things, inaccessible places and immense trines and spaces.

A. What now is the liberty you mean? B. That any man may worship God otherwise than as the aforementioned national Church appoints, and may profess opinions in spiritual matters other than those determined by the said Church, provided that such seeker of liberty do solemnly protest before God that he verily believes his particular opinions to be true, and that the same, with the manner of worship he desireth, is necessary for the peace and welfare of his soul, and that in all other matters he will submit to the laws of his sovereign.

A. What do you mean by liberty? for you said there was no liberty in believing.

B. I mean impunity-that is, no man shall be punished, in life, limb, liberty or estate, for dissenting from the national Church, leaving him to God to be punished for what is sinful therein, reserving still to the sovereign a right of punishing, or suppressing even, the same opinions, if inconsistent with the public peace and welfare of the people, of which the sovereign is to be judge.

A. How may this liberty be perpetuated under all forms and successions of government and changes of Parliament, and what oaths to be taken now or hereafter?

B. It seems to me it can only be perpetuated by the vox populi, or the voice of all the people who have souls to save, who are able to bear arms and are of years of discretion-suppose twenty-one years old. For in these doth visibly, naturally and perpetually lie the infallible or irresistible power concerning these matters of the soul.

A. Can all these people be represented practically and conveniently?

B. Yes; with less trouble, confusion and expense than a knight of the shire is chosen in any county of England.

A. But would not an assembly interfere with the present constitutions of Parliament?

B. No. It seems to me to be a bare council of quite another nature, without any legislative power at all, only to quiet the people concerning invisible and purely spiritual matters.

A. Is there no other way to regulate and perpetuate the liberty of conscience which you have described?

B. I cannot think of any at present, but will consider it further.

SIR WILLIAM PETTY.

A SERENADE.

OOK out upon the stars, my love,

And shame them with thine eyes, On which than on the lights above

There hang more destinies. Night's beauty is the harmony.

Of blending shades and light; Then, lady, up! Look out, and be A sister to the night.

Sleep not! Thine image wakes for aye
Within my watching breast.
Sleep not! From her soft sleep should fly
Who robs all hearts of rest.

Nay, lady; from thy slumbers break,

And make this darkness gay With looks whose brightness well might make

Of darker nights a day.

EDWARD C. PINKNEY.

GEOMETRICAL RATIO OF IN

CREASE.

STRUGGLE for existence inevitably follows from the high rate at which all organic beings tend to increase. Every being which during its natural lifetime produces several eggs or seeds must suffer destruction during some period of its life, and during some season or occasional year, otherwise, on the principle of geometrical increase, its numbers would quickly become so inordinately great that no country could support the product. Hence, as more individuals are produced than can possibly survive, there must in every case be a struggle for existence -either one individual with another of the same species, or with the individuals of distinct species, or with the physical conditions of life. It is the doctrine of Malthus applied with manifold force to the whole animal and vegetable kingdoms, for in this case there can be no artificial increase of food and no prudential restraint from marriage. Although some species may be now increasing more or less rapidly in numbers, all cannot do so, for the world would not hold them.

There is no exception to the rule that every organic being naturally increases at so high a rate that if not destroyed the earth would soon be covered by the progeny of a single pair. Even slow-breeding man has doubled

in twenty-five years, and at this rate in less than a thousand years there would literally not be standing-room for his progeny. Linnæus has calculated that if an annual plant produced only two seeds-and there is no plant so unproductive as this-and their seedlings next year produced two, and so on, then in twenty years there would be a million plants. The elephant is reckoned the slowest breeder of all known animals, and I have taken some pains to estimate its probable minimum rate of natural increase. It will be safest to assume that it begins breeding when thirty years old and goes on breeding till ninety years old, bringing forth six young in the interval, and surviving till one hundred years old; if this be so, after a period of from seven hundred and forty to seven hundred and fifty years there would be nearly nineteen million elephants alive, descended from the first pair.

