In 1761 he published at Augsburg a valuable work entitled 'Insigniores Orbitaa Cometarum Proprietates,' Svo, in which are con tained a formula for determining, in a parabolic orbit, the perihelion distance in terms of two radii vectorce and the difference between the anomalies, and one iu which, the orbit being any conic section, the interval between two times of observation is expressed iu terms of the two radii and the chord which joins their extremities. This is usually called Lambert's Theorem,' and it was certainly discovered by him, though Euler had, long before, given a like theorem for a parabolic orbit. In the same year Lambert published at Augsburg a small work entitled 'Logarklnische Reobenstcole,' in which are proposed some improvements on Gunter's ' Scale ; ' and one entitled Kosmulogische Briefe ueber die Einrichtuog des Welthaus,' Svo, in which be considers that the notion of gravity extends to the fixed eters; and he expresses a conjecture that the solar system may be only a system of satellites with respect to some celestial body.
In 1764 was published, at Leipzig, in 2 vole. 8vo, Lamberre philosophical work entitled I Neues Organon ; ' this is divided Into four parts, of which the first contains the rules of thinking, and the second is on truth considered in its elements; the third is on the external characters of truth; and the fourth, on the means of dis tinguishing the real from the apparent. A sort of supplement to this work was published by him at Riga in 1771, in 2 vols. Svo; it is entitled Archltektonik,' and treats of the metaphysics of mathe matics; the subjects being Unity, Number, Dimensions, Continuity, Limits, and Infinity.
The first mathematical work which Lambert published after he went to reside at Berlin was his ' Beytriige mutt Gebrauche der Mathematik and deren Andweudung ' (3 vols. Svo, 1765 to 1772). This contains some profound Investigations relating to the theory of numbers, and a tract on trigonometry, with notices on what is called tetragonometry ; in it are giveu also soma remarkable propositions relating to the projections of the sphere. In the first of those years
he published 'Description dune Table Ecliptlque ferment un Tableau vrai de touter lee Eclipses, tent de In Lune quo de la Terre;' and in 1770 appeared his Zusdtze zu den Logarithmlscben and Trigouo metriecheo Tabellen,' Svo. He was joined with Bode, Schultze, and Lagrange In the publication (1776), uuder the direction of the Academy of Berlin, of a aeries of Astronomical Tables.
Lambert also wrote a tract on 'Hygrometry,' which was published at Augsburg in 1770 ; and he left one on Pyrometry, which was pub lished at Berlin, in 1779, that is, after his death ; this last contains a biography of the author, by Everhard. Besides these works Lambert wrote numerous papers on scientific' subjects, which were published in the 'Aota Helvetica' and io the '31dmoires ' of the Academy of Berlin. Among the 'Acta' are his Tentamen tie Vi Caloris ejusque Dimension° ; ' a series which goes by his name, and which was after wards generalised by Lagrange, and a 'Memoir on Vibrating Strings.' The ‘Mdmoires' of the Academy contain his papers on the Incom measurability of the Circumference of a Circle to its Diameter ; on Duman Strength ; on Ilydraulic Wheels ; on Windmills; and on Friction. He moreover prepared two papers in which he had dis cussed all the known observations on Jupiter and Saturn; and these were published in the same ' 316moires' two years after his death.
Lambert was endowed with a strong memory and a fertile and well-regulated imagination : his manners were simple, and he ie said, in his dress, to have disregarded the fashions of the time; but be was both esteemed and beloved by those who knew him intimately. He died September 25, 1777, being then only forty-nine years of age. All the manuscripts left by him were purchased by the Academy of Berlin, and were subsequently published by John Bcrnouilli, a grandson of the celebrated John Bernouilli of Basel.