called an axis; but that is emphatically the Axis about which the sphere revolves.

D Every section, or cutting, of a sphere, made by a plane, is a Circle.

A Great Circle is that which passes through the centre of a sphere, and divides it into two equal parts.

A Small Circle is that which does not pass through the centre of the sphere, and therefore divides it unequally.

F The Pole of a Circle of the Sphere, is a point on the surface equally distant from all points in the circumference of that circle.

Every Circle of the Globe, great or small, has two Poles; if the globe or sphere rotate, those are emphatically the Poles which are the extremities of the axis of rotation.

By an optical illusion, an individual in the open air, is impressed with the idea that every part of the expanse above him, is at an equal distance from him. If his finger be pointed to the horizon, and then carefully directed upward till it point vertically, (i. e. to his Zenith,

* Dr. Chalmers.



the pole of his horizon,) unless the individual be elevated he will then have described an exact quarter circle or quadrant of the heavens, and his finger and arm, when moved in this way, are said to have been moved in Azimuth.

The Plane which would be described by splitting the the earth through the station of the observer from the North to the South Pole as far as to the axis, (and through the axis continuously to the opposite portion of the earth's surface,) is the "Plane of the Meridian." This plane may, as easily, be conceived to extend to the heavens, and to be carried, together with the residence of the observer, eastward, by the rotation of the earth on its axis.

When, by such rotation of the earth, this plane is brought to coincide with any heavenly body or bodies, they are said to culminate. When the sun culminates, it is

noon, hence its name "meridian,” (Latin, meridies.)

The boy who runs northward to raise his kite with a north wind, or southward, to raise it with a south one, sees his kite, and the string as it is being elevated by it, "cutting out" the plane of the meridian.


A meridian, strictly speaking, is the plane in which the whole edge of a large cutting instrument would move, both outside the globe and within it; if, from distant space it so advanced and fell upon the globe's surface, as to divide it into two equal parts, by entering it along the whole of a meridional semicircumference; thus cutting through the entire line of axis, and completing the division by passing out in like manner, through the whole of the opposite semicircumference, to persevere in its unwavering course beyond the globe into opposite space,

H Parallel Lines are such as, being in the same plane, will not meet however lengthened.

K Lines, and consequently the planes in which they lie, although they be not strictly parallel, may be considered as parallel, when the point to which they mutually tend is so distant as to render that tendency imperceptible, or insignificant.

LLines and the planes in which they severally lie, although parallel and apart, may be esteemed as one line, or one plane, when considered as extending to an object so remote as to render their distance of separation insignificant.

Thus, the flat roofing of a house, and the several floors in that house, and the tables standing on those several floors, are all parallel and separate, but may be considered as together when referring their several planes to the station of an individual at the distance of four or five miles.

B Hence the Sensible Horizon, or circular limit of our view of the earth, seems to be in the same line, and therefore in the same plane, with the Rational Horizon, or circular limit of our view of the heavens; and may often, without error, be considered as coinciding with it.



Where S R the semi-diameter of the earth, or 4000 miles, is only the twenty-four thousandth part of the distance at which S H' and R H, the planes of the sensible and rational horizon, meet, or where the sun is rising or setting.

c If a disk of wood, as the head of a barrel, when floating in perfect quietness on a calm sea, be supposed to increase all around, until it become the head of a barrel sufficiently capacious to contain the earth, (a globe in a cylinder,) the surface of that disk so enlarged, would describe" the plane of the horizon." It may further be conceived to extend around to the heavens.

D In strictness, only the man whom we have supposed (H on p. 1,) to be floating with his eye level with the surface of calm water, has his sensible horizon corresponding with his rational one; any elevation of the eye above the surface, enabling him to overlook a portion of the convex surface of the earth, and to see below the line in the heavens which is opposite to the earth's centre.*

This "Dip of the Horizon" is appreciable at a height less than that of a ship's deck, and is allowed for in estimating the altitudes of the heavenly bodies for nautical purposes.

F The Clouds and the tops of mountains, glisten with the splendour of the sun before his rising, and after his setting, to the inhabitants of the neighbouring shores.

Mr. Sadler, the aeronaut, who, on one occasion, ascended after sunset from our English coast, witnessed a Western sunrise, as he rapidly attained a considerable elevation.-Sir J. F. W. Herschel.

The uneven appearance of the Eastern edge of the Crescent Moon, is occasioned by the inequalities of her surface; her eminences, as she very slowly rotates on her axis, catching and reflecting the beams of the sun, hours before her valleys and cavities receive them and when she is waning, the same appearance of her Western edge is occasioned by the light which is yet shining on her mountain tops, when their neighbouring valleys have lost it.†


* But the water, the horizontal surface of which bounds the man's view, may be either level with the sea, or on a mountain-top; the height of the mountain being as nothing when compared with the semi-diameter of the earth, which we have seen is, itself insignificant.

+ Those who are in the habit of using astronomical telescopes are often delighted with the beauty of this phenomenon, along the constantly varying boundary of light on the surface of our mountainous satellite. Even an inferior telescope, if on a stand, affords a very interesting view of it.



MA Parallelogram is a four-sided figure, having its opposite sides parallel.

The following are Parallelograms with their distinctions,

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A Trapezium is a four-sided figure, which has not its opposite sides parallel.


N The content of any right angled parallelogram, or Rectangle," (such as figures Nos. 1 and 2,) is found by multiplying its length by its breadth.

P When the Rectangle has its length and breadth equal, it is a Square. Hence the product of any two numbers is called their rectangle; but the product, or rectangle, arising from the multiplication of a number by itself, is called its square.

If we conceive the figure No. 1, with its intersections, to be made of fine wire, and to sink into the thickness of the book, as into wax, until it arrive at a depth exactly equal to its width or length, each of its thirty-six meshes will cut out a little, solid, four-sided prism or pillar, capable of being again divided into six dice-like portions or cubes. Of these little cubes, so constituting the whole cube cut out by the sinking of the figure, there would thus be 6× 6 × 6, or 216.


Hence the product arising from the multiplication of square of any number by that number, is called its Cube. R Ratio is the relation which two numbers, or the quantities which they represent, bear to each other. This relation is ascertained by dividing the one number by the other.

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