But we have better evidence on this subject than mere theoretical calculationsnamely, the numerous recorded cases of the astonishingly rapid increase of various animals in a state of nature, when circumstances have been favorable to them during two or three following seasons. Still more striking is the evidence from our domestic animals of many kinds which have run wild in several parts of the world; if the statements of the rate of increase of slow-breeding cattle and horses in South America, and latterly in Australia, had not been well authenticated, they would have been incredible. So it is with

plants; cases could be given of introduced plants which have become common throughout whole islands in a period of less than ten years. Several of the plants, such as the cardoon and a tall thistle, which are now the commonest over the wide plains of La Plata, clothing square leagues of surface almost to the exclusion of every other plant, have been introduced from Europe, and there are plants which now range in India, as I hear from Dr. Falconer, from Cape Comorin to the Himalaya, which have been imported from America since its discovery. In such cases-and endless others could be given-no one supposes that the fertility of the animals or plants has been suddenly and temporarily increased in any sensible degree. The obvious explanation is that the conditions of life have been highly favorable, and that there has consequently been less destruction of the old and young, and that nearly all the young have been enabled to breed. Their geometrical ratio of increase, the result of which never fails to be surprising, simply explains their extraordinarily rapid increase and wide diffusion in their new homes.

In a state of nature almost every full-grown plant annually produces seed, and amongst animals there are very few which do not annually pair; hence we may confidently assert that all plants and animals are tending to increase at a geometrical ratio, that all would rapidly stock every station in which they could anyhow exist, and that this geometrical tendency to increase must be checked by destruction at some period of life. Our familiarity with the larger domestic animals tends, I think, to mislead us: we see no great destruction falling on them, but we do not keep in mind that thousands are annually slaughtered for

food, and that in a state of nature an equal number would have somehow to be disposed of. The only difference between organisms which annually produce eggs or seeds by the thousand and those which produce extremely few is that the slow-breeders would require a few more years to people, under favorable conditions, a whole district, let it be ever so large. The condor lays a couple of eggs and the ostrich a score, and yet in the same country the condor may be the more numerous of the two; the Fulmar petrel lays but one egg, yet it is believed to be the most numerous bird in the world. One fly deposits hundreds of eggs, and another, like the hippobosca, a single one, but this difference does not determine how many individuals of the two species can be supported in a district. A large number of eggs is of some importance to those species which depend species which depend on a fluctuating amount of food, for it allows them rapidly to increase in number. But the real importance of a large number of eggs or seeds is to make up for much destruction at some period of life, and this period in the great majority of cases is an early one. If an animal can in any way protect its own eggs or young, a small number may be produced and yet the average stock be fully kept up; but if many eggs or young are destroyed, many must be produced, or the species will become extinct. It would suffice to keep up the full number of a tree which lived on an average for a thousand years if a single seed were produced once in a thousand years, supposing that this seed were never destroyed and could be ensured to germinate in a fitting place. So that, in all cases, the average number of any animal or plant depends only indirectly on the number of its eggs or seeds.

In looking at Nature it is most necessary to keep the foregoing considerations always in mind--never to forget that every single organic being may be said to be striving to the utmost to increase in numbers, that each lives by a struggle at some period of its life, that heavy destruction inevitably falls either on the young or old during each generation or at recurrent intervals. Lighten any check, mitigate the destruction ever so little, and the number of the species will almost instantaneously increase to any amount.

NATURE OF THE CHECKS TO INCREASE.

The causes which check the natural tendency of each species to increase are most obscure. Look at the most vigorous species; by as much as it swarms in numbers, by so much will it tend to increase still further. We know not exactly what the checks are even in a single instance. Nor will this sur prise any one who reflects how ignorant we are on this head even in regard to mankind, although so incomparably better known than any other animal. Eggs or very young animals seem generally to suffer most, but this is not invariably the case. With plants there is a vast destruction of seeds, but from some observations which I have made it appears that the seedlings suffer most from germinating in ground already thickly stocked with other plants. Seedlings, also, are destroyed in vast numbers by various enemies. instance, on a piece of ground three feet long and two wide, dug and cleared, and where there could be no choking from other plants, I marked all the seedlings of our native weeds as they came up, and out of three hundred and fifty-seven no less than two hundred and ninety-five were destroyed, chiefly by slugs

For

and insects. If turf which has long been mown-and the case would be the same with turf closely browsed by quadrupeds-be let to grow, the more vigorous plants gradually kill the less vigorous, though fully-grown plants: thus, out of twenty species grown on a little plot of mown turf (three feet by four) nine species perished from the other species being allowed to grow up freely.

