where the series converges much more quickly than in M. Fontaine's form. This series is applied to investigate the lo

garithm of 2 (f when x=1 and the arc of 45° ( ***

when x=1)

2

In the fifth section, is given a second method for making the series more converging, which admits of a more extensive application than the former. The new formula for the inte gral of x px is

)

2"

+

where '," &c. are functions derived from ex.

Section vi. treats of those cases, in which neither M. Fontaine's method nor the two preceding can take place.

After all deductions have been made, there will still remain a very considerable portion of merit due to these mathematical papers. The cultivation of science in Portugal is commenced, and its cultivators will daily acquire new skill and richer materials. If we hope that this new society may emulate that famous Academy which is now no more, we hope for it a portion of fame which none but an enthusiast will despise; if we hope that it may experience a better fate, we shall not less express the benevolence of our wishes, nor the reasonable ness of our expectations."

Eulogium of M. d'Alembert. By M. GARÇAO STOCKLER. M. d'Alembert was a member of this Academy, and this tribute of praise has in consequence been here paid to his memory. Few particulars of his life are related in it, and these are already well known to the literary world. The most essential part of the eulogium, and which stamps some value

Rr 2

on

so far, Wood....e.

1

on it, is the analysis of all the works of this celebrated genius to which task the author of this paper, who is a mathematician*, seems to have rendered himself competent by a deep study of them. The oratorical part of the paper is chiefly of a panegyrical cast, unlike the academical eulogies of Fontenelle, which are the true models of such compositions. The author of a panegyric writes as a warm admirer, who does not wish to find any fault in the object of it; while the writer of an academical eulogium assumes a more impartial tone, which gives more weight to the praise which he bestows. We shall not however throw much blame on a mathematician, for being a warm admirer of d'Alembert.

For an account of Condorcet's ample eulogium on this celebrated man, see M. Rev. vol. lxxvi. p. 238.

This volume is terminated by a catalogue of books composed by several members of the society, and printed by order of the Academy; from which circumstance, it appears that the labours of this literary body have been directed to instruct and enlighten the Portuguese in many different branches of knowlege. We have so few opportunities of receiving Portuguese books, that it will, probably, excite the curiosity of many of our readers, to peruse this catalogue of recent publications in that part of Europe.

1. Breves Instrucçoes, &c. Short Directions to the Corre spondents of the Academy, relative to collecting natural Objects for the Institution of a National Museum. 8vo pamphlet.

2. Memorias Sobre, &c. Memoirs on the Method of perfect ing the Manufacture of Oil in Portugal, presented to the Academy by Mr. DALLA BELLA. I vol. 4to.

3. Memoria Sobre a Cultura, &c. Memoir on the Cultivation of the Olive Tree in Portugal, presented to the Academy by the same Author. I vol. 4to.

4. Memorias de Agricultura, &c. Memoirs of Agricultufe, which have obtained Prizes from the Academy. 2 vols. 8vo. 5. Paschalis Josephi Freirii Mellii, de Historia Juris Civilis Lusitani Liber singularis. 1 vol. 4to.

6. Ejusdem Institutiones Juris Civilis et Criminalis Lusitani. 5 vols. 4to.

7. Osmia, a Tragedy, which obtained a Prize from the Academy. 4to pamphlet.

8. Vida, &c. Life of Edward, Infant of Portugal, by A. DE REZENDE. 8vo. pamphlet.

A memoir by M. STOCKLER, on fluxions, has been noticed in this article.

9. Vestigios,

9. Vestigios, &c. Remains of the Arabic Language in Portugal, or Etymological Lexicon of the Portuguese Words and Names of Arabic Origin, composed by Order of the Academy, by FR. JOHN De Souza. I vol. 4to.

10. DOMINICI VANDELLI, Viridarium Grysley Lusitanicum, Linnaanis Nominibus illustratum. I vol. 8vo.

11. Ephemerides, &c. Nautical Ephemerides, or Astronomical Diary for the Year 1789; calculated for the Meridian of Lisbon. 1 vol. 4to. The same for every succeeding year till 1798 inclusive.

12. Memorias Economicas, &c. Economical Memoirs of the Royal Academy of Sciences of Lisbon. 4 vols. 4to.

13. Collecçao, &c. Collection of inedited Books of Portuguese History, relative to the Reigns-of John the 1st, Edward, Alphonsus the 5th, and John the 2d. 3 vols. folio.

