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line of a polygon meet; and the junctives being intended to denote the fixed numeral positions of all regular polygons that is, a junctive denotes the numeral position in which like phenomena occur from like numerical calculations, applied to any kind of regular polygons. And perhaps this section is not the least useful, in the preparation for eliciting the ratio of the diameter to the circumference of a circle.

The sixth section treats of numbers, or rather, of numerical quantities and positions, as applicable to the admeasurement of all geometric quantities, and of the ratios and proportions of numerical quantities, and is rather a preliminary to the seventh section, which is composed of a logarithmic or geometric table, with the principal adjuncts and junctives annexed, with a short explanation. This is by no means formidable.

The eighth and last section may, perhaps, be esteemed rather more formidable, it being intended to develope or disclose, by means of known and assumed ratios, existing between important lines of the circle and similar lines of its inscribed and circumscribed squares, the true ratio between the diameter and circumference of the circle, which are to result in definite numerical expressions, when involved or evolved to their requisite roots and powers.

Whether the results which are supposed to lead to the final result, according to this method, be true or false, we all the way proceed from certain fixed landmarks, to some certain goal, with our eyes open; each result apparently arising from, or having place in, the relations of the mind, -in the laws of human thought; still being simple and easy of access.

Perhaps I cannot, at this time, better comment on the present section, than by referring to the formula, which I stole from the original, (a little marred in form, as I afterwards discovered,) and furnished for a former number of the Tracts and Lyceum.

It may be supposed, that this method, should it ever be understood, would not essentially differ from an approximating method, and perhaps, from those already extant;

but I believe, whether it elicits the truth or not, it has nothing to do with those methods, nor has it any similarity to them whatever. In this, there is no numerical quantity lost or gained, any more than would be the case in the expression of surd roots by algebraic symbols, until we arrive at the final goal. And perhaps a similitude drawn from Hill's old arithmetic, in the annunciation of a theorem, together with the result, and his comment thereon, may not be wholly inappropriate in the present instance, viz :

In any geometrical progression whatsoever, decreasing and continued ad infinitum, it holds-as the common difference, minus unity is to unity: so is the first or greatest term to the sum of all the following terms, in infinitum; and hence the least term vanisheth.' And now

for his comment. This may appear strange to many, how it should be possible to give the sum of an infinite progression in numbers; whereas, if the work were actually begun, and the terms continued, it would, after a thousand years' labor, and after thousands of millions of terms, never be nearer finishing. And yet that the sum of this infinite progression should be so easily found, it appeared to me, at first, as a notion (if I may so speak) almost divine,' &c.

But, in justice to the author of the subject-matter hinted. at in this article, it is here proper to state, that he does not assume or claim any supernatural power or agency. He claims not to have done more than any other individual might have done, whether it be what they would have done or not; and, as in the old legal trial by battel, he avers that he has not upon him neither bone, stone, ne grass; nor any enchantment, sorcery, or witchcraft, whereby,' &c.

To conclude, it is not my province to say, whether the author's theory (if such it may be called) is true or false : if it be true, then indeed may fancy and imagination intrude themselves into the field of mathematics; nor will they be easily expelled.

March 29, 1834.

A. Y.

THE Latin names of plants, used by botanists, are founded on the principles of genera and species, explained in the last number. English names are frequently made to correspond with these distinctions, but the Latin names always agree with them. A name is given to each genus, and the species belonging to each genus are denoted by adjectives, expressing, in Latin, some quality of the plant, as elegans, handsome; purpurea, purple, &c. Thus Rosa alba means white rose; another species of rose is called Rosa Gallica, or French rose. The Latin words 'alba' and 'Gallica' (white and French) come after Rosa (rose) instead of before, as in English. In the same way they say in French, table ronde, (table round) instead of round table, as we do. As I may have frequent occasion to use the botanical names, I thought it proper to explain them in the simplest manner possible, and I shall endeavor to give with them the correct English signification. And here I cannot help expressing a hope that we may soon see a beautiful structure of botanic nomenclature built up in our own language, accessible to every one.

