(William), who made so much noise early in this century, was born at Auxerre. He followed King Philip V., whose confessor he was, into Spain. He had the greatest influence with that prince until the courtiers, jealous of his power, prevailed upon the king to send him from court in 1706. By dint of solicitations, however, he was recalled in 1716, reinstated in his office, and then enjoyed more power than before. It is said, that when Philip V. disputed with his throne, wished to abdicate it, he confided his design to Daubenton; that the latter, fearing that he should be obliged to follow him to his retreat, discovered this secret to the Duke of Orleans, regent of France, who was at that time projecting the double marriage of Mademoiselle de Montpensier his daughter, with the Prince of Asturias, and that of Louis the XV. with the infanta, five years of age. It is added, that the Jesuit believed it would be for the interest of the Duke of Orleans to dissuade Philip from his purpose; that the Duke of Orleans sent the confessor's letter to the king, who showed it to Daubenton, without saying a single word; that the confessor put a very different construction upon it; that an apoplexy seized him on going out of the chamber; and that he died a short time after in 1723, in the 75th year of his age. This story (for the truth of which we will avouch still the less, that it is not mentioned by the Marquis de Noailles in his memoirs) is related by the author of the Age of Louis XV., who quotes the civil history of Bellando, page 306, Part IV. It is only clear from the memoirs of Noailles, that Daubenton opposed the abdication of the King of Spain. The Abbe Grolier, in a letter inserted in the Annales Litteraires (1777, N° 18.), denies, 179, That Daubenton had revealed to the regent any secret entrusted to him by Philip V. in confession. 240, That this Jesuit died, as Voltaire makes him from the authority of Bellando, an inaccurate historian, whose works were suppressed in Spain. 316, He pretends that Daubenton, far from being a man of intrigue, an ambitious monk, and capable of opposing the abdication of Philip, in order to prevent himself from being removed from court, had solicited permission to leave it several years before. We refer the reader to that Decimals letter, which deserves to be read for the sound criticism which it contains. This Jesuit had preached with some success. There are extant some tolerable funeral orations of his, and a life of St Francois Regis, 12mo.
CIRCULATING DECIMALS, called also recurring or repeating decimals, are those in which a figure or several figures are continually repeated. They are distinguished into single and multiple, and these again into pure and mixed.
A pure single circulate is that in which one figure only is repeated; as .222 &c. and is marked thus .2.
A pure multiple circulate is that in which several figures are continually repeated; as .232323 &c. marked .23; and .524524 &c. marked .524.
A mixed single circulate is that which consists of a terminate part, and a single repeating figure; as 4.222 &c. or 4.2. And
A mixed multiple circulate is that which contains a terminate part with several repeating figures; as 45.524.
That part of the circulate which repeats is called the repetend; and the whole repetend, supposed infinitely continued, is equal to a vulgar fraction, whose numerator is the repeating number or figures, and its denominator the same number of nines: so .2 is = \(\frac{2}{9}\); and .23 is = \(\frac{23}{99}\); and .524 is = \(\frac{524}{999}\).
It seems it was Dr Wallis who first distinctly considered or treated of infinite circulating decimals, as he himself informs us in his Treatise of Infinites. Since his time many other authors have treated on this part of arithmetic; the principal of these, however, to whom the art is mostly indebted, are Messrs Brown, Cunn, Martin, Emerson, Malcolm, Domn, and Henry Clarke, in whose writings the nature and practice of this art may be fully seen, especially in the last mentioned ingenious author.