lines would be the least possible. From the answer to such questions always requiring the sum of certain squares to be made the least possible, the method derives its name. It is not of course asserted, that the process described would infallibly discover the place where the chalk mark existed; but if the same person were to try the method upon a hundred such targets, losing at the rate of a given sum for every inch by which he was wrong, he would certainly lose less by acting in the manner described than by any other process.

Singularly enough, it was not as a result of the theory of probabilities, but as a convenient and easily practicable process, that the method of least squares first appeared. Legendre and Gauss, independently of each other (though the former first published it) saw the utility of such an addition to astronomical computation. It is to Laplace that we owe its introduction as the best theoretical mode of ascertaining the most probable result of discordant observations. His investigation wants clearness and elegance; but is in other respects one of his most brilliant labours. The beauty, generality, and simplicity of the result secured for it an immediate admission into every process, though the demonstration is of a kind which there are not many to understand the process is one which has the air of being highly probable, and seems in itself to be free from objections which might be proposed against any other method. But at the same time it appears to us, that many have used it without a thorough comprehension of its meaning; and just as we now say that astronomy must have stopped its career of increasing accuracy, if the method of least squares had not been introduced, so we will venture to hope the time must come when the same remark shall be made upon an improved and extended way of using it.

The difficulty of admitting several points connected with the theory of probabilities, arises from the neglect to make an important distinction; namely, between the correctness or incorrectness of the hypothesis assumed, and that of the inferences which are drawn from it. Let it be proposed to apply mathematical reasoning to the valuation of the credibility of evidence, and the answer appears simple-namely, that such a proposition must be the result of an overheated imagination. This would be a fair answer if it were required to apply calculation to the character and actions of a given man, with a view of ascertaining whether he were likely or not to tell the truth in a particular case. Mathematics will not tell us whether A and B are credible witnesses, nor whether, supposing them credible, their evidence will be as much as should in prudence be considered sufficient for the establishment of any particular point. Nor will mathematics enable us to measure a length in feet, or to reason upon

it, unless we first know by other than mathematical means, what is that length which it is agreed to call a foot. But let a foot be known, and we can then assign lines, areas, and solids, by means of numbers; and, in like manner, let the credibility of one witness be given, and we can then determine that which results from the joint evidence of two or more, or from the evidence of any number, contradicted by any other number. By the credibility of a witness, we are supposed to mean the probability that an assertion advanced by him will be correct, the moment before the assertion is made.

For instance, suppose it admitted that a jury of twelve men, all equally likely to be correct in any particular verdict, decide wrongly once out of fifty times. It is matter of pure algebra to find out how often each of them, using his own unassisted judgment, would come to erroneous decisions. It is also the province of algebra to determine how often a jury would err, if, upon the preceding hypothesis as to the correctness of twelve men, the number were reduced or increased. Laplace, and others before him, have made extensive applications of analysis to such questions; but their labours in this respect have been misunderstood, and always must be, until the province of mathematical reasoning is better understood by the world at large.

We have now, we believe, briefly touched upon the principal subjects which are to be found in the Théorie des Probabilités. The subject is one which must make its way slowly, having to extricate itself from its old connexion with games of chance, before it can take its proper place as an agent in statistical and political enquiry. One of our principal objects in writing the present articles has been to show that the nature of probability may be treated, and its results applied, without the mention of dice or cards. Laplace himself has introduced a few problems connected with common gambling, in some instances on account of their historical notoriety, in others because they afforded easy and striking examples of the application of generating functions, the theory of which was introduced in his work. But the greater part of the treatise is full of such questions as those which have been alluded to in the preceding pages, bearing in the most direct manner on the way to draw correct inferences from physical and statistical facts.

If we can make a few reflecting individuals understand, that, be the theory of probabilities true or false, valuable or useless, its merits must be settled by a reference to something more than the consideration of a few games at cards, we shall have done all which we ventured to propose to ourselves.

ART. XI.-Summary Review of Italian and German Catholic Literature, from January to June 1837.

HE field of Italian Catholic Literature is neither as varied nor as extensive as that of France, Germany, and England. Italy has not, like France, suffered from the ravages of systematic infidelity, nor has the press teemed with two classes of works, entirely opposite in their nature, one of which is filled with attacks on every thing that is Catholic or that is Christian, while the other is employed in exposing the errors and confuting the attacks made in the former. This description of works has appeared chiefly in France, during the last and present century, and each day a new party of combatants has appeared on the lists: but, from these systematic attacks, Italy has been free, and consequently, in a notice of its literature at the present period, the reader is not wearied with a continual series of works, in the very titles of which, every Christian discerns a fresh insult on his religion. Italy has, moreover, maintained in a very large majority the religion of ancient times; nor are the different states divided into an endless variety of religious opinions. England and Germany hear of nothing, in religious literature, except the controversial publications of one or other of these parties; each sect in England or Germany has its apostles and its champions, whose works, applauded by their own party, and censured and condemned by the rest of the nation, agitate the minds of men, and too often, unfortunately, break the bonds of charity and peace. Italy, on the other hand, has felt the benefits and seen the advantages of uniformity in belief. From these two classes of combatants-those who attack religious opinions in particular, and those who endeavour to uproot religion altogether-literature in general has acquired a tinge, which affects, more or less, nearly all works, even though not professedly on religious subjects; and the opponents of these two parties, seek, in like manner, to stamp on their works the impress and seal of their body, and they endeavour to influence, through them, the manner of thinking of their readers, even in religious matters. The people of Italy have always been accustomed to consider every thing in a Catholic view; and the absence of such parties has also produced the absence of that character which has marked the productions of other countries, and which has insinuated into all literature the peculiar tenets of the authors of works, or the party to which they belong.

