1878.] Mr Qlaisher, On factor tables. 115 



ein Yorbericht zur ausfiihrliclien Besdireibung der nenen Fac- 

 torentafeln und ihrer Berechnungsart.' This is not a draft of tliat 

 which actually appears as an introduction to Felkel's Table, which 

 is very different. I have quoted the title in full, because it 

 contains the first formaP mention of the extension of the table 

 to 10 millions. The date at the end of the Nachricht is June 1, 

 1776, but as Bernoulli remarks in a note, this is extraordinary, 

 as the date of the letter is September 10, and Felkel did not 

 allude to it in his letter of June 24. 



It seemed to me likely that the extension of the limit to 10. 

 millions both in this Nachricht and also in the title of the work^ 

 itself was due to the announcement of Hindenburg's table, which 

 was to extend to 5 millions ; and that if the latter had not ap- 

 peared Felkel would have fixed 2 millions as the limit or would 

 have fixed no limit at all. But this is not the case, for in a letter 

 of August 13, the day on which Lambert sent Hindenburg's 

 circular to Felkel, he also writes to Hindenburg and says that 

 Felkel in a recently printed circular has spoken of 10 millions ^ 

 In a note, the words (added on the margin of a Latin circular of 

 date June 10, 1776) are given as ' Tabulae continuantur usque ad 10 

 Milliones ; et priBterea primas Millionis omnes factores singillatim 

 exponuntur.' It thus appears that the proposed extension to 10 

 millions was not suggested by a desire to surpass Hindenburg. 

 Felkel was very enthusiastic, and infatuated with his system of calcu- 

 lation ; he continually speaks of the ' natural beauty of his plan,' &c. 

 In a letter to Hindenburg of October 5, 1776, Lambert remarks that 

 Felkel is always printing circulars instead of the table itself, from 

 which he infers that Felkel does not receive so much support at 

 Vienna as he expected ; and in a letter of September 27 Hinden- 

 burg says that it is certain that Felkel has safely received the 

 announcement of his table, as his own words occur in Felkel's new 

 Nachricht. It seems clear from the correspondence that when 



1 In this very first letter to Lambert (January 15, 1776), Felkel, after saying 

 that by the aid of his machine he can extend the table to a million within a year, 

 proceeds : "Und da die Zeit noch mehrere Vortheile anbieten diirfte; so will ich 

 die Hofnung nicht aufgeben, solche innerhalb mehreren Jahren auch bis 10 

 Millionen darzustellen " {Briefwechsel, v. p. 37). 



^ The fact that Felkel's title-page describes his table as extending to 10 

 millions has often led to mistakes, as it has been supposed by writers who have 

 not seen the book to actually reach tliis extent ; and Muxhard even, by a misprint, 

 no doubt, speaks of the table as extending to 100,000,000. 



^ The words are worth quoting: "Ich erwarte hierauf keine andere Antwort, 

 als dass Herr Felkel selbst dieser Dritte seyn werde. Denn in einer neuen gedrukten 

 Nachricht hat er bereits von 10 Millionen gesprochen. Erist so voUer Triumph, 

 dass die Ersparung von Zeit und unnothiger Miihe gar keinen Eindruck auf ihn 

 macht, und dass er sich auch nicht besinnt, dass eigentlich mehr seine Methode 

 und Maschine, als ein unnothiger Gebrauch derselben ihn beriihmt macheu 

 konnen " {BriefwecJisel, v. p. 152), 



Vol. in. Pt. iv. 9 



