LAMBERT, Johann Heinrich, a natural and moral philoso-
Lambert. pher of great talent and originality, born on the 29th of August 1728, at Mühlhausen, in Upper Alsace, was the son of a French refugee in a very humble station, and one of a numerous family.
His early studies were only assisted by the instruction he obtained at a small free school in his native town. His father, who was a tailor, could scarcely even afford him leisure from mechanical labour. He was obliged to read and write in the night; and, in order to procure candles, he made little drawings for sale, while he was watching the cradle of his infant sisters. Having learned to write a good hand, he obtained some employment as a copying clerk in the chancery of the town, which he gave up when he was only fifteen, upon being appointed book-keeper at some iron-works in the neighbourhood. At seventeen he became secretary to a Doctor Iselin, who was the editor of a newspaper at Bâle, and who became his firm friend through life. He had now time to render himself familiar with the works of Wolf, Locke, and Malebranche, to which he was in a great measure indebted for the correct logical method that he ever afterwards followed in his researches; having, however, confirmed and improved it by the study of the mathematics, to which he devoted himself with great zeal, and which, after all, constitutes the best practical school of genuine logic.
In 1748, he removed to Coire, having been recommended by Iselin, as private tutor to the family of the president, Count Peter de Salis, whom he undertook to instruct in history and religion, as well as in languages and science. The library of his patron was extensive; he profited by it in all its departments; and his residence at the house of an accomplished statesman, frequented as it was by the best-informed persons of different countries, and with different pursuits, could not but greatly contribute to the extension of his knowledge, and the improvement of his taste. He even amused himself with some poetical exercises in various languages, which must, at least, have been of advantage to his style in prose. He felt the importance of his literary and scientific pursuits to himself and to the world; and in 1752 he determined to keep a journal of all his studies, which he continued throughout his life. He began to publish a variety of fugitive pieces, on different subjects, in the newspapers and in other periodical works of the day, some of which attracted the notice of his learned countrymen; and, in 1764, he was made a member of the Physico-Medical Society, then lately established at Bâle, to the Transactions of which he contributed many interesting papers. In 1756 he went to Göttingen with two of his pupils, and in 1757, to Utrecht. The next year the party returned to Coire, by way of Paris, Marcellies, and Turin. At Paris he paid a visit to D'Alembert, who does not appear at that time to have appreciated his merit very highly, though he afterwards rendered him some services with the King of Prussia; but he became more intimately acquainted with Messier the astronomer.
In 1759 he quitted the family of the Count de Salis, and went to settle at Augsburg, having a small salary as a member of the Electoral Academy of Bavaria. From 1761 to 1763 he was again at Coire and in its neighbourhood, being employed in fixing the boundaries between the country of the Grisons and the Milanese territory. Towards the end of 1763, having had some disputes with the Bavarian academicians, he went to Leipzig, and the next year to Berlin, where he was made a member of the Royal Academy of Sciences, and where he continued to reside during the remainder of his life, receiving many marks of favour from the discriminating liberality of Frederick: thus, in the year 1770, he was made superior counsellor of the Board of Works, with an additional salary. He contributed a number of valuable memoirs to the collection of the Academy; and in 1774 he undertook the di-
rection of the Astronomical Almanac, for which he was admirably qualified. He was also a constant writer in the journal published by Nicolai, under the title of the Universal German Library; and he kept up a very extensive correspondence on various subjects of literature and science.