The publications in Italy may be divided, on religious sub

jects, into two classes: the first comprises all those works which treat of the doctrines or mysteries of religion, whether in the severer form of theological treatises for the use of the clergy, or in the more familiar one of popular instructions; the second class contains those numerous works which tend to excite devotion, or to clothe it with expression. From these two classes we except, of course, works of general literature, history, and the arts, which do not partake of a religious character; and we except, likewise, works of periodical literature, the chief of which we intend to mention at present.

The first of these is the Annali delle Scienze Religiose, from the title of which, an idea may be formed of the subjects on which it treats. It is published quarterly, at Rome, under the direction of the Abate de Luca, assisted by several of his friends, and is conducted with much ability.

The Propagatore Religioso, is published at Turin. The subjects of this publication resemble those of the former work; and to the end of each number are generally appended literary notices.

The Pragmalogia Cattolica resembles the latter; it is published at Lucca.

The Memorie di Religione, di Morale e di Letteratura, appears at Modena; the title sufficiently explains the kind of subjects which it selects.

With the exception of the Annali, these publications are monthly. In Biblical Literature, the principal recent publications are:

La Sacra Bibbia di Vence, giusta la quinta edizione, del Sigr. Drach, con atlante e carte: per cura del Prof. Bartolomeo Catena, Bibliotecario dell' Ambrosiana.-This work is not yet completed. Eight octavo volumes of it have appeared at Milan, and the remainder is in course of publication.

La Sacra Bibbia secondo la Volgata, colla Versione di Monsgr. A. Martini, e colla Spiegazione, &c. di L. J. Maistre de Sacq.-This work is also publishing at Milan, and will be completed in twenty volumes octavo.

La Sacra Bibbia seconda la Volgata: tradotta e con annotazioni di chiarata di Mgr. Martini. Florence. 3 vols. 8vo. 62f. 58c.

A new edition of St. Augustine's works is in course of publication at Venice, and is dedicated to his Holiness Gregory XVI. Sancti Aurelii Augustini Opera, studio monachorum S. Mauri, post editionem, Parisiensem, Antverpiensem, et Venetam. Three volumes, folio, have appeared.

Amongst the Theological Works may be noticed the following:Il Trionfo della Santa Sede, in 4 vols. 8vo. Venice.-This splendid work is from the pen of his Holiness the present Pontiff, and has appeared in several forms, at Venice and in other places.

Lectiones Theologica quas in Collegio Romano habebat Joannes Perrone, S. J.-This work is intended to form a complete course of modern and ancient dogmatical theology. The learned author is Pro

fessor of Theology in the Roman College, which is under the direction of the Jesuits. Four volumes, octavo, have been printed, and a fifth is now in the press: three others will complete the work. We propose to give a more detailed account of this able work on a future occasion. Opere Complete di Liguori. Venice, 16mo.- Volumes 67-8 have just been published.

Lezioni di Diritto Canonico; corredate di Note e d'Illustrazioni dal Prof. P. Vermiglioli. Perugia.- To be completed in 5 vols. 8vo. two of which have been printed.

Connected with Ecclesiastical History are the following:

I Secoli Cristiani, ossia Storia de Cristianesmo, del Abate Ducreux. Vigevano. 4 vols. 8vo.

Two editions of the Magnum Bullarium Romanum, are in preparation at Rome. The first is to be a complete edition of the entire work; two parts are to be published every month, each of them to contain ten sheets: the subscribers' price will be two francs for each part. His Holiness has graciously ordered all the Archives to be opened to the editors, and has afforded them every encouragement in their undertaking. The other edition will contain merely the supplement, from 1758 to 1830, and will be completed in the same form and at the same price, with the foregoing. Two volumes have already been published.

The Biographical Works are chiefly-Vita di S. Filippo Neri, scritta da P. G. Bacci. Venice. 8vo. 3 vols. Raccolta di Vite di Sancte Vergine e Vedove. Turin. A new edition of the Life of St. Philip Neri is commenced at Rome.

The Books of Instruction are very numerous, but we can mention merely a few of them. Collezioni di Opere di Religione distinta in tre Classi. Vols. III, IV, V, VI and VII, have just been published at Venice; they contain-Introduzione allo Studio della Religione, del Cardinale Gerdil; Testimonianze tratte della Filosofia di Bacone, Cartesio e Malebranche; Trattato di Bossuet della Cognizione di Dio e di se medesimo; Della existenza di Dio, di Fenelon. Each volume 87c.

Opere, di Segneri. Milan. To be complete in four large, or ten small volumes. It will form the most accurate edition of the works of this most eminent preacher.

Raccolta di Opere Sacri, per uso di ogni fedel Cristiano, publishing in parts at Leghorn.

Spiagazioni Evangeliche per tutto l'Anno, di G. Maggi. Milan.

2 vols. 4to.

Quadro del Cristianesmo.

Ferrara. 1 vol 8vo.

Biblioteca per parochi di Campagna. Venice. 8 vols. 8vo. Each volume 1fr. 74c.

Compendio della Dottrina Cristiana, exposto da Mgr. F. Bonesio, Vescovo di Bobbio. Cremona. 1 vol. 12mo.

Compendio del V. Testamento. 1 vol. 8vo. Venice.

Discorsi Morali tratti dai Santi Padri. Naples. 1 vol. 8vo. Della vera Autorita de' Santi Padri, del Sacer. D. Zelo. Naples.