1878.] ilfr Glaisher, On factor tables. 119 



Tafeln, Felkel proposed to give the least factor in figures, in 

 accordance with the advice of Lambert {Briefwechsel, v. p. 241). 



§ 11. In 1798 Felkel edited at Lisbon a Latin edition of the 

 Zusdtze, under the title Supplementa Tabidarum (see § 5). In the 

 Prcefatio Interpretis he states that the Zusdtze, though one of 

 Lambert's best works, has not obtained the publicity it deserves, 

 through being written in German, and accordingly the Royal 

 Academy of Lisbon have commissioned him to make a Latin 

 translation \ 



Felkel then proceeds to give an account of himself and his 

 works. He did not commence the study of mathematics till 

 he was 85 years of age, and a difficulty in 'remembering and 

 imitating' removed from him all hope of attacking the higher 

 branches of the science. By reading Euler's Algebra of 1768, in 

 which the difficulty of resolving large numbers into their factors 

 is pointed out, he was led to consider the subject of factor tables ; 

 and he proceeds : " Extemplo missis libris tardisque Scholasticorum 

 viis^ ad Tabulas Factorum consuetudine majores construendas 

 me composui, confecto paucis diebus instrumento, cujus ope me 

 victorem omnium difficultatum et Computatorum quotcunque 

 semulantium fore non dubitavi ; basimque impressam pro aliquot 

 millionibus procuravi. Accidit hoc Octobri 1775, tempore scilicet 

 feriarum." He then mentions that he was confirmed in his in- 

 tention by the Zusdtze, and entered into correspondence with 

 Lambert. The instrumentum is of course the machine^, and the 

 basis impressa was, I suppose, a bla.nk form corresponding to a 



1 Felkel prefixes a Prcefatio Interpretis, and he adds at the end an account 

 of his labours and researches, and what he had proposed to accomplish. He also 

 appends many notes to Lambert's introduction. Although the introduction to 

 the Zusdtze of 1770 is in German, the headings of the tables are in Latin : and 

 till I saw the book I was never able to understand why the factor table should be 

 generally quoted as " Tabula numerorum, &c.," as from Felkel's statement it 

 seemed that the work was in Grerman. On the first page of the tables, after the 

 German introduction, there occm-s the title I. H. Lambert Supplementa Tabularum 

 logarithmicarum et trigonometricarum, and this explains the fact that the work 

 is sometimes called the Supplementa Tabularum in writings between 1770 and 

 1798, when evidently the Zusdtze is referred to. As regards the factor table 

 Lambert only gave the least factor in the Zusdtze, but in the Supplementa of 1798 

 all prime factors except the greatest are given, the least factor being printed in 

 figures and the other factors denoted by single letters. The powers of the factors 

 are also shown : ex. gr. for 24,563 we have Ip given, / denoting 11. Felkel 

 thus carries out here on a small scale the proposed arrangement for the iciederauf- 

 lebende Tafeln, viz. to give the least factor in figures, and the others by means 

 of letters. 



2 These words recall the subject of the engraving on the title-page of Felkel's 

 factor table. 



^ In the British Association Report I said of Felkel that I had "seen (in 

 some work of reference) a number of mathematical contrivances assigned to him 

 as their inventor." This no doubt must refer to his machine, wliich was made of 

 different sizes, t&c. 



