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By R. Bartoszyński, J. Łoś, M. Wycech-Łoś (auth.), Jerzy Neyman, Lucien M. Le Cam (eds.)

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Additional info for Bernoulli 1713, Bayes 1763, Laplace 1813: Anniversary Volume. Proceedings of an International Research Seminar Statistical Laboratory University of California, Berkeley 1963

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He adds "I should naturally have waited so that the researches of M. DE LAGRANGE could be published before mine but having just written on the subject, I want to communicate this as a supplement to it, which is all that was wanting to make it complete, besides rendering to the memoir of M. " LAGRANGE took all this very well, and indeed, apart from his lapse over THOMAS SIMPSON, he seems to have been an admirable person in every way. He wrote with the usual florid politeness of the day to LAPLACE, and bowed himself out of that particular line of research, but he remained friendly with him all his life.

L' ((IY,) TM ...... N (0,1), as t ...... 00. By Raikov's theorem, Y~/T2 ...... 1 in probability, and since E (Y~/TII) = 1, it follows [1, p. 528] that the Y~/TII are uniformly integrable. But then Y ...... 0 as t ...... 00. On the other hand, 11< maxEY~ (X = T2 The corollary follows from the first inequality in the theorem. Proof of Corollary 2. The hypotheses imply that 8 ~ minEY~ ~ maxEY~ ~ Vk ~~, E 26 ROBERT COGBURN and it follows easily that and the corollary follows from the second inequality in the theorem.

He read his first paper on astronomy to the Academy of Sciences in 1773 - it was published in 1776 - and demonstrated that apart from secular periodic variations, the mean distances of the planets from the Sun are invariable. This was a good original piece of Some Notes on Laplace 37 work for a young man of 24; he succeeded where NEWTON had been unsure and although his method of attack had been foreshadowed by LAGRANGE his pertinacity brought him reputation and started his successful career. The warmth with which the paper was received also perhaps inspired him to cheat a little.

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