The plants of our country, though much neglected, are, undoubtedly, if we knew how to estimate them, an invaluable treasure. Without entering into the enthusiastic notions of itinerants and quacks, who, without difficulty, can make earth produce remedies for every disease, I doubt not that the service which the medicinal virtues of some plants might render would be immense. The Indians were acquainted with the virtues of many plants, and used them successfully in the cure of the few maladies to which they were subject. They, too, knew how to stay the venom of the rattlesnake. But they are gone; and with them have perished, in a great measure, their knowledge and their acquirements.

Among other things, the confusion of names, of which I have spoken, forms a serious obstacle to the communication and obtaining of information concerning our plants. Those who profess to be acquainted with them are frequently ignorant persons, who, if they really know any valuable remedies or other useful properties of plants, cannot be relied upon in the descriptions or names they give. The medical profession usually find it cheaper to buy their roots ready dug, ground and labelled, than to seek and prepare them themselves. That the properties of our plants have not at all been investigated, I do not say; but I do say, that they have not received that attention they deserve. Not only their medical properties, but their uses in numerous branches of the arts, sciences and domestic economy, remain an almost unexplored field; and we may, in course of time, find ourselves in possession of treasures we little think of. And I should be happy were I to be successful in the endeavor to point out some of the openings upon this field. The worth of a science is, invariably, especially by those who form the great mass of society, measured by its actual utility in the service of the wants and conveniences of mankind. On this point our science has much to gain, and needs to be studied more particularly in reference to this.

CULTIVATION OF EXOTICS.

The important object of horticulture is, to assemble together, for the inhabitants of one climate and one country, the valuable productions of many countries. It is but justice to remark that our horticulturists are deficient in attention to what ought to be the great object in view in this department. Plants merely showy and ornamental are allowed to absorb the attention, and take the place of others, whose introduction might, on account of some important properties, prove a lasting benefit to the country, and insure to the introducer the gratitude and thanks of posterity. St. Pierre, the French naturalist, proposed to erect monuments to those who had thus contributed to the vegetable wealth of his own country. A beautiful idea this;-but to whom could we erect such monuments?

We know not yet to what extent the process of naturalizing plants may be carried; but there is no doubt, that by a systematic course of practice, much more advantage might be taken of it than is actually done. Enough has already been effected to induce us to believe that much more is possible. Nature does, by degrees, adapt herself to soil and climate; and, though the view may be regarded as visionary, it is certainly not contrary to analogy, to presume that future ages may see the rugged soil of New-England flourishing with the rich and costly productions of the torrid zone. But, independently of such views, I would urge the horticulturist, the florist, and the naturalist, to consider the subject, and to aim, in the prosecution of their business, to advance, in this way, the happiness of mankind, and especially, the prosperity and national advantages of our country.

TIMBER TREES AND FUEL.

Our country is rich in useful forest trees. Besides representatives of all the species of Europe, we have numerous others, utterly unknown in that quarter of the globe. The timber-trees of France and England are but about thirty-seven species, whilst we possess more than a hundred.

The rapid consumption, and, we fear, in some instances, improvident waste of wood-fuel, affords some cause of alarm, lest, ere many years shall have passed away, we shall be deprived of the valuable services our forests are now rendering us; that, unless special measures be taken to preserve the growth of wood, we shall be able neither to build proud ships upon our waters nor to frame dwellings on the land, nor to enjoy our pleasant wood fires. We may, and soon must, build with stone and burn coal, both in country and city.

But, for the beauty of our lands and of our landscapes, spare the trees. For the health, comfort and advantages of agriculture they may preserve to posterity, spare them. They are guardians of our soil. How much the preservation of a healthy climate, and especially of a sufficient degree of moisture in our atmosphere and earth may depend upon them, cannot be said; nor how far local cir