but a glorified body, and thereby recovering the completeness of human nature-receive its full fruition of happiness; inasmuch as its restored powers, its capacities for action, enjoyment and advancement, can then be instrumental only to its endless progress in the knowledgewhich is the love-of God.

LITTLE CHILDREN.

"Of such are the kingdom of Heaven."

And yet we check and chide

THE airy angels, as they float about us,

With rules of so-called wisdom, till they grow
The same tame slaves to custom and the world!
And, day by day, the fresh, frank soul, that looked
Wistfully from those eyes, and smiling played,
'Mid the wild roses on that dimpled cheek,
And modulated all those eager tones,
And danced in those light footfalls, to a tune
Heart-heard by them-inaudible to us,

Folds closer its pure wings, whereon the buds
They caught in Heaven, already pale, and pine,
And shrinks amazed and scared back from our gaze!
And so the evil grows. The graceful flower
May have its own sweet way, in bud and bloom,
May drink and dare, with upturned gaze, the light,
Or nestle 'neath the guardian leaf, or wave

Its fragrant bells to every rover-breeze,

:

Or wreathe, with blushing grace, the fragile spray,
In bashful loveliness ;-the wildwood bird
May plume at will his wings, and soar or sing ;-
The mountain-brook may wind where'er it would—
Dash in wild music down the deep ravine,
Or rippling drowsily in forest haunts,
Dream of the floating cloud-the waving flower,
And murmur to itself sweet, lulling words,

In broken tones. How like the faltering speech
Of early childhood! but our human flowers-
Our soul-birds, caged and pining, they must sing
And grow,-not as their own, but our caprice
Suggests, and so the blossom and the lay
Are but half-bloom and music at the best ;-
And if, perchance, some brave and buoyant soul,
More bold or less forgetful of the lessons
God taught her first, disdain the rule-the bar-
And wildly beautiful, rebellious rise,

How the hard world-half-startled from itself,
Frowns the bright wanderer down, or turns away
And leaves her, lonely, in her upward path!
Thank God! to such His smile is not denied.

THE PHILOSOPHY OF NUMERATION.

It is a curious fact that, while different nations have distinct languagesin some instances, altogether dissimilar-yet all agree in their mode of numbering, by never advancing beyond ten without beginning anew, and thus combining ten and ten, and tens with tens, in orderly steps to millions.— Why have nations been restricted to the number ten? This question may appear of no practical utility, either for intellectual amusement, or the acquisition of wealth; but I affirm that a correct answer will include a law of mind which governs our religious, moral and political doctrines, as well as our mode of calculating dollars. The popular and universal answer which philosophers have given, is expressed by Dr. Thompson, in his "Progress of Physical Science." He says:

"The decimal mode of numeration has been adopted by almost all nations— evidently because man has ten fingers, and because men were in the habit of reckoning on the fingers, and after coming to an end, they begin again. If the number of the fingers had been twelve instead of ten, the mode of numeration would certainly have been duodecimal instead of decimal; and this mode would have had its conveniences, which the decimal mode wants."

I dissent from the conclusion, totally, that the number of man's fingers suggested the decimal mode; and I will try to prove that, to number things, and to distinguish good actions from others, bad, require an identical mode of thinking. Numbers, when applied to things, as, I tree, 2 trees, are termed concrete; but when unapplied, as, 1, 2, 3, they are termed abstract. Logicians admit that numbers were and are acquired first in the concrete, before the abstract. Therefore, since numbers in the concrete stand first for analysis, and thus denote an adjunct meaning by which grammarians designate them adjectives, it follows that we should clearly ascertain whether we have one or several modes of comparison; for under some modes of comparison our method of numbering must be constructed.

We will name those three lines successively, A, B, C, and consider each as possessing a property of extension. If we confine our attention to that property, we see that B is longer than A, and C is the longest of the three. If we reverse our comparisons, and consider C as short, we see that B is shorter than C, and A is the shortest of the three. A, B, C, thus denote the three degrees of comparison, (as they are named by grammarians, though they should say three degrees of relation;) and I must prove that those degrees are confined to three, and thus result from a law of mind which governs, accordingly, our mode of numbering.

