110 Mr Glaisher, On factor tables. [Feb. 11, 



ware in der That erwiinscht, wenn wir von 1 bis anf 1000000 und 

 noch weiter die 'Theiler der Zahlen durch blosses Aufschlagen 

 einer Tafel haben konnten." And he then adds that to a man so 

 unwearied and resohite (einem so unverdrossenen wackern Mann) 

 he has in his Beytrdge promised, as far as depends upon him 

 (Lambert), the same inimortality that Napier, Briggs, Vlacq, 

 Justus Byrgius, Rheticus, Pitiscus, Gardiner, and Sherwin have 

 obtained by their tables. 



These earnest appeals had, as we shall now see, the double 

 effect of inducing several calculators to apply themselves to the 

 formation of extended factor tables, and of causing Lambert to be 

 the nucleus of a considerable correspondence relating to them. 



With regard to the tables contained in the Beytrdge and 

 Zusdtze, it seems strange that Lambert should urge the extension 

 of the table in the Beytrdge to 102,000, when this had been done 

 long before by Pell and Kriiger, and should publish this extension 

 himself in the same year in the Ziisdtze. But this is explained 

 by Lambert himself in the Introduction to the latter work as 

 follows, He copied the Beytrdge table from Poetius, altering the 

 form only, and at that time he knew nothing about Pell's table 

 beyond what is stated by Poetius. Lagrange, however (to whom 

 Lambert had sent some copies of the Beytrdge table), found that 

 Pell's table extended to 100,000, and then he and Lambert be- 

 came acquainted with Kriiger's and other tables, and the latter 

 printed Kriiger's (or Jager's) table to 102,000 in the Zusdtze. He 

 remarks that Anjema's table is the only one that forms a separate 

 work, and that we should scarcely look for a factor table in 

 Kriiger's Algebra or Poetius's Arithmetic. In several cases, he 

 knows that the factor table has been torn out from Kriiger's 

 Algebra and retained, the rest of the book being thrown away, 

 and he himself bought such a copy at the sale of Konig's books at 

 the Hague in 1758. 



Gauss, in his letter to Encke of December 24th, 1849 {Werke, 

 t. ii, p. 446) states that in the list of primes in the Zusdtze the 

 chiliad 101,000 — 102,000 ' swarms with errors'. Six of the errata 

 given in vol. ill. of the Beytrdge (see the note on the preceding 

 page) relate to primes in this chiliad, 



§ 7. The first part of the fifth volume of Joh. Heinrich 

 Lamberts... deutscher gelehrter Briefwechsel. Herausgegeben von 

 Joh, Bernoulli (Berlin, 1785) contains 242 pp. ; and nearly the 

 whole of the contents of the part (which was issued as a separate 

 volume) relates to the construction of factor tables. There is a 

 correspondence between Lambert and von Stamford and Rosenthal, 

 between Lambert and Felkel, and between Lambert and Hinden- 

 burg, and there are also explanatory additions and notes by the 



