On the Tchebychef Inequality of Bernstein

This gives a lower limit for P which is often unsatisfactory. Improvement of this result requires further hypotheses. As is well-known, Pearson, Camp, Guldberg, Meidel, Narumi,2 and Smith8 have attacked this problem with considerable success. Another interesting and important attempt in this direction due to S. Bernstein seems to have generally escaped attention in the English-speaking world, at least, since it has been published only ill Russian.4 Because of the latter fact, it seems necessary to give