Studies in the History of Probability and Statistics. XXVI

SUMMARY Mr 0. B. Sheynin has recently called attention to a most remarkable paper by Ernst Abbe, presented in 1863, in which Abbe derives not only the x2 distribution, but R. L. Ander- son's (1942) distribution of the serial correlation coefficient. The paper itself is rather long, but an abstract is given as ? 2 of this note. The paper is a superbly competent piece of work and perhaps the most remarkable anticipation of later studies of distribution theory that has yet come to light. Abbe was born in 1840, the son of a master spinner at Eisenach. His childhood was one of privation; his father worked on his feet 16 hours every day with no break for meals. Ernst, however, won scholarships and was helped through his studies by his father's employer. He received his doctorate at Jena at the age of 21 with a dissertation on thermo- dynamics. Two years later he was appointed professor, the paper under notice here being a dissertation for the acquisition of Venia Docendi in the Faculty of Philosophy. What further contributions Abbe might have made to distribution theory must remain a matter of speculation. In 1866, at the age of 26, he was approached by Carl Zeiss with some optical problems and the remainder of his life was spent in theoretical and practical research in optics and astronomy. He is, in fact, an outstanding example of scientific genius combined with practical inventiveness. Moreover, when he became a wealthy man in later life, having been taken into partnership by Zeiss, he introduced into industrial relations measures which were not to become general for another half-century, the eight-hour day, paid vacations, sick-benefit, pensions, severance pay, annual bonuses among others. The dissertation, an abstract of which follows, is published in Abbe's collected works (1906). For the biographical details I am indebted to the extensive account of his life and works by Volkmann (1966). I cannot find that Abbe ever returned to the subject of the dissertation, but he was never eager to publish his work and his private papers, if they still survive, might possibly contain something of interest.