14. Avisos, &c. Interesting Advices respecting apparent Deaths. 8vo pamphlet.

15. Tratado, &c. Treatise on the Physical Education of Children, for the Use of the People of Portugal, by FRANCIS DE MELLO FRANCO. 1 vol. 4to.

16. Documentos, &c. Arabic Documents of Portuguese History, transcribed from the Originals in the Tower of Tombo, (the Royal Archives in Portugal,) and published with the Portuguese Translation, by FR. JOHN DE SOUZA. I vol. 4to.

17. Observações, &c. Observations on the principal Causes of the Decline of the Portuguese Power in Asia, written by Diego de Couto, &c. by Mr. AMARAL. I vol. 8vo.

18. FLORA COCHINCHINENSIS sistens Plantas in Regno Cochinchina nascentes. Labore ac Studio JOHANNIS DE LOUREIRO, Regia Scientiarum Ulyssiponensis Academia Socii. 2 vols. 4to.

19. Synopsis Chronologica, &c. Chronological Synopsis of Materials for the History and Study of Portuguese Literature. By Mr. FIGUEIREDO. 2 vols. 4to.

20. Tratado, &c. Treatise on the Physical Education of Children, for the Use of the People of Portugal, by M. ALMEYDA.. I vol. 4to.

21. Obras Poeticas, &c. Poetical Works of PETER ANDRADE CAMINHA. I vol. 8vo.

22. Advertencias, &c. Advices respecting the right or wrong Use of the Mineral Waters of Caldas da Rainha, by Mr. Ta-, VARES. 4to. pamphlet.

23. Memoirs of Portuguese Literature. 6 vols. 4to.

24. Fontes proximas, &c. The immediate Sources of the Code of Portugal of Philip the 2d, by Mr. FERREIRA GORDO. I vol. 4to.

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25. Dic

25. Diccionario, &c. Dictionary of the Portuguese Language. I vol. folio.

26. Compendio, &c. Abridgment of the Theory of Limits, or Introduction to the Method of Fluxions, by Mr. STOCKLER, Member of the Academy. 1 vol. 4to.

27. Ensayo, &c. An Economical Essay on the Trade of Portugal, and its Colonies, by Mr. AZEREDO COUTINHO. I vol. 4to. 23. Tratado, &c. Treatise on the Art of Surveying Lands, by Mr. CABRAL. 1 vol. 8vo.

29. Analyse, &c. Chemical Analysis of the Mineral Waters of Caldas, by Dr. Withering, Member of the Academy. Published in English and Portuguese, by Order of the Society.

If any of the more recent publications here enumerated should reach our hands, we shall endeavour to make our read

to here, ers farther acquainted with their contents.

from page 579
Correa ART. XVII. Flore Danica Iconum Fasciculus Vicesimus.

Folio.

Hafnia, 1797. Sold in London by Mr. White. THE descriptions which accompany these excellent engravings are so extremely brief, that we cannot pretend to give a very critical account of the performance; especially as it is impossible for us to gain access to the plants which are here represented: but we scruple not to avow our full persuasion that the plates are indeed most admirably executed. The publica tion of this work commenced in the year 1761; and it has been continued with uncommon regularity, considering the nature of the undertaking, and the accidents and interruptions to which, in a series of so many years, it must naturally have been exposed,

ART. XVIII.

M.
GIRARD (Ingénieur des Ponts et des Chaussées) has pub-
⚫lished a treatise on the Resistance of Solids. Of this
work, in point of criticism, we are unable at present, from
want of time, to say any thing definite: but a superficial glance
over its contents, and a hasty perusal of some of its parts, afford
us reason to think that it is by no means an unimportant nor an
i-executed work. It is divided into four sections, the first two
of which are purely theoretical; the third contains experiments
made on the resistance of oak and fir; and the fourth is parti-
cularly destined to theoretical considerations and experiments,
relative to the inflexion of bodies supposed to be perfectly elas-
tic. What is written seems to be written with considerable
perspicuity, and the experiments apparently have been made
with method and exactness. In our next Appendix, we shall be
able to give a fuller and more particular account of the work.

G.

Wood

INDEX

To the REMARKABLE PASSAGES in this Volume.

N. B. To find any particular Book, or Pamphlet, see the
Table of Contents, prefixed to the Volume.