1878.] Mr Glaisher, On factor tables. 113 



nouncedS He concludes with the words "Die Sache durfte 

 kiinftig in der Geschichte der Mathematik einen ziemlicben Raum 

 einnehmen." This closes the correspondence with Rosenthal, and 

 there is no further information about Oberreit's table and its 

 continuation in this volume ; but in the first volume of the 

 Brief wechsel (no date, but preface dated 1781) Bernoulli states 

 that at that time Oberreit's manuscript was in the hands of 

 Professor Schulze, of Berlin. This is the Schulze who published 

 in 1778 the well known 'Sammlung logarithmischer, trigonome- 

 trischer und anderer. ..Tafeln.' In his letter to Dase, printed in 

 the introduction to the seventh million (§ 17), Gauss speaks of 

 'Rosenthal's manuscript to 750,000 which was in Kastner's hands,' 

 The full sentence is, " So hatte z. B. Oberreit die Tafel bis 500000 

 berechnet und in Lambert's Hande gelegt ; Rosenthal eine bis 

 750000, die in Kastner's Handen w'ar." But, as we have seen, 

 Rosenthal's work was only a continuation of Oberreit's, and ex- 

 tended from 725,000 or 750,000 to 1,000,000. 



§ 8, The correspondence with Felkel consists of 13 letters, 

 and there is an appendix by the editor, the whole occupying 

 pp. 33 — 134. All Felkel's letters relate either to his table, which 

 has been described in § 4, or to his machine, and are written 

 from Vienna. His first letter is dated January 15, 1776. He 

 states that he is induced to write to Lambert by the contents of 

 §§ 15, 16 of the Beytrdge, and that he has found a method of 

 exhibiting all the [prime] factors of the numbers not divisible 

 by 2, 3 or 5 from 1 to 144,000 on 12 ordinary sheets of paper, so 

 that any one can see the factors at a glanced He also mentions 

 his machine, made of I'ods, by means of which he believes that 

 the table could be continued to 1,000,000 in the space of a year. 

 There is also added a draft announcement or advertisement, for 

 obtaining subscribers for the table from 1 to 144,000, in which 

 it is stated that if the table be favourably received the con- 

 tinuation to 1,000,000 will be published within a year. He 

 submits this to Lambert and asks for his support. After this 

 request has been made a second time, Lambert replies as we 

 know, suggesting that as the first million is being calculated by 



1 The whole sentence is worth quoting: " Diese Herren wollen, wie es scheint, 

 einander zuvorkommen, anstatt dass unstreitig besser ware, wenn der eine da 

 anfienge, wo der andere aufhoret. Der eine riihmt seine Maschine, der andere 

 seine Methode. Die Zeit muss lehren, was an beiden ist, und was dann ferner zu 

 thun seyn wird. Noch ist die Frage, ob nicht noch mehrere mit solchen Tafeln 

 hervorriicken werden. Die Saclie durfte kiinftig in der Geschichte der Mathematik 

 einen ziemlichen Raum einnehmen." (Briefwechsel, v. p. 30.) 



^ The words are "dass man solche mit dem ersten Blicke finden kann." It 

 will be seen from the description given of the mode of using the table in § 4 that 

 this is rather an exaggeration. The 12 sheets (Bogen) are the 24 folio pp. forming 

 the principal table. 



