+ 1 $3 and ex 16 8 + &c. from which we derive 16 128 12288 98304 This is the limit to which ftends as a increases, and with which it coincides when x is infinitely great. It remains now to apply the formula that have been investigated. If, in the equation, ß2zr=fyrdr (8), we substitute q+y' for y, we shall get qr Sy'rdr + and the smaller the diameter of the tube, the more 1 nearly will this equation approach to 6% = 1⁄2gr. Therefore, being the diameter of the tube, the va lue of 4,6% will be equal to ql, that is, to the product of the elevation or depression by the diameter of the tube, when the bore is very small. When mercury is contained in tubes of glass, the value of 4ẞz, assigned by the English philosophers, is .015; and Laplace, from the experiments of Gay Lussac, makes it equal to .01469. There is also some uncertainty in the value of z, or the cosine of the angle of contact, which seems to be between the limits 0.75 and 0.729. We may assume 462.015, and z = .735, 1 whence 6=1; these numbers being recommended 14 by their simplicity, and lying between the limits of the errors of observation. ries denoted by λ, and the coefficients of the series for f, will therefore be known in numbers, and hence ƒ may be found. Again, when x = 0, we have s= 2z x.λ 22 If we compute the value of the limit to which f approaches when l is very great, we shall find f= 0.9635: And hence, in the case of tubes with very large diameters, we have FONTANA (FELIX), a distinguished physiologist and experimental philosopher, was born 15th April 1730, at Pomarolo, a little town in the Tyrol. He began his studies at the neighbouring city of Roveredo, and continued them in the schools of Verona and Parma, and afterwards in the universities of Padua and Bologna. He then visited Rome, and went to Florence, where he obtained from the Emperor Francis I. who was at that time Grand Duke of Tuscany, the appointment of Professor of Philosophy at Pisa; but the Grand Duke Peter Leopold, who was also afterwards Emperor, invited him to settle at Florence, and gave him an establishment connected with his household, as Fisico or naturalist, and as Director of the Cabinet of Natural History, which was afterwards rendered, by his exertions, one of the principal ornaments of the city of Florence. Fontana became the author of many well known works on physiology, natural philosophy, and chemistry. In 1757, he was engaged in an investigation, tending to confirm the doctrines of Haller respecting the irritability of the muscles, considered as a distinct quality inherent in those organs. Haller has published several of his letters as a part of his own Mémoires sur les parties sensibles et irritables; and the subject has afforded to Fontana the materials of several successive essays. 1. De irritabilitatis legibus nunc primum sancitis. Atti di Sienna, Vol. III. p. 209. (1767.) 2. Ricerche filosofiche sopra la fisica animale. 4. Flor. 1775. This volume contains only the Essay on the Laws of Irritability, stating, first, the general outline of the doctrine, then enter. ing into the different intensity of the property of irritability, and its loss by exhaustion or by inactivity, and discussing the action of the heart, and the peculiarities of the death occasioned by electricity. 3. An other link of the same chain of investigation is found in the earlier publication De' moti dell' iride. 8. Lucca, 1765; showing that the contraction of the pupil depends on the effect of light falling on the retina, and not on the iris itself, and establishing an analogy between the motions of the uvea, and the semivoluntary actions of the muscles of respiration. 4. One of the most important of Fontana's works is his Ricerche fisiche sopra 'l veleno della vipera. 8. Lucca, 1767; containing an immense multitude of experiments, calculated to show that the poison of the viper acts by mixing with the blood, and destroying the irritability of the muscles to which it is conveyed, but that the bite of the European viper, though fatal to small animals, is scarcely ever capable of producing any immediately dangerous effects on the human frame. 5. The same matter was republished, with many additions, in the Traité sur le venin de la vipère, sur les poisons Américains, sur le laurier-cerise, et sur quelques autres poisons. 2 v. 4. Flor. 1781. Germ. Berl. 1787, together with some observations on the primitive structure of the animal body, experiments on the reproduction of the nerves, and remarks on the anatomy of the eye. 6. In 1766, our author published an essay entitled Nuove osservazioni sopra i globetti rossi del sangue. S. Lucca; con futing the assertions which had lately been advanced by Della Torre, respecting the complicated structure and changes of form of the globules of the blood. 8. In the next year Osservazioni sopra la ruggine del grano. 8. Lucca, 1767, describing an animalcule like an eel, to which he attributes the rust of coin, but which has not always been found by subsequent observers in similar cases, perhaps for want of an accurate distinction of the disease intended. 9. There is also a Lettre sur l'ergot. Journ. Phys. VII. p. 42. 10. The Lettera sopra le Idatidi e Fontana. le Tenie. Opuscoli Scelti. VI. p. 108. Milan, 1783, 14. Mr Fontana entered also very minutely, but 19. To the Memoirs of the Italian Society Fon- the attention required for the completion of his col- Fontana. 22. He was also the author of a few other chemical and mineralogical papers of less importance, for instance of an Analyse de la Malachite, Journ. Phys. XI. p. 509; and, 23. A Lettre sur du vitriol de Magnésie trouvé dans des carrieres de gypse, en Piémont, Journ. Phys. XXXIII. p. 309. 24. His last work is entitled Principes raisonnés de la génération. He was also meditating an essay on the revivification of animals; but he did not live to complete it. A collection of his works, translated into French by Gibelin, was published at Paris in 1785, entitled Observations Physiques et Chimiques. Fontana had become acquainted with a great number of contemporary men of science, by having travelled in various parts of Europe, for the purpose of enriching the cabinet of which he was superintendent; the same official situation brought him into contact with all foreigners of distinction who pass ed through Florence in their travels; and he seems to have enjoyed a more extensive reputation than many philosophers of deeper research and more irresistible penetration. He wore the habit of an ecclesiastic, and was not uncommonly called Abbé; he was well received in the best societies, though his manners are said to have been sometimes a little at variance with the dress which he adopted. He was treated with great respect by the French generals, when they took possession of Tuscany in 1799, and hence he became the object of some suspicion upon the return of the Austrians, especially with the insurgents of Arezzo, who preceded them, and by whom he was for a short time imprisoned. His last, illness was occasioned by an accidental fall in the street, on the 11th January 1805, and he died the 9th March 1806, at the age of seventy-five. He was buried in the church of the Holy Cross, not far from the tomb of Galileo. His Eloge was pronounced by Professor Mangili in the university of Pavia, the 12th November 1812. (CUVIER, in Biographie Universelle, Vol. XV. 8. Par. 1816.) (0. R.) FONTANA (GREGORY), a profound mathemati. He received the first rudiments of his education at |