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These heads are called Umbels, and the smaller are called Umbellules. How many

umbels are there on the plant?

You say there are 4 stalks, each of which supports one umbel: how many spokes on this umbel? And on the other three Are the number of spokes in each umbel alike? Four times 40, are how many?

Each larger spoke supports one umbellule; in each umbellule, how many smaller spokes áre there? How many in each umbel?

We find 30 smaller spokes in each umbellule ; in each of the umbels 1200 smaller spokes; how many then in the four umbels?

The number of unbellules on the 4 stalks, is -how many times as great as that of the umbels?

You perceive then, that the number of umbellules is 40 times that of the umbels.

The number of smaller spokes contained in one umbel, is-how many times as great as the number of larger spokes in one umbel?-And, the number of the smaller spokes, taken collectively, is how many times as great as of the larger taken collectively?

There are taken collectively, or in the 4 umbels together, 4 times 40, i. e. 160, larger spokes, and 4 times. 40 times 30, i. e. 4800 smaller spokes; or, to each of the 160 larger spokes, together contained on the 4 stalks, there are 30 smaller spokes: how many divi

sions of the 4 stalks are there into the 160 large spokes-how many subdivisions are there into the 4800 little spokes ?*

As a commencement of such exercises, the children might be told to find 2 leaves-3 leaves, growing together on a plant. They will not unfrequently find a few combinations of leaves, either on the same, or on different plants, containing numbers successively increasing. In the Galium, they will find leaves growing, 4, 5, 6, 8 in a whirl.-In the Syngenesia class (compound flowers) many interesting observations may be made-the corn-flower, the tansy, the mill-foil, &c: may be examined in the way of comparison; in looking at the dandelion, and many of the plants which resemble it in appearance, the peculiar structure of the florets of the receptacle, and the manner in which the seeds sow themselves may be remarked. While these exercises are going on, the mind may, by simple means, be prepared for taking an interest in every branch of natural science.

* The collected numbers of little spokes, may be taken as a multiplication of the larger spokes, and the larger spokes as a multiplication of the stalks. Or, the number of the stalks (four) may be considered as entering so many times (ten) into the greater divisions, or larger spokes of one umbel; and so many times into the different numbers of subdivisions; e. g. so many times (300) into those contained in one umbel, then so many times (1200) into the collected subdivisions of the four umbels. A variety of exercises might be given adapted to the capacity of the pupils.

The principles of natural Geography may be given in a simple manner, before the children are introduced to artificial Geography; the windings of a stream might be followed, the directions of its course be observed-the spots which lie nearest home might be considered with relation to east, west, north, and south; then their position with respect to each other, &c:afterwards, these considerations might gradually be extended. A journey affords a favourable opportunity for such exercises; even within the compass of a walk much may be done. We may, at least, proceed so far as to prepare the mind for a beneficial use of the representations on the map and globe.

The subjects upon which we have very slightly touched, are of wide extent. The method so imperfectly and briefly suggested, might, we conceive, be applied with advantage to almost every object of human study. TRUTH should be sought in every thing, both as means and end:-artificial signs should be used, only when the mind has been opened to the consciousness. of the realities signified. If this cannot always be done, it should at least be done as far as possible. The subjects of study may be chosen. according to the peculiar circumstances of the individual; but the method may be advantageously pursued by all.

A few additional remarks will conclude this part of our little work.-We should accustom children to generalize by degrees. A mind

which comes to general conclusions before it has the knowledge of particular facts, will often fall into error-a mind which is satisfied with the investigation and knowledge of facts, has done but half its work. To assist the mind in steering between these two extremes, should be one great object of the Instructor-let the perceptive faculties of children be early exercised, and their reflective be at the same time gradually called forth; thus knowledge and reflection may go hand in hand.-Let children be taught to ascend from the minute to the vastlet them again be exercised in descending from the vast to the minute. The process of number may be continually going on within the mindwe branch out from unity to multiplicity; we retrace multiplicity to unity.-The child should be continually led up to the great Unity, which is God; in going into multiplicity, he should be taught always to take the unity as its

centre.

We remarked, that children who have been accustomed to enter into minute detail, are gradually prepared for comprehensive views. At times a lesson something like the following might be given.

UNIVERSE.

You have heard of the word Universe: did

you ever consider its meaning?

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It may be used in different senses; sometimes it may signify the solar system-sometimes all

the systemis of worlds which God has made. The word Universe is well calculated to bring to our mind the most expansive and sublime ideas; we cannot grasp them in their full extent. We will, however, try to give a sketch, though a faint and imperfect one, of what we mean by the word Universe.

Consider for a moment the globe we inhabit. What do you call it with relation to the solar system?

It is only one out of several planets. And round what great body do these planets move? Are they at different distances from the sun? Have you any idea of these distances?

[The Teacher may tell the children, that of the eleven planets yet discovered, the nearest is 37 millions of miles, and the farthest 1800 millions of miles from the sun.]

Think then of the sun as the centre, and of all the planetary bodies as revolving round him, at different immense distances.

Think of the rapidity with which these bodies move, the motion of the slowest planet (the Georgium Sidus) being about 16,000 miles an hour, and that of the swiftest (Mercury) more than 105,000.

Consider that some of these bodies are attended by moons which revolve round them, as they revolve round the sun.

Think also of the comets moving in their elliptical orbits. In order that you may form

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