He was regularly in the habit of writing or reading from five in the morning till twelve, and again from two till midnight; a degree of application unquestionably far beyond that which would have been best calculated for producing the maximum of valuable effect. Perhaps, if he was paid for writing by the ream, he may have earned as much from the booksellers as he would have done by a more judicious economy of his powers; but a nervous system, attenuated by the daily study of seventeen hours, could never have been capable of being employed in any very elevated flights of genius, or in the invention of any sublime or exquisite novelties, either in science or in literature; and it is only wonderful that he did anything so well, as almost to form an exception to this general remark. He was indeed supposed to have injured his health by continued application, and he died consumptive, on the 25th September 1777, at the age of forty-nine. He had never been married. His person was of the middle size, with an interesting and expressive countenance; he was animated and lively in conversation, and liked discussion, but not disputation. He had no literary quarrels; and his criticisms were not offensive, even when they ceased to be flattering. His morals were strictly correct, but his manners were not altogether in unison with those of the society to which his talents had elevated him. He is said to have been timid, awkward, slovenly, and fond of low company; but upright, patient, unostentatious, and compassionate; essentially modest, but as ready to assert his own merits as to admit his defects. He had a happy facility in managing the instruments of computation, especially in the arrangement of converging series; and he had a peculiar talent for expressing the results of observation by an analytical formula, having first thrown them into the form of a geometrical diagram to assist his invention; a process which he employed with regard to the probabilities of life in London, and to the inequalities of Jupiter and Saturn. In short, after Euler, Lagrange, D'Alembert, and Daniel Bernoulli, there are few mathematicians and natural philosophers of any age who can be put in competition with him, and still fewer who benefited the public by so many diversified labours.
It would be hopeless to attempt to pursue his indefatigable pen through all its wanderings; and a complete catalogue of his works would be as useless as it is unattainable. A man who wrote so incessantly must have written many things which were destined to oblivion from their first production. It will be sufficient to mention the most remarkable of his works, without any very strict regard to the priority of their publication.
1. In the Acta Helvetica of the Society of Edin. II. 1752, we find an Essay on the Force and Measurement of Heat, a subject which the author resumed in the latter part of his life. 2. A General Series, somewhat resembling Taylor's, Act. Hel. III. 1758. 3. Meteorological Observations, ibid. 4. He also published a paper on the Vibration of Chords, in the same collection.
5. Les Propriétés les plus Remarquables de la Route de la Lumière par les Airs, et en général par plusieurs milieux Refringents, Hague, 1759, in 8vo; German by Tempichof, Berl. 1773. This work does credit to the ingenuity and mathematical abilities of the author, though its results may be obtained in a simpler manner by some methods more recently invented.
6. La Perspective Libre, Zurich, 1759, 8vo; another edition in German. The second German edition, 2 vols. 8vo, Zurich, 1773, contains some additional matter, especially a system of geometry, depending, as it is said, upon the ruler alone, without any other instrument. Such a system must, however, have been extremely limited in its application, much more so than Mascheroni's Geometria del Compasso.
7. Photometria, sive de Mensura et Gradibus Luminis, Colorum, et Umbrae, Augsb. 1750, 8vo. This original and interesting volume includes and supercedes the greater part of Bouguer's experimental determinations. It contains the important discovery, that a lum-
Lambert. nous surface emits its light with equal intensity in all directions; together with some improvements in the theory of twilight, and an investigation of the comparative light of the sun and moon, and stars and planets.
8. Insigniores Orbis Cometarum Proprietates, Augsb. 1761, 8vo. We here find the elegant theorem for expressing the relation of the area of a sector to the sides of the triangle inscribed in it. This theorem had been demonstrated with respect to the parabola by Euler in 1740; but Lambert first extended it to the other conic sections, and he certainly re-invented the whole, without being aware of what Euler had done. It may be found, together with a concise demonstration, and a further account of this work, in the translation of Olbers' Essay on Comets, published in the Journal of the Royal Institution.
9. Cosmologische Briefe, Augsb. 1761, 8vo. A French translation of these Letters on the Universe appeared in the Journal Hérétique de Neuchâtel, 1763-4; an extract was published by Merian, with the title of Système du Monde, Bouillon, 1770, Berlin, 1784, in 8vo; and a translation by Darquier appeared at Amsterdam, 1801, in 8vo. The whole work is written in a popular style, and adapted to the taste of general readers. The author's favourite idea was to make the sun a sort of planet, revolving round some other great body; and he supports the opinion by an argument derived from the supposed insufficiency of the laws of gravity, as relating to the solar system, for explaining some of the inequalities of the motions of Jupiter and Saturn, which have, however, since been reduced to the general analogy by Lagrange and Laplace.
10. Zusätze zum Traité de Nivellement Von Picard, 12th August 1761, explaining some improvements on Picard's level, executed by Brandt, an ingenious artist, whom Lambert also assisted in the improvement of Gunter's sliding rule. 11. He published an explanation of this scale, entitled Logarithmische Rechenstabe, 12th August 1761.
