120 Mr Olaisher, On factor tables. [Feb, 11, 



page of the printed table \ The next three paragraphs, as they 

 are important, and as also they are obscure in places, I quote 

 in full : _ 



" Quo in negotio ne conamina aliorum unita, aut deliberationes 

 jam superfluse moram aut pra^ventionem causarent, ojopressi omnes, 

 absolutis una manu duabus millionibus spatio 16 mensium, ex- 

 positisque prseter consuetudinem aliorum omnibus cujusvis numeri 

 Factoribus ; subministrante pro typo sine mora incepto impensas 

 Imperatore Josepho II. 



"Effectus supra omnium fidem fuit, doloque extraneorum centre 

 eruditionis propiorum prsevalente desistendum a typo ad 408000 

 progresso, reconditis Tabulis in serario Principle. 



" Cognita tandem methodi meas prsestantia anno 1784 a di- 

 versis Academicis extraneis prgeprimis Berolinensibus, concurrenti- 

 busque in partem operis reformat! (nomine : Tahulce Factorwn 

 redidivce) nee recepto prime Originali ad hunc finem necessario, 

 anno 1785 computavi pro secunda vice, spatio temporis angustiore 

 Tabulas Factorum usque ad septuplum impressarum, seu ad limi- 

 tem 2,856.000. Et hoc intuitu certum est me prope 5 Millionum 

 computatarum auctorem extitisse." 



Here Felkel says that the two millions required 16 months 

 to calculate, while in the circular upon the wideraujiehende Tafeln 

 he said the "work grew from nothing to over two millions within 

 18 months." It does not seem to be clear to what ' oppressi omnes' 

 refers, nor how the "craft of foreigners nearer to the centre of 

 erudition" caused the cessation of the printing at 408,000, nor 

 why the tables were retained in the Treasury. 



Felkel's method no doubt became known to the Berlin mathe- 

 maticians in 1784 through Bernoulli's researches in connexion 

 with the publication of Lambert's correspondence. 



It will be seen that Felkel here distinctly states that in 

 1775 — 1776 he had continued the table to two millions, and this 

 is in complete agreement with what is stated in the correspondence 

 with Lambert and in the Kachricht von den wiederauflehenden 

 F actor entafeln. Also in 1785 he calculated the table de novo from 

 1 to 2,856,000, this latter number being as he states seven 

 times 408,000, so that there is no possibility of a misprint. The 

 two millions added to 2,856,000 give nearly 5 millions, and 

 this is, without any doubt, what Felkel means when he says 

 " prope 5 millionum computatarum auctorem extitisse." But in a 

 note to p. xiv. of the Introductio he states distinctly that in 1785 

 he had calculated the table from 1 to 5 millions. His words are 

 "non solum inveni formam omnes divisores numerorum, excepto 

 maximo, ab 1 usque 1,008.000 in spatio 42 plagularum repra;- 



^ See Brief 10 eclisel, v. p. 232. 