It is evident, that all lines which differ from B in length, must be longer or shorter; hence, three degrees exhaust our consecutive comparisons, for B remains unchanged, whether we assume it to be long or short. This mode of comparison, which requires two reversed degrees of relation correlative to a condition assumed, includes the meaning of all such words as

true, false, right, wrong, just, and unjust. For example: the following pro positions require an identical mode of comparison:

All lines which differ from B in length must be longer or shorter.
Every assertion must be true or false.

In the first, we assume that the condition of B must be both long and short, according as we reverse our comparisons; and in the second, we assume that every assertion must agree or disagree with its application.— Grammarians say that such words as true, and infinite," are always, literally, in the superlative degree; because, by expressing a quality in the highest degree, they carry in themselves a superlative signification." This may appear plausible, yet it is very unsound, and the sophistry lurks in the meaning of two words-" highest degree.' The author saw that in using such words, we cannot say of a proposition, it is most true-hence he inferred that all such adjectives are always in the superlative degree. Whereas, our inability to advance to a degree of relation which increases from that which is already true, arises from this fact-that we cannot rationally apply such words as true, perfect, and infinite, unless restricted to that mode of comparison which requires two reversed degrees correlative to a first condition assumed. That such words as infinite are always in the comparative degree, and never in the superlative, may require a further illustration.

When we say long, longer, longest, our first degree, named the positive, is assumed; then the comparative and superlative consecutively follow.But long and short denote degrees which are first apprehended by perceiving two reversed things correlative to a first condition assumed. Therefore, the fundamental mode of comparison-that mode which is the basis of all others consists in two reversed degrees correlative to a first, and which first is analogous to that degree which grammarians name the positive.

In the aforesaid example, B can be affirmed the longer only on this condition-that A was admitted to be long before B was compared with A; then C is compared with B and A. Now, this principle should be clearly understood that, in any number of consecutive comparisons, we first require two things, one of which is assumed, (i. e., not compared,) and by which we determine the other's degree of relation. Then, if we annex another degree, we introduce a new element into our comparisons, which may be termed the correlative. When two things are compared, one is relative to the other; but when three things are compared consecutively, each is correlative with the others. This distinction between relative and correlative, as applied to numeration, has been totally disregarded by all authors whose works I have read, except Bishop Berkeley, and William Hazlitt, in his Essay on Locke, and from which I will quote in due time.

In the above example we are required to see B relative to A, then C correlative with B and A, before we advance to D; we then find that A, B, C are each perceived twice, and only twice-whence each becomes correlative, (i. e. reciprocally relative.) Now, if we annex D, it is clear that A, B, C, D must each be seen three times to become correlative throughout. And if we annex E, then each must be seen four times to become correlative as aforesaid, and so we may continue annexing. But we first proved that a thing is only seen twice to become correlative; therefore, when a thing is seen three or more times, and still conceived to be only correlative, it is seen absurdly and in contradiction to a law of mind which universally go

verns our comparisons, by confining them to three degrees of relations.Thus much appeared necessary to elucidate the principles of the three modes of comparison, and to prove that all agree in having only three degrees of relation. Under that law, the mathematician's "celebrated problem of the three bodies" must be arranged, and a theologian's trinity-for the ancient Egyptians had their trinity, and innumerable other triple parts of knowledge, including all the axioms of geometry.

Hazlitt very truly says:

"It is strange that Mr. Locke should rank among simple ideas that of number, which he defines to be the idea of unity repeated. But how this idea of successive or distinct units can ever give the idea of repetition, unless the former instances are borne in mind, I cannot conceive. There might be a transition from one unit to another, but no addition or aggregate formed. As well might we suppose that a body of an inch diameter, by shifting from place to place, might enlarge its dimensions to a foot or a mile, as that a succession of units, perceived separately, should produce the complex idea of number. The natural fool that Mr. Hobbes speaks of may be supposed to observe every stroke of the clock, and nod to it, or say one, one, one; but he could never know what hour it strikes, according to Mr. Hobbes, without the use of those names of order, one, two, three, &c., nor, according to my notion, without the help of that orderly understanding which first invented those names, and comprehends their meaning. On the material hypothesis, the mind can have but one idea at a time, and the idea of number could never enter into it."

Hazlitt might have added, that all mathematicians, without an exception, have written as erroneously about numeration as Mr. Locke himself.