The amount of food for each species of course gives the extreme limit to which each can increase, but very frequently it is not the obtaining food, but the serving as prey to other animals, which determines the average numbers of a species; thus there seems to be little doubt that the stock of partridges, grouse and hares on any large estate depends chiefly on the destruction of vermin. If not one head of game were shot during the next twenty years in England, and, at the same time, if no vermin were destroyed, there would, in all probability, be less game than at present, although hundreds of thousands of game-animals are now annually shot. On the other hand, in some cases, as with the elephant, none are destroyed by beasts of prey; for even the tiger in India most rarely dares to attack a young elephant protected by its dam.

Climate plays an important part in determining the average numbers of a species, and periodical seasons of extreme cold or drought seem to be the most effective of all checks. I estimated (chiefly from the greatly-reduced numbers of nests in the spring) that the winter of 1854-5 destroyed four-fifths of the birds in my own grounds; and this is a tremendous destruction, when we remember that ten per cent. is an extraordinarily severe mortality from epidemics with man. The

action of climate seems at first sight to be quite independent of the struggle for existence, but, in so far as climate chiefly acts in reducing food, it brings on the most severe struggle between the individuals, whether of the same or of distinct species, which subsist on the same kind of food. Even when climate for instance, extreme cold-acts directly, it will be the least vigorous individuals or those which have got least food through the advancing winter which will suffer most. When we travel from south to north or from a damp region to a dry, we invariably see some species gradually getting rarer and rarer, and finally disappearing, and, the change of climate being conspicuous, we are tempted to attribute the whole effect to its direct action. But this is a false view: we forget that each species, even where it most abounds, is constantly suffering enormous destruction at some period of its life from enemies or from competitors for the same place and food; and if these enemies or competitors be in the least degree favored by any slight change of climate, they will increase in numbers, and, as each area is already fully stocked with inhabitants, the other species must decrease. When we travel southward and see a species decreasing in numbers, we may feel sure that the cause lies quite as much in other species being favored as in this one being hurt. So it is when we travel northward, but in a somewhat lesser degree, for the number of species of all kinds, and therefore of competitors, decreases northward; hence, in going northward or in ascending a mountain, we far oftener meet with stunted forms, due to the directly injurious action of climate, than we do in proceeding southward or in descending a mountain. When we reach the Arctic regions

or snow-capped summits or absolute deserts, the struggle for life is almost exclusively with the elements.

That climate acts in main part indirectly by favoring other species we clearly see in the prodigious number of plants which in our gardens can perfectly well endure our climate, but which never become naturalized, for they cannot compete with our native plants nor resist destruction by our native animals.

When a species, owing to highly favorable circumstances, increases inordinately in numbers in a small tract, epidemics-at least, this seems generally to occur with our gameanimals-often ensue; and here we have a limiting check independent of the struggle for life. But even some of these so-called epidemies appear to be due to parasitic worms. which have from some cause-possibly, in part, through facility of diffusion amongst the crowded animals-been disproportionally favored; and here comes in a sort of struggle between the parasite and its prey.

On the other hand, in many cases a large stock of individuals of the same species, relatively to the numbers of its enemies, is absolutely necessary for its preservation. Thus we can easily raise plenty of corn and rapeseed, etc., in our fields, because the seeds are in great excess compared with the number of birds which feed on them; nor can the birds, though having a superabundance of food at this one season, increase in number proportionally to the supply of seed, as their numbers are checked during winter; but any one who has tried knows how troublesome it is to get seed from a few wheat or other such plants

garden: I have in this case lost every single seed. This view of the necessity of a large stock of the same species for its preser