PAFNUTIY LVOVICH

CHEBICHEV (1821-1894)  , Russian mathematician, was born at Borovsk on the 26th of May 1821 . He was educated at the university of Moscow, and in 1859 became professor of mathematics in the university of St Peters-burg, a position from which he retired in 1880 . He was chosen a correspondent of the Institute of France in 186o, and succeeded to the high honour of associe etranger in 1874 . He was also a foreign member of the Royal Society of London . After N . I . Lobachevskiy he probably ranks as the most distinguished mathematician Russia has produced . In 1841 he published a valuable paper, " Sur la convergence de la serie de Taylor," in Crelle's Journal . His best-known papers, however, deal with prime numbers; in one of these ("Sur les nombres premiers," 185o) he established the existence of limits within which must be comprised the sum of the logarithms of the primes inferior to a given number . Another question to which he devoted much attention was that of obtaining rectilinear motion by linkage . The parallel motion known by his name is a three-bar linkage, which gives a very close approximation to exact rectilinear motion, but in spite of all his efforts he failed to devise one that produced absolutely true rectilinear motion . At last, indeed, he came to the conclusion that to do so was impossible, and in that conviction set to work to find a rigorous proof of the impossibility .

While he was engaged on this task the desired linkage, which moved the highest admiration of J . J .

Sylvester, was discovered and exhibited to him by one of his pupils, named Lipkin, who, however, it was afterwards found, had been anticipated by A . Peaucellier . Chebichev further constructed an instrument for drawing large circles, and an arithmetical machine with continuous motion . His mathematical writings, which account for some forty entries in the Royal Society's catalogue of scientific papers, cover a wide range of subjects, such as the theory of probabilities, quadratic forms, theory of integrals, gearings, the construction of geographical maps, &c . He also published a Traite de la theorie des nombres . He died at St Petersburg on the 8th of December 1894 .