Vol. for 1818.-HISTORY.

One of the most interesting articles in the historical chapter of this volume is M. Biot's Report of the Operations undertaken with a View to determine the Measure and Curvature of the Earth, in which the members of the French academy have always borne a very active part. The labours of MM. Delambre and Mechain, in relation to the measurement of the French arc, are already well known to our readers, through the medium of the "Base du Systéme Mètrique décimale:" (see Review, vol. 1. p. 463.) but the continuation of their arc into Spain and to the island of Formentera, the nature of that operation, the difficulties attending it, and its final results, have not yet been presented to the public. This report of M. Biot, who was actively engaged in those labours, although nothing more than a general statement, becomes therefore highly interesting *; particularly in the part relating to M. Arago, which is so singular and even romantic, that we cannot resist the temptation of laying it before our readers in the words of the author.

It will be necessary, however, to make a few remarks by way of introduction. The French geodesists, as we have before observed, having completed their arc from Dunkirk to Barcelona, were desirous of extending it as far southward as they could, and at length decided on fixing their final station in the little island of Formentera. With this view, a request was made to the Spanish government to unite two of their philosophers with MM. Biot and Arago, in order to conduct this labour between them; and application was made to the English government, to grant to those who were concerned in the undertaking a safe conduct, which was of course given. Thus prepared, the gentlemen proceeded in their operations, which presented some extraordinary difficulties. In the first place, in order to connect the island of Ivica with the Spanish stations, it was necessary to form a triangle which should have its summit in that isle, and its base in Barcelona: this base measured thirty-five leagues, and the sides about forty-one leagues: but these leagues being 2000 toises, the measures answer to about eighty-eight English miles for the base, and 103 miles for the side of the triangle. Great attention therefore became indispensable in selecting the stations best calculated for seeing the requisite signals at these distances, which were necessarily strong lights by night. After two months of the most patient watching for the light in the island of Ivica, it

* See some observations on this subject in page 494. of this Appendix.

was at length recognized; its place was fixed by means of another station; and the operations went forwards, although under some difficulties and hardships on the part of the observers, as favourably as they had any reason to expect. Having at length completed the chain of triangles which connected Spain with Ivica and Formentera, M. Biot returned to Paris; while M. Arago remained in Ivica, to connect with their other stations one that was chosen in the island of Majorca, which was not at first contemplated. Now commenced the singular and disastrous adventures of the latter philosopher, with whom M. Biot had left the safe-conduct obtained from the English government; and it is remarkable that, although the vessel in which M. Biot passed to Spain was boarded by a corsair, and he had left his protection behind him, yet he succeeded in reaching Spain in safety, though his colleague was doomed to suffer the most alarming and vexatious captivity.

While we,' says M. Biot, followed peaceably in France the calculations which were necessary to complete the operations, and to determine the results, M. Arago had been much less successful. As long as he had to contend only with the obstacles of nature, his perseverance and ability insured him success. He had already completed the triangles which served to connect the two stations, and to determine the terrestrial arc comprized between them, when, in company with M. Rodriguez, he passed over to Majorca, and immediately established himself on the summit of a high mountain called Puch de Galatzo. He had observed the signals at Ivica, and a sufficient number of meridian transits to determine the difference of longitude between the two stations:-a few days more, and the result of his observations would have been invariably fixed-but, all on a sudden, a report spread amongst the people that the object of these instruments, the fires, and the signals, was to direct the enemy towards the island, and to shew him the road. Nothing was now heard but the cry of treachery and death; and the people were preparing to go to Galatzo in arms. Happily, M. Arago was apprized of their design, and, clad in the habit of a peasant of the island, he escaped to Palma, carrying with him his observations; which already contained the requisite elements for computing two degrees of longitude. Having arrived there without detection, he repaired on board the ship which had brought him, where he hid himself for two days; and in the mean time he sent some of the crew of the vessel to collect and to save his instruments, which the peasants engaged in his service had faithfully guarded.

'Soon, however, he found himself a prey to new alarms, for the ship to which he had retreated was no longer an inviolable asylum. Either through treachery or from fear, the Spanish officer who commanded it, and who had hitherto been our friend, refused, notwithstanding his promises, either to protect M. Arago

or

or to take him to France. Even the Captain-general of the islan could save him only by shutting him up in the citadel, where he remained many months a prisoner; having not only to regret his liberty, but being frequently in fear of his life. At one time, the fanatical monks attempted to corrupt the soldiers of the guard to destroy him. Still, however, his friend Rodriguez abandoned him not in his misfortunes; incapable of any dereliction either of friendship or of honour, he went every where, intreating, pressing, and demanding the liberty of his colleague, and representing strongly the injustice of his detention. At length he obtained his friend's deliverance; and M. Arago was allowed to pass to Algiers in a small vessel, having for his pilot a Majorcan sailor named Damian, who had always manifested towards us the greatest attachment and devotedness.

At Algiers, M. Arago was received by M. Dubois-Thainville, the French consul, and was highly indebted to his kindness; through which he was soon embarked on board an Algerine merchantvessel, in order that he might return to France. After the most pleasant and happy voyage, he arrived within sight of Marseilles, and already considered himself as in the harbour, when a Spanish privateer, seeing the ship enter a French port, attacked it, captured it, and carried it into Rosas. M. Arago might yet have escaped, being borne on the ship's books as a German merchant : but, by the most unfortunate chance, a sailor who had formerly been with us, and was now in the service of the privateer, recognized him; an exclamation escaped him; and M. Arago was plunged with all his companions into the most frightful captivity.

