the explanation of the motion of the lunar apsides. This motion, left unexplained by Newton, seemed to him at first inexplicable by Newton's law, and he was on the point of advancing a new hypothesis regarding gravitation, when, taking the precaution to carry his calculation to a higher degree of approximation, he reached results agreeing with observation. The motion of the moon was studied about the same time by Euler and D^Alembert. Clairaut predicted that "Halley's Comet," then expected to return, would arrive at its nearest point to the sun on April 13, 1759, a date which turned out to be one month too late. He was the first to detect singular solutions in differential equations of the first order but of higher degree than the first.
In their scientific labours there was between Clairaut and D'Alembert great rivalry, often far from friendly. The growing ambition of Clairaut to shine in society, where he was a great favourite, hindered his scientific work in the latter part of his life.
Johann Heinrich Lambert (1728–1777), born at Mühlhausen in Alsace, was the son of a poor tailor. While working at his father's trade, he acquired through his own unaided efforts a knowledge of elementary mathematics. At the age of thirty he became tutor in a Swiss family and secured leisure to continue his studies. In his travels with his pupils through Europe he became acquainted with the leading mathematicians. In 1764 he settled in Berlin, where he became member of the Academy, and enjoyed the society of Euler and Lagrange. He received a small pension, and later became editor of the Berlin Ephemeris. His many-sided scholarship reminds one of Leibniz. In his Cosmological Letters he made some remarkable prophecies regarding the stellar system. In mathematics he made several discoveries which were extended and overshadowed by his great contemporaries. His first research on pure mathe-
