1878.] Mr Glaisher, On factor tables. 105 



p. 10, Lambert distinguishes between a factor and divisor as fol- 

 lows: "I understand by factors those primes, or their powers, which 

 multiplied together give the number, ew. gr. 10,829=7^.13.17. 

 These factors have the advantage that all the other divisors 

 (Theiler) can be easily found, for 7 . 7 = 49, 7 . 13 = 91, 7.17 = 119, 

 13 . 17 = 221, 7.7.13 = 637, 7 . 7 . 17 = 833, 7.13.17 = 1,547 are 

 the other divisors." This definition does not appear to be very 

 generally followed, and factor and divisor seem to be used merely 

 to denote any number that divides the given number without re- 

 mainder. 



§ 4. Chernac at the end of his historical notice upon factor tables 

 states that he has not been able to see Felkel's table, but that 

 Krause states that letters of the alphabet are employed in it to 

 denote the divisors. The table is so curious and rare, and, 

 besides, the facts connected with its calculation and publication 

 are so remarkable that I here give an account in some detail. 



Of the work itself I have seen only two copies ; one of which 

 belongs to the Royal Society, and the other to the Graves 

 Library, at University College, London. The former has a German 

 title-page. "Tafel aller Einfachen Factoren der durch 2, 3, 5 

 nicht theilbaren Zahlen von 1 bis 10 000 000. Entworfen von 

 Anton Felkel, Lehrer an der k. k. Normalschule. I. Theil. Ent- 

 haltend die Factoren von 1 bis 144000. Wien, mit von Ghelen- 

 schen Schriften gedruckt 1776 ;" the introduction is in German, 

 and is dated " Wien den 30. September 1776." There are 26 

 large folio pages of tabular matter, giving all the prime factors of 

 numbers up to 144,000. The Graves copy has the Latin title- 

 page, "Tabula omnium factorum simplicium, numerorum per 2, 3, 

 5 non divisibilium ab 1 usque 10 000 000. Elaborata ab Antonio 

 Felkel. Pars I. Exhibens factores ab 1 usque 144000. Vindo- 

 bonie, ex typographia a Gheleniana 1776." The introduction is 

 also in Latin, and is dated "Yiennee, die 1 Aprilis, 1777." 

 This is followed by 58 pages of tables, giving the least factors of 

 numbers up to 336,000 ; and then occurs a fresh title-page, 

 " Tabula factorum. Pars III. Exhibens factores numerorum ab 

 336001 usque 408000." [The figures '336' and '408' are 

 evidently printed over the figures ' 144 ' and ' 336 ' which have 

 been partially obliterated, and the first stroke of the III. in ' Pars 

 III.' is a little out of its place, and seems to have been added 

 subsequently.] After the title-page to part III. there are 12 pages 

 of tables, giving the factors of the numbers from 336,000 to 

 408,000. 



The contents of the German and Latin introductions are sub- 

 stantially the same, but the latter contains an errata-list which 

 does not appear in the former. 