Before we dispute about an effect we should first know what it is. What do 1, 2, 3 represent, when applied to 1 tree, 2 trees, 3 trees? They denote the place-properties of trees when perceived correlative, according to a mode of comparison wherein we consecutively advance from a place assumed.— And since all things possess a place-property, numbers can be applied to all. A single method of producing an effect must precede a compound method of producing like effects, because the last is composed of the first. Our mode of numbering is a compound; therefore every language includes a prior method to numbering, whereby things are seen correlative by means of their place-properties. In the English language, the following words comprise that prior mode :

This man and first man are different phrases only so far as this and first belong to two methods of performing acts alike. This, that and yon comprise a mode of themselves, therefore it has an end; first, second and third belong to a method without end, nevertheless both methods have a like beginning; and the one which has an end, so far as it extends, agrees with the other which is endless. The mere practice of that simple mode, being included under a law of mind which governs all men's comparisons of all things, would direct nations to construct modes of numbering, necessarily identical in their fundamental principles. They could differ only in the symbols or characters used in notation, and in their extent of combination.

It is not requisite that I should present the various kinds of symbols which mankind have used in notation. I have proved that when things are seen correlative, three are seen in relation to each other; then, if we annex another three, we introduce a new element into our comparisons, which may be termed the element of combination. Consequently, every mode of numbering presupposes that a given collection of things must be seen cor

relatively, and thus consecutively combined into a whole, or aggregate.— Our mode of combining must accord with our prior mode of seeing things correlatively placed, because combination includes correlation. Accordingly, the number nine among all nations denotes the first combination of things when seen correlatively placed; one three relative to another, and both correlative to a third three. Hence all nations actually stop or inclose their numbers at 9; and they do so inevitably, in accordance with a law of mind which universally governs their comparisons. Ten (10) literally means one inclosure, and town, tun, and ten are all derived from one root. Town formerly signified a collection of houses surrounded by a wall. (See Horne Tooke's Diversions of Purley.)

1, 2, 3, 4, 5, 6, 7, 8, 9.

The above figures denote our numbering to the extent of nine. The first is named the unit by arithmeticians, but unit is a very vague term-being often confounded with unity, and oneness, and other relations. Still it conveys an important meaning when we arrive at it naturally in its proper place. All the above figures are first acquired by reading them from the left to the right, and the scale is constructed by simply seeing things cor relative, and thus consecutively combining them so that each figure in succession shall denote its own degree of relation and all previously ascertained. Observe, that each successive figure from the beginning represents not merely its own, but also several other degrees of relation; and how could man's fingers have suggested the mode of combining those degrees? All arithmeticians answer, because man has ten fingers; but logicians might retort, that such an answer is merely begging the question. They may as truly say, that a man stops at ten because he had previously ten about him, and that previous ten was born in him or to him, like his legs, and not the result of any mode of comparison. But I have proved that ten must result from comparisons; therefore, to compare the conclusion of ten with the concluded number of man's fingers, we merely obtain the quality of two results or sums. Accordingly, all ignorant persons who use their fingers in relation to numbers are addicted to reckon with them-not merely to num ber.

The scale of numbers aforesaid clearly indicates that the man who first constructed it was a patient thinker. He was familiar with a state of mind and could thoroughly analyze it, and which is composed of several distinct perceptions appertaining almost simultaneously to one thing; yet we speak as though we have only one perception of such a complex thing. He had previously been familiar with seeing heaps or collections correlative to each other; his next step was to combine those collections as far as he could correlatively, without assuming a new beginning; and he thus naturally arrived at nine. To distinguish that 9 from his second 9, he quite as naturally reversed his former mode, and used two symbols to denote the first nine inclosed, thus 10, which means one combined collection. Having advanced thus far, all future progress was easy, for he had only to combine 9 again, and then say two tens, or 20, and so repeatedly to one hundred. Now, unit denotes a degree of relation not comprehensible till seen correlative with ten and hundred. Unit, ten, hundred, denote degrees of rela tion, not merely of single things, but of single combinations seen correlatively.

999.

Those represent nine hundred and ninety-nine; and 9 thus occupies the unit's place as naturally as it stands in the ten's and the hundred's place.