1777. Next year he inserted new experiments into the volume of the Academy, the object of which was to discover the law according to which the resistance of an angular prow diminishes in proportion as it becomes more acute.

The Course of Mathematics of Bossut, at the time when the different treatises were composed, were successively published, received much praise for the order, clearness, method, and philosophical spirit, observed in it. The historical prefaces which commence each volume were particularly praised. This book long shared equal popularity with that which Bezout had composed for the artillery and marine. Both of them were of great service to the pupils for whom they were destined. They have of necessity lost a part of their celebrity, since a single establishment has been formed for the instruction of those destined to serve the state in all the corps which had formerly their particular books and examiners. But this popularity continued long enough to reward the author for so many labours, and made him nearly independent at the time when the political storms threw the fortunes of all into confusion. Bossut was then deprived of the chair of hydrodynamics established for him, and which had existed only for a few years. He had been previously deprived (not without murmuring at the injustice of mankind) of that place of Examiner which he had filled with probity, and to the general satisfaction of the pupils of Government, In lieu of these places of Examiner, Professor, and Academician, Bossut obtained only some transitory aid voted by the advice of the Board of Consultation, and a lodging in the Louvre, which he enjoyed only a few years. It was then that he buried himself in that retirement which his age and the state of his income rendered necessary for him. Here he received some consolations. The Institute restored to him a part of what he had enjoyed as a Member of the Academy of Sciences. He was named one of the Examiners of the Polytechnic School, and when after more than 50 years of services age and infirmities obliged him to retire, his salary was continued, which he so well deserved not to lose,

It was in this solitude and absolute separation from society that he wrote his history of the mathematics, of which two editions were sold in less than six years. Two volumes are very little for so vast a subject. Mathematicians accordingly will find the work too incomplete and superficial. But it was not for them that he had written it. We see by the reflections which he made on the History of Montucla that he was sensible of the spirit and manner in which such a work should be composed. But he adds immediately, that his design is not to give that profound history in which all the parts of mathematics should be analyzed, and which may to a certain amount save the trouble of reading the authors themselves, especially those whose methods are antiquated. "He attempts only to give a general sketch of the progress of mathematics from their origin to the present time, to honour the memory of the great men who have extended its empire, and especially to inspire youth with

a taste for these sublime studies." He remembered doubtless what he himself had felt on reading the writings of Fontenelle.

The first edition only bore the modest title of Essay. He acknowledged afterwards that he was satisfied with its success. His Essay had been translated into different languages. It was well arranged, clear, and well written. He acknowledges at the same time that the second edition, entitled General History, was less fortunate, and had been very severely criticised. The cause which he assigns for this difference is, that in the Essay he had refrained from speaking of living authors, whereas when he continued his history to our own time he could not but find judges more difficult to satisfy. Without denying absolutely the justice of this remark, we must acknowledge likewise that the reasons which he assigns for certain omissions appear very weak. The most disinterested readers must see that different modern works are not appreciated with a care and details proportional to their importance. The author, who had given an interesting account of the discussions between Newton and Leibnitz, and the more recent disputes of the two protectors of his youth, Clairaut and d'Alembert, was more sparing in speaking of authors whom he had studied with more care, and for whom perhaps he had not the same affection. This restriction is equally apparent in what he says, and in what he suppresses; and this part of the work requires to be done over again." His great age and his infirmities deprived him of the hope of doing better, or being more happy." But he thinks that "his work is of a nature to be perfected by successors more capable of fulfilling his intentions."

2

These intentions were to be just and impartial; but he wished that others should be with respect to him what he wished to be with respect to others. He acknowledges in a posthumous manuscript which has been sent us "that he always had a harshness of character, which often injured him with those who only knew him superficially. He did not easily grant his confidence; he believed all mankind in general dissemblers and deceivers; but when he gave himself up to the natural frankness of his soul, he brought into the commerce of life an effusion of true feeling, which procured him a great number of devoted friends, especially in the Military Corps of Engineers.'

"He abhorred impostors of all kinds," said he, likewise; "he had often the imprudence to make them acquainted with his opinions; but he was always in search of true merit."

"He was obliging; and he complains bitterly of ungrateful persons."

"He was persuaded that men who owed every thing to him had shown the greatest rancour against him, and had given themselves a great deal of trouble to prevent him from obtaining places to which he had never aspired.'

It is not surprising that with such opinions, embittered by solitude, and strengthened by the kind of abandonment in which he thought himself placed, after having enjoyed a rank and influence

the diminution of which he exaggerated, he was not very anxious to point out the merit of contemporaries, whom he thought in general unfavourably disposed towards himself. We find the effect of these opinions in a very bad-humoured preface to his Mathematical Memoirs, published in 1812. These memoirs are those which had gained prizes, and been published at the time by the Academy of Sciences. He adds to them some notes on his History of Mathematics. He there explains or demonstrates theorems which he had too much abridged; but he adds nothing to fill up the blanks which had excited the outcries of which he was so sensible.

We must lament that he was so long the dupe of a cloudy imagination, which rendered the last years of his life unhappy. Before age, infirmities, and the loss of his places, had laid open this disposition to misanthropy, he appeared to us to be filled with benevolence. I shall always recollect with gratitude the notice which he paid as Director of the Academy of Sciences to the first essays which I presented to that body; and yet he knew that I was particularly connected with an astronomer whose friend he was not, and of whom he must have considered me to be the pupil and protegé., I may add that I never found the least change in his disposition towards me, though I ventured to express an opinion opposite to his with regard to some points of ancient astronomy.