12. Remarks on Incommensurable Quantities, Mém. Ac. Berl. 1761. A demonstration of the incommensurability of the circumference of a circle to its diameter, which has been adopted by Legendre in his Geometry. It depends on the method of reducing a fraction to its lowest terms, as laid down by Euclid, and on the properties of continual fractions; an expression is obtained for a tangent in terms of the arc from the quotient of the series for the sine and cosine, and the continual fraction thus obtained is proved to be infinite. It is also shown that the ratio of the arc to its tangent can never be expressed by any finite quadratic surds. 13. On the Specific Gravity of Salt, and of its Solutions, M. Berl. 1762.
14. Novum Organum, Leipzig, 1763, in German, two vols. 8vo. An attempt to restore and improve the Aristotelian method of syllogism, in which the author is allowed to have displayed much ingenuity, though its success was greatly limited, on the one hand, by the sober good sense of the empirical reasoners of the school of Bacon and Locke, and on the other, by the wild enthusiasm of the German innovators, who were beginning to be intoxicated with the high-sounding phrases and exaggerated pretensions of the disciples of Kant. A manuscript Latin translation of the work, by Pfleiderer, was once in the possession of the late Lord Stanhope.
15. A paper on Trigonometry appears in the Nov. Acta Eruditorum for 1763. 16. In the Berlin Memoirs for the same year, we find an Essay on Acoustic Instruments, investigating the best forms for hearing-trumps. 17. Remarks on the Properties of Equations of all Degrees. 18. On Divisors of Equations, which may be found without solving them. 19. On some Measurements relating to the Intellectual World; that is, on probabilities and expectations.
20. Beiträge zur Mathematik, Berlin, 1765, 1770, 1772, in four vols. 8vo: a collection of essays on every department of mathematical science. The first volume contains Remarks on Trigonometry and on the Certainty of Observations: on the Divisors of Numbers, and on Annuities; the second, Tables of the Moon; an Essay on Dialling, and on Geographical Projections, with the Elements of Tetragonometry, a subject which was afterwards resumed by the younger Mayer; in the third volume there is an Essay on Interpolation, Remarks on Celestial Maps, with other articles.
21. Description of a Table of Eclipses, Berl. 1765, with the easiest mode of computing them. 22. In the Memoirs of the Academy of Berlin for 1765, we have a paper on Projectiles, including the effect of resistance. 23. In those of the Academy of Berlin for the same year, some remarks on the Improvement of Terrestrial Measurements; and, 24. Meteorological Observations. 25. In the Nov. Acta Erud. for 1765, an attempt to employ Calculation in the Moral Sciences. 26. On the Magnet, Ac. Berl. 1766. 27. Another paper on Magnetic Currents. 28. A Magnetic Chart was published separately the same year. 29. Remarks on the General Outlines of the Ocean, Ac. Berl. 1767. 30. A General
Solution of the Problem of Three Bodies by means of Series, ibid. Lambert. 31. Notes on Richer's Philosophical Algebra, 1767.
32. Remarks on the Velocity of Sound, M. Ac. Berl. 1768; an unsuccessful attempt to reconcile the theory with observation. It was reserved for Laplace, by a single happy suggestion, to remove the whole difficulty. 33. On Photometry, as applied to Painting, ibid. 34. Trigonometrical Observations, ibid.
35. De Topici Schediis, 1768. 36. Remarks on the Divisors of Numbers, Nov. Act. Erud. 1769. 37. Anmerkungen über die Branderschen Micrometern, Augsb. 1769. Brandt's micrometers were of glass.
38. Experiments on Hygrometry, M. Acad. Berl. 1769; relating to evaporation, and to the indications of hygrometers, especially those of catgut.
39. Supplementa Tabularum Logarithmicarum, 8vo, Berl. 1770; with a valuable introduction in German, on the abridgment of computations.
40. Anmerkungen über die kraft des Schießpulvers, 8vo, Berl. 1770. In this investigation of the force of fired gunpowder, the author attacks several points in the theory of Robins, published a few years before.
