It is more easy to blame any notation on this subject, than to point out one in which all would be disposed to unite: the following are those which have been proposed for this case by other writers on the subject:

I MNk

In respect to the duplication of indices, Mr. Jones has a decided majority against him. But with regard to such a set of tables as the present, the preliminary treatise becomes comparatively unimportant. They are so cheap, that we have no doubt one or more treatises will be written, which will dispense with tables, and refer to those of Mr. Jones. It has hitherto been a drawback to the exertions of elementary writers in this respect, that, owing to the scarceness or dearness of former works, it has not been advisable to write treatises on the subject without a copious appendix of tables. Besides this, the time has hardly been till now, when there was anything like so general an agreement as to the table which should be used, as now exists with respect to the Carlisle. We should very well like to see Mr. Jones arrive at the honour of being the table-referee of two or three writers, treating the subject in different modes, according to their views of the way in which it can be best elucidated or systematized. A person may now write on logarithms, without the necessity of publishing a table; and such will be, for some time to come, the case with life annuities: for until the materials of the Registrar General and the Actuary of the National Debt Office come to the public view with some specific results, particularly on the difference between male and female life, we see little chance of the Carlisle Table being disturbed; and possibly no such thing may take place even then.

The accuracy of the tables is the next point for consideration. We have been informed that there is an error affecting the annuities at 34 per cent., arising from a singular cause, one of the sort against the effects of which it is almost impossible to guard in computation: this is to be removed

*

* One would suppose, for example, that when two able computers, in different parts of the country, are employed upon the same question, and produce the same result at the end of a long calculation, their two works agreeing figure for figure throughout, their result might be depended upon. Yet it has been known that two such persons have made precisely the same mistake, in merely taking out the same logarithm, there being no more reason why they should

by cancelling the requisite number of pages, if our information be correct. Much depends, as to the reception they will get, upon the explanations to be given in the preface. We can only say hitherto, that as far as our means go of comparing them with preceding tables, or with private manuscripts, we have found them accurate. For the rest, they must of course gradually establish their own character; and this we think they will do. From our private information, we should say that every proper step has been taken to insure accuracy. Besides, we count somewhat upon the general character of such tables, which is very good. Of all the tables printed by actuaries, it has very rarely happened that frequency of error, in computation or printing, has occurred.

We shall now describe the contents of the tables, as far as the Carlisle Table is their basis; and from this the great bulk of Mr. Jones' tables are calculated. We put in italics the tables which, to the best of our knowledge, are new in print, or the novel circumstances in which they differ from preceding ones.-Numbers living, &c. with logarithm and complement of the number which complete each age; and mean duration.-Barrett's tables for single lives (D, N, S, M, and R) for 3, 3, 4, 4, 5, and 6 per cent.; with D, N, and S, for 7, 8, 9, and 10 per cent.-Annuities on single lives at 3, 4, 5, 6, 7, 8 per cent.; also at 31, 41, 9, and 10 per cent.: the 3, 4, and 4 carried to five decimals.-Annuities on two lives, to every pair of ages, at 3, 4, 5, and 6 per cent.; also at 3 and 4 per cent.-Chance of living a year, with its logarithm.-Present value of assurance on a single life at 3, 3, 4, 44, 5, 6, 7, 8 per cent.-Probability of survivorship, as in Milne.-Barrett's table (D and N) for two joint lives, and every pair of ages, at 3, 3, 4, 4, 5, and 6 per cent.

Mr. Jones has also given brief tables on two joint lives from the Chester Table, being the first time, as far as we remember, that male life has been distinguished from female

agree in that mistake, than in any other that could be imagined. A hundred millions to one against such a thing occurring at any given trial, would be unfairly small odds; and yet it is known to have happened. It happened to ourselves, a few weeks ago, to be trying to ascertain from what formula a certain table was constructed. From the heading we made it out, as we thought; and on applying it to an instance in the table, we found 23:59, the number in the table being 23-597. Nevertheless, it turned out that we had totally mistaken the nature of the table, and that we had no more right to expect an agreement in any one figure, than if we had picked a formula at hazard out of any book on algebra. Every person who computes will occasionally find what he will be inclined to look at as an unprecedented coincidence.

in such tables. We do not think it necessary to detail what has been done on the Northampton Table, &c.; and we conclude our account with expressing our firm opinion that Mr. Jones is entitled to the gratitude of all who have to solve questions in such subjects, and has established his own reputation on a solid basis.