We may place his omissions in a more favourable point of view, though we cannot pretend to excuse them entirely. A great work on transcendental mathematics is not read with the same facility as a work of history or literature. To understand its merit, to be able to explain its plan, and to point out the most interesting parts of it, a degree of labour and attention is requisite of which old age is no longer capable. A mathematician possessed of the true genius of invention may astonish us by new productions at an advanced period of life. These productions will be the developements of former ideas, to draw the consequences from which no opportunity had previously occurred. But he would be terrified at the thoughts of following for a long time the steps of another mathematician. It was in town that Lagrange composed his last works, and at the same time he avowed the necessity of going to the country to form an exact idea of the new methods of M. Gauss.

Bossut wished to be just and impartial; and he wished it in consequence of that harshness of character of which he accuses himself, and of which he had given numerous proofs, We shall only notice one.

At the time that he was Examiner of Engineers, the Comte de Muy, at that time Commander of the Order of the Holy Ghost, and Governor of the Province, and afterwards Marshal of France and Minister at War, had personally recommended to him a number of pupils, who, by a singular fatality, were almost never worthy of being admitted, and, who were in fact rejected. The Comte de Muy had expressed some dissatisfaction at this. When afterwards he became Minister at War, and when, according to the

custom, Bossut went to him for the first time with a statement of the examination which had been made, the Minister signed the promotion without hesitating, addressing to Bossut these words, equally honourable to the Minister and the philosopher: "I subscribe blindly, for I have already experienced that it is not necessary to examine after you."

Bossut was a great admirer of Pascal, whose works he published in 1779. He had collected with the greatest care all the Thoughts and other unpublished pieces furnished him by manuscripts and authentic copies. For the first time, Pascal appeared in a complete form. The editor did not wish to conceal or suppress any thing, not even the note written about a month after the accident at Neuilly. It was for this edition that Bossut composed his discourse on the life and writings of Pascal, which he republished afterwards as soon as an opportunity occurred. It was of all his works that which had been written with most attention to the style, and in which he had given his own opinions on subjects of literature, science, and religion. He saw in Pascal "a singular phenomenon that deserved to be often recalled to memory. This profound reas soner was at the same time a rigid and submissive Christian." We see that Bossut wished here to draw his own character. Destined in his youth for the church, known till 1792 under the title of Abbé, if his passion for mathematics, and his duties as a Professor, to which he was called so young, did not permit him to devote himself entirely to the ecclesiastical state, he preserved at least its manners for a long time, and maintained the opinions belonging to it all his life long.

He died on the 14th January, 1814. His place in the Institute has been filled up by M. Ampere,

ARTICLE II.

On Septaria. By Dr. C. Wilkinson, of Bath, M. G. S.

DEAR SIR,

(To Dr. Thomson.)

DURING a visit I made at Harwich last May in company with my learned friend the Hon. Gen. Sir B. Henniker, Bart. I had fres quent opportunities of examining the cliffs, and the progressive formation of septaria, These cliffs are about 30 or 40 feet above the level of the sea, and consist of a large proportion of ferruginous elay, some silex, and carbonate of lime. After every shower of rain, if the water absorbed be removed by evaporation, or expanded by frost, large portions of the cliff become detached, fall on the shore, and become exposed to the influence of spring tides. During the period of my residence in that sea port, I observed that in the

space of two or three weeks the detached portions acquired in many instances almost a flinty hardness. These ate broke into small pieces of about 2 lb. weight, placed in a kiln similar to a limekiln, and exposed nearly to the same degree of heat: when re moved from the kiln, they are reduced to a fine powder in a grinding mill, and then constitute the same cementing material as what is known under the name of Larkin Cement.

The cliff, when examined in situ, has all the appearance of an uniform argillaceous mass, except in some parts, separated by whitish thin horizontal layer, which consists principally of carbonate of lime. Most of the portions at the period of being detached have an homogeneous appearance. During the period of desicca tion a very curious change takes place. The exterior part hardens first, to a certain extent; and as this change is advancing towards the central portion, a fissure is produced, and the carbonate of lime, which retains its soft state much longer than the argillaceous portion, is mechanically separated from the clay, and pressed into this divided part. In its first stage I have remarked it to be near half an inch below the surface of the detached portion. In this state it is soft, but not fluid. After two or three days the calcareous matter becomes level with the surface, and in many instances projecting above. As the carbonate of lime hardens, a species of crys tallization takes place, from which cause there is an additional protrusion of the substance. During these processes there are transverse fissures in different directions, considerably smaller than the first separation. These smaller clefts are filled in a similar manner. When perfectly hardened, and cut through, a complete septarium is observed to have been formed. It appears that the carbonate of lime is mechanically mixed with the other portions; and when it exists beyond a certain proportion, from remaining softer longer than the other parts, becomes mechanically pressed in that direc tion where it meets with the least resistance, viz. the central part: when the proportion of carbonate of lime is small, it remains intermixed with the clay. From this circumstance we observe many of the hardened portions without any calcareous septa.

It appears probable that metallic veins may be formed by a similar process; in the first instance an apparently homogeneous soft mass; and that during the subsequent periods of consolidation, the metallic mass, undergoing this change more slowly, may be similarly determined in any fissure formed by the desiccation of the other materials. If different metallic substances should require different periods for consolidation, we may form some idea of the formation of cross courses.

I moulded into an oblong form some of the detached portions of the cliff; the first-formed fissure was longitudinal; such was to be expected, as the resistance in that direction would be the least.

In Cornwall we observe the principal metallic veins are copper, and these are generally in the direction E. and W. If we consider Cornwall as a large oblong mass, the longitudinal diameter will be