41. Hygrometrie, 4to, Augsb. 1770.
42. On Divisors for the Light of Lamps, M. Acad. Berl. 1770.
43. On Ink and Paper, ibid. 44. Analytical Observations, ibid.; relating to the general theorem resembling Taylor's, which was further discussed by Euler, and modified by Lagrange. 45. On Taxometry, or the Measurement of Order, ibid.; considered as comparable in degree, and expressible by numbers.
46. Architectonik, 2 vols. 8vo, Riga, 1771; a logical and metaphysical treatise on the most simple bases of philosophical and mathematical knowledge, written in 1763. The last part, which relates to magnitude, is the most approved; but the whole work was never much read, being partly superseded by the more ostentatious novelties of the day.
47. In the Berlin Memoirs for 1771, we find papers on Meteorology. 48. On the Atmospheric Influence of the Moon. 49. On Achromatic Telescopes of one kind of Glass only. 50. On the Apparent Paths of Comets. 51. On the Grounds of Superstitious Belief, as compared with Probability.
52. Ueber das Farbenpyramide, 8vo, Berl. 1772; a description of a pyramid of wax, intended for the illustration of all the possible varieties of combination of the primitive colours.
53. Astronomisches Jahrbuch, Berl. 1774-9, in 8vo; an accurate and extensive ephemeris, with many original communications annexed to it.
54. In the M. A. Berl. 1772, a paper on Friction; supposed to follow the law of the resistance of fluids, with some remarks on that resistance. The opinion of the uniformity of the force of friction, which was even at that time general, was somewhat too hastily rejected by the author; but his computations may still be of use in some cases. 55. On the Fluidity of Sand; as resisting motion. 56. On Hygrometry; continued. 57. On the Density of the Air, with respect to sound and to refraction.
58. M. A. Berl. 1773: A Ballistic Scale, for determining the paths of projectiles in the atmosphere. 59. Physical Observations, relating to Meteorology and to Optics. 60. On the Satellite of Venus; affording a remarkable instance of misapplied labour and ingenuity. 61. A Second Essay on Taxometry. 62. A Note on the Inequalities of Jupiter and Saturn; intended to confirm the principles advanced in the Cosmological Letters. The detail was reserved for a subsequent volume.
63. M. A. Berl. 1774: On the Temperament of Musical Instruments. 64. On the Aerial Perspective. 65. Report on a Bedstead for Sick Persons.
66. M. A. Berl. 1775: On the Elasticity of the Air. 67. On Wind-mills, and on the Force of the Wind. 68. On the Sounds of Flutes; an elaborate comparison of the various tones of a flute, with the theory of Daniel Bernoulli for determining the sounds of compound organ-pipes.
69. M. A. Berl. 1776: On the Strength of Men employed in Labour. 70. On Imperfect Fluids.
71. M. A. Berl. 1777: On the Elasticity of the Air.
72. M. A. Berl. 1779: Two Memoirs on the Inequalities of Jupiter and Saturn.
73. Pyrometrie, 4to, Berl. 1779; a posthumous work, upon a subject which had long occupied the author's attention; with a Preface by Karsten, and a Biographical Memoir by Eberhard.
74. A Paper on Annuities, Leips. Magaz. 1780.
75. Deutscher Gelehrter Briefwechsel, Berl. 1781-7, in 5 vols. 8vo; published by John Bernoulli, and consisting principally of the author's correspondence with Holland, Kant, Karsten, Segner, Basedow, Scheibel, and Brandt. The contents are more fully described by Lalande. Bibl. Aut. p. 581.
76. M. A. Berl. 1783: On Friction.
Lambourn
I
Lamennais.
77. Logische und Philosophische Abhandlungen, Berl. 1787, in 2 vols. 8vo. Edited by J. Bernoulli.
78. On the Theory of Parallel Lines, Hindenburg, Arch. der Math. 1. (Bernoulli in Neues Litteraires, 8vo, Berl. 1777; Eberhard in Pyrametris Briefwechsel, III., Phil. Mag. May 1804; Atkin's General Biography, vi. 4to. Lond. 1807; Servius in Biographie Universelle, xxiii., 8vo, Par. 1819.) (T. Y.)