108 i/r Olaisher, On factor tables. [Feb. 11, 



The headings of tables A and B, and of the principal table, as far 

 as 144,000, are in German in both copies ; but the headings of the 

 portion 144,000 to 408,000, in the Graves copy, are in Latin. 



In the Graves copy table B follows table A and precedes the 

 principal table, and in the other copy table B is placed at the 

 end, after the principal table. 



On the title-page of the work is a large engraving representing 

 Felkel turning in contempt from a disordered cabinet of books of 

 general literature\ Basedow, Curtius, Gottsched, &c., to a neatly 

 arranged cabinet of mathematical books, Euler, Kastner, Newton, 

 Maclaurin, &c., the book which is open in his hand being Lambert. 

 An apparatus, consisting of eight rods in a frame, is resting 

 against the table ; this is no doubt Felkel's machine for forming a 

 factor table, referred to hereafter. 



On a scroll over the top is written " (Gramma)tici certant, 

 geometras vera sequntur. Bella odi, pacem diligo, vera sequor." 

 The beginning of the first word is hidden by a fold of the scroll, 

 ' tici ' alone being visible, but the word is probably Orammatici, in 

 allusion to the line, ' Grammatici certant et adhuc sub judice lis 

 est ' (Horace, ^rs Poetica, 78). 



§ 5. At the time of writing the British Association Eeport 

 I knew nothing of Felkel except what he states himself in the 

 Latin edition of Lambert's Zusdtze zu den Logarithmischen und 

 Trigonometrischen Tabellen (Berlin, 1770), which was translated 

 into Latin by Felkel, after Lambert's death, and published at 

 Lisbon in 1798, under the title, J. H. Lambert supplementa tabu- 

 larum logaritkmicarum, et trigonometricarum auspiciis alince 

 academict} regi'ce scientiarum Olisiponensis cum versione introdu- 

 tionis (sic) Germanicce in Latinum sermonem, secundum ultima auc- 

 toris consilia amplificata. Cur ante Antonio Felkel. Olisipone... 

 MDCCXCVIII. He there states that he had continued his table to 

 5,000,000 (this statement will be referred to in § 11). I also 

 quoted Gauss's remark which occurs in his letter prefixed to Dase's 

 Seventh Million (see § 17), viz. " Felkel hatte die Tafel in Manu- 

 scripte bis 2 Millionen fertig und der Druck war bis 408000 fort- 

 geschritten, dann aber sistirt, und die ganze Auflage wurde ver- 

 nichtet bis auf wenige Exemplare des bis 336000 gehenden Theils, 

 wovon die hiesige Bibliothek eines besitzt.' 



Recently, however, I found that a great deal of light was 



5 are excluded — occurred to. Felkel independently, or was suggested to him by 

 Euler's -writings. Hindenburg in a letter to Lambert of December 22, 1776, draws 

 his attention to Euler's arrangement and compares it with Felkel's {Briefweclisel, 

 V. pp. 200, 201). 



1 In the British Association Report, 1873, p. 36, I have said " military books." 

 But the authors of the books seem to be chosen so as to represent literature 

 in general. 



