"Mannert, K., de Numerorum, quos arabicos voc., vera origine pythagorico; e. Fig. aen. 8vo. Nürnberg, 1801." Oscar Heun. Cambridge, Feb. 11. 1850. _Arabic Numerals_ (No. 15. p. 230.).--Your correspondent should consult Peacock's "History of Arithmetic" in the _Encyclopædia Metropolitana_; and, if he can get them, the notes to Chasles' _Aperçu Historique des Méthodes en Géométric_, and various papers of Mr. Chasles, published in the _Comptes Rendus_ of the French Institute. He may perhaps find some information in De Morgan's _Arithmetical Books_, particularly at p. 14. M. * * * * * THE FRATERNITY OF CHRISTIAN DOCTRINE--CHAUCER'S NIGHT CHARM. In a little work by Costanzi, entitled _Le Istituzioni di Pieta che si esercitano in Roma_, &c., and published A.D. 1825, in Rome, where the schools under the management of that brotherhood are in great favour, "C.F.S." will find much to interest him on the subject, though not exactly in the order in which he has put his queries (No. 14. p. 214.), nor to their full extent. Mr. Thoms, to whom English mediæval literature is so much beholden, asks very earnestly for some information about "the white Paternoster" and "seynte Petres soster," (No. 15. p. 229.). Perhaps the following guesses may not be without use. First, then, about the "white Paternoster:" Henry Parker, a Carmelite friar of Doncaster, who wrote his admirable _Compendiouse Treatyse, or Dialogue of Dives and Pauper_, during the reign of Edward IV., speaking against superstitions, and especially "craftes and conjurations with holy prayers," says: "They that use holy wordes of the gospel, Pater noster, Ave, or Crede, or holy prayers in theyr wytchecraftes, for charmes or conjurations--they make a full hye sacrifice to the fende. It hath oft ben knowen, that wytches, with sayenge of their Pater noster and droppynge of the holy candell in a man's steppes that they hated, hath done his fete rotton of. Dr. What should the Pater noster, and the holy candell do therto? Pau. Ryght nought. But for the wytche worshyppeth the fende so highly with the holy prayers, and with the holy candell, and used suche holy thinges in despyte of God therefore is the fende redy to do the wytche's wylle and to fulfyll thinges that they done it for. 'The Fyrst Command,' cap. XXXV. Fol. 52. Imprynted by T. Berthelet, 1536. 12mo." That the Pater noster used sometimes to be said with the wicked design of working ill to individuals, and by those who were deemed witches, is clear form the above extract: may not, then, this "wytche's" Pater noster be the "white" Pater noster, against which the night-spell in Chaucer was employed? "Wyche" may easily be imagined to have glided into "white."