since they shew us a large portion of people looking seriously forwards to that awful event which must at some time happen to all, and endeavouring as far as they can to guard those who are now depending on them for support from the consequences of such a visitation. Many wives and helpless children, but for the facilities offered by these institutions, might and in all probability would, from holding a respectable rank in society, be plunged into the depth of wretchedness and want, by the premature death of an affectionate husband and tender parent. In no country in the world have such institutions acquired that high degree of respectability, which they have attained in this; no other government is calculated to inspire so much confidence for the deposit of money for such purposes; and to no people are these institutions so important as to the English; the middle class of society bearing a much larger proportion to the whole population in this empire, than in any other.

Such being the value and interest of assurance-companies, it is highly desirable that the principles on which they are founded should be well understood; and we are therefore always disposed to view in a favorable light any work that is intended to convey such information. We may not uniformly approve the arrangement or the execution, but we shall never fail to applaud the motive. In the work before us, for example, we find, much room for objection on the former of these heads, and particularly respecting the notation; which we consider as not only Gothic in its appearance, but extremely inconvenient in its application. Of all the alphabets known in the present day, we can recollect none, except the Hebrew and the Chinese, so improper for algebraical purposes as the old English, which seems to be a great favorite with Mr. Milne. We have also the common Roman letters under all the variety of forms that can possibly suggest themselves to the printers of lottery-hand-bills; in one place in plain black lines, and in others with open lines; and with dashes, indices, and parentheses, out of number. This peculiarity we cannot but consider as deducting seriously from the merits of the performance; which in other respects certainly contains much useful and important information.

The first volume is opened with an introduction, giving an historical view of most of the early attempts at establishing this branch of analytical calculation on correct mathematical principles but we were much surprized to find so little notice of recent authors; and particularly that the most scientific work which has yet appeared on this subject, Baily On the Doctrine of Life Annuities and Assurances, is not even mentioned.

mentioned. We regret this omission for two reasons; in the first place, because it leaves incomplete the information which the author seems desirous to convey; and, secondly, because we think that, had he examined that book with attention, it might have furnished him with some useful hints relative to the arrangement of his materials. The other chapters in this volume relate to compound interest and annuities certain; the probabilities and expectations of human life, death, and survivorships; the construction of tables of mortality; annuities on lives; assurances on lives; assurances on súrvivorships and on successive lives: then follow extensions of the preceding theories, valuation of policies of assurances, &c., an illustration of the preceding theories by numerical examples, and office-calculations.

Chapter i. of Vol. II. treats on the progress of popu lation; and here the author appears to have taken great pains to acquire information from various sources, independently of what is furnished by preceding writers. The chapter certainly contains a great portion of novel and original data: as much with reference to this particular branch of the statistics of England, Scotland, and Wales, as to the particular doctrine of life-annuities and assurances. The first subject discussed is one which has been assumed as a sort of axiom by a celebrated writer; viz. that the population of a country has a tendency to increase in a geometrical progression; with a comparison of the increase of births and deaths with the price of wheat in different years. As we consider this subject to be both curious and important, it may be useful to lay some of the author's facts and inferences before the reader, premising that they are drawn from authentic documents. The numbers of marriages, baptisms, and burials, are taken from the abstract of answers and returns to the population-act, passed in 1811; the number of conceptions in each year is assumed to be the same as the number of baptisms in the year following; and the prices of wheat are those which were given in the appendix to the Report of the Committee appointed to inquire into the high price of Bullion, printed by order of the House of Commons in 1810.

We cannot give the table formed from these documents, but the following observations drawn from it will not, we presume, be uninteresting:

It will be observed, that any material reduction in the price of wheat is almost always accompanied by an increase both of the marriages and conceptions, and by a decrease in the number of burials; consequently, by an increase in the excess of the births. above the deaths.

G 4

Also

Also, that any material rise in the price is generally attended by a corresponding decrease in the marriages and conceptions, and by an increase in the burials; therefore, by a decrease in the excess of the births above the deaths.

Thus it appears, that an increase in the quantity of food, or in the facility wherewith the labouring classes can obtain it, accelerates the progress of the population, both by augmenting the actual fecundity, and diminishing the rate of mortality; and that a scarcity of food retards the increase of the people, by producing in both ways opposite effects.

This table also shows, that an increase of food increases the actual fecundity, not only by promoting new marriages, but by rendering those already contracted more prolific. Thus,

Whereby it appears, that a fall of 10s. 3d. in the price of the quarter of wheat, was attended by an increase of 4,271 in the number of the annual marriages, while the annual conceptions were augmented by nearly twice that number. Again,

• Where the increase of the conceptions, accompanying the fall of wheat, was more than double that of the marriages.