As far as we have yet spoken of the work, we have considered the actuary only; but we are now to ask what remains to be done? Considering the importance of extending this branch of knowledge, inasmuch as it will be to every man more or less connected with the mode of employing what he can save from his earnings, we see before us a reservoir from which much knowledge may be distributed. The new tables (Barrett's method) will enable an arithmetician of the most ordinary character to solve very complicated questions by simple operations, and ordinary problems still more easily. The extension of this knowledge, in the absence of all aid from government, is positively the only mode of saving the foolish from unprincipled or rash and ignorant combinations against their earnings. Until any man may hope to find among his friends some one or other who can give him an answer to a simple question, there will always be a class of persons who have in such matters nothing to trust to, except the professions of a prospectus. Nay, if only one man out of twenty among the educated classes had been able to use one or two of the more simple tables in this work, we think it would have been almost impossible for the West Middlesex swindlers to have succeeded to anything like the extent which they did. Those who will bear in mind that one man tolerably versed in these matters, may be but another name for several widows and orphans saved from destitution, will see few better works, few more enlightened charities, than lending his help to spread the information: and if it happen that the Society for the Diffusion of Knowledge hereafter finds, that, in its former efforts for the improvement of friendly societies, and its present attempt to lay a basis of sound knowledge under the whole subject, it has contributed to save the unwary from ruin, and the ignorant from becoming a prey to fraud, it will feel this one success alone a sufficient set-off against the sneers of the fine, and the enmity of the bigots; if, indeed, it do not reckon as such, the having made the attempt, and had the intention, and carry the success to the balance.

ART. IV. Encyclopädie der Deutschen National-literatur, von O. L. B. Wolff. (Encyclopedia of German National Literature, by O. L. B. Wolff.) 4to. Leipsig: 1834-40.

THE

HE treaty of Westphalia, concluded in 1648, was a precious boon to Germany. After a contest of thirty years, which had spread desolation over the surface of that once-flourishing country, during which whole districts had been devastated, and the track of War,

"doomed to go in company with pain

And fear and bloodshed, miserable train !"

was marked out by the ruins of entire towns and villages, and by cities half-depopulated, it brought a breathing-time of repose and restoration, as necessary to the well-being of her people as it was precious and welcome. The air, which the brute clangour of the war-bugle had violated, was filled with songs of cheerfulness and gratulation; the field, rent by the hoof of the charger and the artillery-wheel, now bore but the trace of the productive plough; and to the rapid and destructive evolutions of a licentious soldiery, Pappenheimers and Pandours, Frank and Swede, "blue, white, and red, with all their trumpery," now succeeded the movements of the thoughtful scholar, the enquiring traveller, the toiling husbandman, and all the tranquil and humanizing interchanges of commercial and social activity.

All the curses of war, however, (that sacrifice of abomination that man offers to the evil one), cease not with it; such, as the punishment of our wilfulness, is the law and constitution of the thing by the decree of heaven. The foot of the stranger no longer oppressed the soil of Germany,-" peace was within her walls, and plenteousness was in her palaces," but a subtle and wide-spreading infection had shown itself, that threatened to eat into the very core of the national heart. This arose from the extensive influence the French had acquired in the affairs of Germany at the close of the war. This ascendancy soon made itself felt in the manners and literature of the country, producing the most injurious effect on its moral and intellectual life, and fatal for some period to the free development of the vigorous mind, honest character, and national spirit of her people.

Among all classes but the peasantry, instigated by the nobility, a taste for everything French was diffused; customs,

dress, amusements, in the habits of domestic, and the proceedings of public, life. A writer* of the time thus reproaches his compatriots:-"There is no doubt, which many have remarked, that if our forefathers, the ancient Germans, could rise from their graves and revisit Germany, they would never believe that they were in their father-land among their own countrymen, but suppose themselves to be on foreign ground, amidst unknown and very different men; so great are the changes which have occurred-I will not say in a thousand, but in a few hundred, years. Among these not the least is, that the French (who by these Germans were not held in any particular esteem), are now everything with us. We have French attire, French dishes, French furniture, French language, French manners, French vices, and even French diseases are most abundant. These ancestors, instead of beholding in their beloved Germany men resembling themselves, would find it occupied by German-Frenchmen, who have so completely departed from their ancient customs, that nothing remains indicative of the past. They would regard us as changelings and bastards; and, with our Frenchified little beards, would rather deem us weak and cowardly women than sightly and brave men. They would pour on us their rough and energetic reproaches, or, not esteeming us even worthy of their scorn, with bitter mockery cast us from them." The native language, already extensively corrupted by the introduction of a multitude of foreign words, making it resemble, as Jean Paul afterwards described it, "a Prussian regiment, which contains deserters from all nations," was cast aside, as unworthy and unfit for literary purposes. Latin was employed by the learned, while French was the language of courts and high society; and the literature of the country was modelled upon the showy, but lifeless, specimens, destitute of all internal feeling, all fervour and force of imagination, of the so-called golden age of Louis XIV.

A nation like the Germans, radically of so much native vigour and intellectual aspiration, however seduced by the

* Thomasius, born 1655, died 1728, who vigorously attacked the perverted taste of the day. He lectured at Leipsic in 1688, where he excited the indignation and virulent opposition of the cotemporary literati devoted to the then unnational system, by publishing the programme of his lectures in the vernacular language of his country; by his innovations in many of the vitious usages of the day; and his determined freedom of thought and expression. He deserves lasting honour for his exertions to procure the abolition of torture, trials for witchcraft, and other inhuman and ignorant practises of that time.