1878.] Mr Glaisher, On factor tables. 121 



sentandi, verum etiam reipsa opus spatio 16 mensium usque ad 

 2,016.000 confecl, annoque 1785 (aniraatus applausu diversorum. 

 Academicorum) ad 5,000.000 usque continuavi." 



It seems to me very unlikely that Felkel continued the table 

 up to 5,000,000, and I think this last statement mvist be incorrect ; 

 possibly the 5 may be a misprint for 3, but in that case probably 

 the word 2^'^^ope would have been added. I draw particular atten- 

 tion to this matter, because it would be a very remarkable circum- 

 stance if Felkel had really carried the table as far as five millions. 

 In the British Association Report (p. 37) I have quoted without 

 remark the last statement of Felkel, merely adding a reference to 

 p. vii. of the Prcefatio Interpretis ; as I was unable to explain the 

 discrepancy, and supposed that at all events Felkel could not have 

 been mistaken in describing his own work as extending to 

 5,000,000. But I now think that the account in the Prcefatio 

 Interpretis must be the correct one. 



To continue Felkel's account of himself; he states that he 

 was sensible that so large a table could not be printed, so that his 

 jjroject of finishing the ten millions was always deferred. He 

 considered wdiether he could not devise something more portable, 

 and in 1793—1794 he constructed 15 'bases' on this number of 

 sheets, by the aid of which numbers up to 24 millions^ could be 

 resolved into their factors, the least factor not exceeding 400; and 

 he found a method of extending the table to 100 millions on 65 

 'bases.' Felkel also describes work that he performed in con- 

 nexion with periodic decimal fractions, or rather periodic fractions 

 to any radix m. He went to Lisbon in 1791. 



In a notice of the Siupplementa contained in vol, ll, of Zach's 

 Monatliche Gorresponclenz (1800), pp. 222,223, it is stated that the 

 translator is the same Felkel who published the great folio factor 

 table to 144,000. The work was ready in manuscri|)t to two 

 millions, and jDrinted to 408,000 at the cost of the Treasur3^ 

 But as there were no purchasers, the whole edition, except a few 

 copies, was used for cartridges in the Turkish war^ The manu- 

 script which was seized had at length been given back to Felkel, 



1 In the Pro Notitia, at the end, he says 24,600,000. 



- The original passage runs: "Das Werk war im Manuscript bis 2 Millionen 

 fertig, unci bis 408000 auf Kosten des k. k. Aerariums gedruckt. Weil sich aber 

 keine Abnehmer dazu fanden, so wmxle die ganze Auflage vor Ausbruch des letzten 

 Tiirkenkrieges zu Infanterie-Patronen-Papier verwendet ; nur weuige vollstandige 

 Exemplare wm-den dem Vulcan entrissen. Der Verfasser hat das Manuscript, 

 welches in Beschlag genouamen war, aus der Kriegs-Canzley wieder zuriick 

 erhalten ; gegeuwjirtig halt er sich in Lissabou auf, wo er einer, vor uns liegenden 

 Lateinischen Anklindigung zu Folge, mehrere Tabellen herauszugeben gedenkt, 

 worunter auch Factoren-Tafeln bis auf 246000000." In a review of Cheruac's 

 Crxhrum in the Gottingische gelehrte Anzeigen (1812, March 23), Gauss refers to 

 this passage, and concludes " So ging eine verdienstliche vieljahrige Arbeit fiir 

 das Publicum verloren " (Gauss, Werke, ii. p. 182), 