But the mass of the population seems not to have recovered so quickly from the effects of the great dearth of 1800 and 1801; for although wheat was 50s. a quarter lower in 1802 than in 1801, and this fall was accompanied by an increase of 23,000 in the annual marriages, the conceptions only rose 21,000; and a further fall of 11s. in the price the year following, was attended by an augmentation of 4000 in the marriages, and only 400 in the conceptions; after this, however, these last resumed their usual

course.

By the actual fecundity, that part only of the absolute physical power of propagation is here to be understood, which the actual circumstances allow of being developed.'

• The

The relations between the decrements in the annual marriages and conceptions that accompany the rise of wheat, are generally similar to these; but, in the conceptions, not quite so regular; perhaps for this reason, that rising prices may deter from marriage, without the scarcity being so great, as to render those already married less prolific.'

After this long quotation, we must be concise in enumerating the remaining contents of this volume; the most important of which are, on the Carlisle Table of Mortality; the Reduction of Mortality by Vaccination; the Population and Mortality in England and Wales, and the Mortality in marshy Situations; on the comparative Mortality occasioned by different Diseases, by different Seasons, and in the two Sexes; on the Law of Mortality in Sweden and Finland; at Montpellier, and in the whole kingdom of France; &c. &c. These are followed by a variety of tables necessary for the computation of the several cases that may present themselves, with notes and illustrations; and an appendix, containing the investigation of particular formulæ, closes the volume.

Having thus endeavoured to give a sketch of the subjects contained in the work, we beg to make a few remarks relative to some essential matters that appear to be omitted.

Besides the business carried on by the different assurancecompanies, we have in this country a number of local societies for the benefit of old age and widows, the members of which undertake to manage their own concerns, and therefore stand much in need of correct information. Dr. Price did not deem those associations undeserving of his serious attention: we find also a chapter devoted to this subject in Baily's work above mentioned; and we conceive that they ought to form a part of every treatise on the doctrine of assurances; since without repeated warnings from men of science, who are alone capable of judging of the correctness of the principles on which such societies are founded, they are liable to form schemes of relief wholly inconsistent with their capabilities, and which therefore in a few years terminate in their dissolution, leaving many deserving claimants in penury and distress. Some instances are specified in the second volume of the author last mentioned. We have also at this moment before us the laws and regulations of a society of this kind, formed in one of the most respectable counties in England, and consisting of more than 800 persons; designed for the relief of the widows of deceased members, or of their orphans, till they attain each the age of 16 years. The payment of the members is made quarterly, and amounts, according to the ages at which they entered, to il., il. 10s., or 21. annually: the original pension to the widows was rol. per

ann.

ann, and the same to the children, if no widow survived, till the youngest child arrived at the age of 16 years. Unfortunately, one of the articles provides that, when the stock of the society shall amount to a certain sum, the pensions are to be raised to 151.; and when to another certain sum, to 20l.; and again to 251., and so on; and this latter sum is now actually received: but nothing can be a worse criterion than the amount of stock, without reference to the number of members; and there can be no doubt that the society to which we allude, notwithstanding its present apparent prosperous state, is paying more than its means will allow when, after a few years, its original members shall begin to fall off. We are always sorry to see such laudable intentions, as evidently dictated the formation of this and similar societies, defeated by an ignorance of the principles which should govern them; and we cannot but consider it as the duty of every author, writing on subjects like those that are contained in the present treatise, to turn his attention to these minor societies: holding out a hand to guide them, in their deficiency of scientific knowlege, towards the attainment of their truly commendable wishes,the establishment of a fund for the permanent relief of their widows and orphans.

ART. XIII. Anacreontis Teii Carmina Latinè reddidit Gul. Jac. Aislabie, A. M. Subjiciuntur Anacreontis Epigrammata et Theocriti Anacreonticum in mortuum Adonin. 12mo. pp. 47. sewed. Ridgways.

MR. AISLABIE has added his university-degree to his name,

which is a sufficient intimation that this version of Anacreon is not to be considered as a lusus juvenilis, but the work of a more matured scholar. Indeed, we suspect that, unless he could have comforted himself with the thought, "Et nos ergo manum ferulá subduximus," he would scarcely have shewn up an exercise bearing so many marks of haste and carelessness. Several of Anacreon's odes have been at different times rendered into elegiac verse, and we recollect to have seen detached pieces in print, although we cannot immediately say where: but a complete version was certainly not an inelegant occupation for the vacant hours of a gentleman and a scholar. Mr. A. dedicates his little volume to the Earl Grey, assuring that nobleman that he is in affability, elegance, and love of literary pursuits, what Anacreon is in poetry; and the author proceeds to enforce the value of this compliment, by stating that he expects nothing in return for it: he himself being, he adds, not like Anacreon, but like