calculation, there are two manuscripts, one deposited at the Observatory, and the other in the library of the Institute, at Paris. Each of the two manuscripts consists essentially of seventeen large folio volumes, the contents being as follows:-- Logarithms of numbers up to 200,000 8 vols. Natural sines 1 " Logarithms of the ratios of arcs to sines from 0^q.00000 to 0^q.05000, and log sines throughout the quadrant 4 " Logarithms of the ratios of arcs to tangents from 0^q.00000 to 0^q.05000, and log tangents throughout the quadrant 4 " The trigonometrical results are given for every hundred-thousandth of the quadrant (10´´ centesimal or 3´´.24 sexagesimal). The tables were all calculated to 14 places, with the intention that only 12 should be published, but the twelfth figure is not to be relied upon. The tables have never been published, and are generally known as the _Tables du Cadastre_, or, in England, as the great French manuscript tables. A very full account of these tables, with an explanation of the methods of calculation, formulae employed, &c., was published by Lefort in vol. iv. of the _Annales de l'observatoire de Paris_. The printing of the table of natural sines was once begun, and Lefort states that he has seen six copies, all incomplete, although including the last page. Babbage compared his table with the _Tables du Cadastre_, and Lefort has given in his paper just referred to most important lists of errors in Vlacq's and Briggs's logarithms of numbers which were obtained by comparing the manuscript tables with those contained in the _Arithmetica logarithmica_ of 1624 and of 1628. As the _Tables du Cadastre_ remained unpublished, other tables appeared in which the quadrant was divided centesimally, the most important of these being Hobert and Ideler's _Nouvelles tables trigonométriques_ (1799), and Borda and Delambre's _Tables trigonométriques décimales_ (1800-1801), both of which are seven-figure tables. The latter work, which was much used, being difficult to procure, and greater accuracy being required, the French government in 1891 published an eight-figure centesimal table, for every ten seconds, derived from the _Tables du Cadastre_.