This agreement in the greater part of the results is the more striking, that the coefficients have been obtained from very unequal masses of plants. In France 3645, in Germany only 1844 phænogamous plants have been employed, in order to determine the particular proportions of the families. Since the two countries border on each other, the species should in like manner be much the same. The agreement of the results within limits thus marked (the greater part commonly within of difference), prove two facts equally remarkable: 1st, That the 1700 to 1800 species of phænogamous plants which the French catalogue has more than the excellent catalogue of M. Schrader employed for Germany, are distributed among the different families almost in the same proportions which we observe among the plants common to the two countries: 2d, That the species of Leguminosa, of Cruciferæ, and of Umbelliferæ, which Germany would appear to possess exclusively, are substituted in France by a nearly equal number of species belonging to the same families. In general, where the greatest discrepancies are observed, they may be attributed to the circumstance, that Germany is situate more to the north than France is. We know that the Cyperaces and the Ericeæ increase so rapidly towards the north pole, that, while in the temperate zone the Cyperacea are, and the Erices, in the frigid zone there is of Cy10 peraceæ, and of Erices. On the other hand, the proportions of the Orchideæ, of the Malvaceae, and of the Euphorbiaceae, increase with equal rapidity towards the south. On comparing the preceding table with the table of the three zones, (the torrid, the temperate, and frigid), we observe the same laws. I have added to this comparative table of the vegetation of France and Germany the arrows which, in the general table, indicate the directions of increase, from the pole to the equator, and from the equator to the pole. It is a very remarkable circumstance, also, that the coefficients of the families do not change so much, if, instead of examining extensive countries which have from 2600 to 3800 species of phænogamous plants, we confine our researches to an extent of some square leagues; for example, to the Flora of Berlin, which, according to the work of M. Kunth, comprehends only 900 species. In that small extent of land, the Leguminosæ are,

(in the whole of France, in the whole of Germany); the Glumaceæ, (in France, in Germany,) of the whole mass of phænogamous plants.

In the same way that the system of climates of the New Continent differs essentially from that of the Old, on account of the unequal distribution of the heat among the different parts of the year, so also the system of agroupment of American plants has its peculiar features. It is to the new researches of botanical arithmetic that we owe the knowledge of these contrasts between the temperate zones of the two worlds. I have thrown together in the following Table the results of the American Flora of Pursh and of the French Flora of M. Decandolle. I have added certain coefficients of the European frigid region, in order to show how much of a boreal character the American temperate region presents in the five families of Ericeæ (and Rhododendra), Coniferæ, Amentaceæ, Umbelliferæ, and Labiata.

160

The differences which are manifested in this table between the two continents, bear, not merely upon the five last families, which might be called boreal forms, but also upon the Cruciferæ, the Junces, and the Cyperaceae, which are equally rare in the torrid zone and in the temperate zone of the New Continent.

It is conceived that the inquiries regarding the numerical proportions of vegetable families, will present results much more interesting when the Floras of different countries shall be circumscribed within more precise geographical limits, and when botanists shall attend more particularly to the principles according to which varieties and species ought to be distinguished. The catalogues which we see under the vague name of Flora of the United States of America, comprehend countries placed in very different climates, from 18° to 9° of mean temperature. Here we have a difference of climate as great as in Europe be

tween Calabria and Austria. When the vegetation of South Carolina, of Pennsylvania, and of New England, shall be described individually, and with the same degree of exactness, we shall notice a regular increase and decrease in the numerical proportions of families from south to north. At present, we only know the general mean of these partial proportions. Many countries seem richer in plants, because the botanists have inconsiderately elevated varieties to the rank of species. In another country, the travellers often neglect the plants which they believe to be the same as those of their own country. But when we attend to the great divisións, and when the number of species which we compare is very considerable, our researches are favoured with happy compensations. It is thus that the new Floras, much more complete of America and Lapland, published by Messrs Pursh and Wahlenberg, have not sensibly altered the numerical proportions which we find on confining ourselves to the old Floras of Michaux and Linnæus, (Berl. Jarhb. der Pew. b. i. s. 24.). Whatever may be the corrections which shall be made in my work, I am persuaded beforehand, that the more that exact observations are accumulated, and the more we look beyond the same hemisphere, the same system of agroupment, the partial variations of the coefficients will be found not to be made by sudden starts, but according to invariable laws. It may be that the tropical proportion of the Malvaceæ is ' or 'z, instead of, but it is not the less certain, that the Leguminosa and the Malvaceae increase toward the equator, while the Juncea and the Erice increase toward the pole. One may recall in doubt the quantities of the variations, the rapidity of the increase, but not its direction.