I shall say nothing here of what he had to suffer while in prison; it will be sufficient to state that the Dey of Algiers was soon informed of the insult which had been offered to his flag, demanded prompt satisfaction, and insisted on the restitution of the vessel, the equipage, the merchandise, and all the passengers; menacing that, in case of refusal, he would declare war. It was necessary to comply with these urgent conditions; and M. Arago again embarked, and again set sail for Marseilles. He was once more within sight of the port, when a dreadful storm from the north-west drove the vessel back with irresistible force, and carried it towards the coast of Sardinia. Here was another danger: the Sardinians and the Algerines being at war, to land on this shore was to fall into another captivity. It was therefore determined, notwithstanding the distance, to take shelter on the coast of Africa; and the vessel, lowering its colours, at length sought refuge in the port of Bougie, three days' journey from Algiers.

Here they learned that the Dey, who had so powerfully protected them against the Spaniards, had been killed in a tumult, and another Dey had been elected in his place. The officers of the port examined the vessel carefully; and the weight of the cases containing the astronomical instruments excited violent suspicions. "What can they contain that is so heavy, if it be not gold; and why are so many precautions taken to prevent

their being opened, if they contain any thing else but sequins ?" Not being able to obtain these cases from the officers, and unwilling to trust to the uncertainties of a barbarous negociation, M. Arago, in the habit of a Turk, and in company with some other persons, under the conduct of a saint of the country called a Marabou, returned by land to Algiers; traversing the intervening mountains, we may imagine with what perils. The Consul, much astonished to see him in this costume, received him again with the same kindness and benevolence as before, and the instruments were officially reclaimed. The Algerines, convinced that they were brass, and not gold, considered them no longer as of any value, and gave them up. The opportunities of returning, however, had become rare and difficult, and it was necessary for M. Arago to remain six months at Algiers. At length, the Consul himself, called to Paris by the Emperor, embarked with his family, and took M. Arago with him, in a vessel of war belonging to the regency. Arrived a third time off Marseilles, they met an English squadron greatly superior to them, which ordered them to return to Minorca. All obeyed the command, except the individual vessel in which M. Arago was embarked; and of which the captain, more venturesome than the others, profited by a favourable breeze, set sail, and entered the port. Thus terminated so many remarkable disasters; and M. Arago returned to the bosom of his country, to receive the reward of his talents and exertions. He now occupies a place in the Institute in the section of astronomy, a distinction which he has well merited by his perseverance and his ability.'

M. Biot now proceeds to give a statement of his voyage to Shetland; in the course of which he expatiates in glowing terms on the hospitality and benevolence of Scotland, and on the learning and talents of its men of science. We have had occasion already to advert to this voyage, (see note, p. 519.) and to express our regret that a corresponding disposition was not displayed by all parties. Had M. Biot been contented to act on terms of equality and reciprocity, we are convinced that all would have passed in the most amicable manner; and he would not then have found it necessary either to suppress the names of his companions, or to have spoken of them as mere appendages to his retinue.

We discover no other article in this introductory chapter which calls for particular remark; unless, indeed, it be one preceding that from which we have so largely extracted. We allude to a report by MM. Prony and Molard, on the memoirs of two scientific tailors, the one resident at Paris, M. Beck, and the other M. Chomereaux, of Brie-Comte-Robert: each of whom appears to have been endeavouring to reduce the mystery of the shears to mathematical principles. The memoirs are not given at length, or we should probably have been amused by learning that the collar of a coat was deduced from

some transcendent hyperbola, and that the front of a pair of pantaloons might be reduced, by means of generating functions, to the curve of the choncoid of Nicomedes! The reporters are of opinion that these gentlemen are intitled to the thanks of the Institute.

MEMOIRS.

On the Flux and Reflux of the Sea. By M. DE LAPLACE. The nature of this paper we have already explained in reporting the historical part of the preceding volume; and we can do no more in the present instance, the nature of the formulæ and investigations being too abstruse for us to attempt to convey to the reader any idea of the analytical principles on which they depend.

On the periodical subterraneous Inundations which take place in certain Quarters of Paris. By M. GIRARD. Only a local interest belongs to this discussion; and it is not very intelligible, except to those who have a knowlege of the particular spot to which the observations apply.

On the Integration of certain Linear Equations to partial Differences, and especially the general Equation of the Motion of elastic Fluids.-This article, by M. POISSON, is by far the most important mathematical memoir in the present volume. It is known that algebraists have already arrived at the integration of all equations of partial differences of the first order, whatever may be their form, and the number of independent variable quantities which enter into them. At least, they have reduced this integration to that of a system of differential equations of the first order, the same in number as the variables; and hence they have shewn that the equations of partial differences, of this order, involve no other difficulty than those of the common differential equations. This, however, is far from being the case if we pass to the higher orders, for then the equations have difficulties belonging exclusively to themselves; that is to say, difficulties which cannot be referred to the imperfections of the simple integral calculus. Here, in order to obtain the integration, analysts have conceived the idea of expressing them by definite integrals, relative to certain auxiliary variables not appertaining to the question; and this new field, opened to the researches of geometers, has furnished a method, if not of completing, at least of much extending the processes of integration. Euler may be said to have first indicated the employment of this artificial mode of operation; and Laplace extended it still farther, by applying it to the linear equations of partial differences. M. Poisson is following the steps of the above celebrated mathematicians, but has very prudently declined the hopeless task of rendering this method general;