On comparing the coefficients which belong to the same families, in different zones, we find, in the rapidity of the increase, contrasts strongly marked. In the Old Continent, the proportions of the Gramineæ, the Leguminosa, and the Euphorbiaceæ, change much less from the temperate zone to the equator, than from the temperate zone to the pole.

Those who are accustomed to consider each phenomenon in an absolute and irrelative point of view,-who regard the mean temperature of places, the laws which are observed in the variations of terrestrial magnetism, with the proportions between births

and deaths, as daring hypotheses, and as vague, theoretical speculations,-will probably look with contempt on the discussions which form the principal object of this memoir. Those, on the other hand, who delight to contemplate the mutual concatenation of organized beings,-who are aware that the numerical results correct themselves by the accumulation and the careful investigation of particular facts,-will cherish a kind of research, which throws light upon the economy of Nature,-on the connection which is observed between the climates and the form of beings,on the distribution of plants and of animals in the different regions of our planet. It is only by the numerical examination and the comparison of species, that we can form a correct idea of the state of the vegetation of a given country ;of the general influence which the temperature exercises over the frequency of certain forms, near the equator, in the mean parallel, and towards the polar circle;-of the characteristic features which distinguish, in isothermal zones, the two systems of agroupment of the Old and the New World *.

ART. VII.-Notice respecting Roman? Vessels found in Scotland on the Estates of Sir JoHN Hл, Bart.

THE two figures Plate II. Fig. 3. and 4. represent vessels

found on the estates of Sir John Hay, at Linton and at Eshiels in Tweeddale.

For the use of such as have not made descriptive botany their particular study, and who are yet desirous of acquiring a knowledge of the investigations which have been attempted in the different branches of the natural sciences, we shall add in this place the names of some of the most common plants which characterise, if we may so speak, the tribes or families which are frequently the subject of discussion in this memoir. (The translation of the following is modified so as to give an English reader an idea of the families). Juncea (Rushes); Cyperacea (Hard or Moor Grasses, Cotton-Grass); Graminea (Corn, Grasses); Composite (Dandelion, Thistles, Sunflower); Leguminosa or Papilionacea (Vetches, Pease, Clover); Ru biaceae (Rennet, Madder); Euphorbiaceae (Sun-spurge, Dogs' Mercury); Labiata (Mint, Thyme, Rosemary); Malvaceae (Mallows, Hollyhock); Umbellifera (Carrot, Hemlock, Chervil, Carraway); Crucifera (Mustard, Cresses, Radish, Turnip).

The great mass of plants which cover the globe is divided by botanists into Phænogamous (those having visible flowers), and Cryptogamous or Agamous (Ferns, Lichens, Mushrooms).

Both of these were imbedded in the peat; and the smallest, which resembles a modern coffee-pot, is from the last of these places. A leg had been broken from it, which was replaced with a new one by the person into whose possession it first came. It has been cast in one piece, and shews that the workmen were expert in the art of moulding. That it was intended for boiling some fluid which was to be used hot, is plain enough.

The other is a common cooking-pot, the very model of our own. It is a much ruder piece of casting than the last, but is extremely substantial and weighty, as indeed is the former. It is 10 inches high: the coffee-pot is 8.

Both of these vessels are made of the same composition of tin and copper as the celts, and other well known instruments of the Romans, commonly called Roman Bronze.

It is probable that they are Roman utensils, as these places also lie within the limits which this people occupied when in Scotland. The remains of a station have indeed been traced near to Linton.

EDINBURGH, April 1822.

ART. VIII-Some Account of those Manuscripts in Great Britain, which contain the Greek Text of the Mathematical Collections of Pappus. By S. P. RIGAUD, Esq. M.A. F.R.S. Savilian Professor of Geometry, and Professor of Experimental Philosophy in the University of Oxford, &c. &c. Communicated by the Author.

TH

HE Mathematical Collections originally consisted of eight books. Fabricius, indeed, in his Bibliotheca Græca, seems to think that the number might have been greater, but he speaks with hesitation," nam in præfat. ubi duodecimum librum allegare videtur (pag. 252.), incertum est propter luxata versionis verba, an alterius potius scriptoris (Euclidis fortasse) librum duodecimum elementorum intelligat." The passage referred to occurs in the end of the preface to the seventh book, and if Fabricius had looked to the Greek text, as given by Halley in in his edition of Apollonius de sectione rationis, he probably would have entertained no doubt. Some of the manuscripts