116 Mr Glaislier, On factor tables. [Feb. 11, 



Felkel published the first part of his table he had not calculated 

 more than two millions. See also §§ 10 and 11. 



Ill November, 1776, Felkel sends Lambert the first part 

 (1 — 144,000) of his work, which has been described in § 4 ; and 

 also some errata in iti Lambert replies on December 12, thanking 

 Felkel for the table : he considers the arrangement in eight 

 columns excellent, and the combination of letters and their use 

 ingenious ; but, he points out, the only object of the employment 

 of letters is to save room, and he finds that the actual factors might 

 have been written in figures without more space being occupied. 

 He recognises also that Felkel's table could not well have been 

 combined with any other table. Mention is then made of Felkel's 

 machine (which is frequently referred to in the correspondence): 

 it is a very simple contrivance, consisting of rods of different 

 lengths, by means of which the measurements were to be made^. 

 In the same letter Lambert also states he has received from 

 Hindenburg his book, Beschreihung einer ganz neuen Art. . .(see § 9). 

 As this closes the correspondence between Lambert and Felkel 

 it is convenient here to give some account of Hindenburg's method 

 and proposed table, and to resume Felkel's history in § 10. 



§ 9. The correspondence between Lambert and Hindenburg 

 occupies pp. 137 — 221, and consists of 11 letters, extending from 

 August 3, 1776, to December 22, 1776. As Hindenburg's table 

 was never published, it is sufficient to state the contents of the 

 correspondence very briefly. On August 3 Hindenburg sends 

 Lambert the Nachricht of his proposed table ; the publication of 

 this Nachricht having been accelerated by Felkel's announcement. 

 Hindenburg proposes to give only the least factor of all numbers 

 not divisible by 2, 3 or 5 from 1 to 5,000,000, together with a list 

 of primes between these limits. 



Lambert's letter to Hindenburg on August 13 (on this day 

 he wrote to all his factor table correspondents) is an interesting 

 one, as he there freely gives his opinion of Felkel. A quotation 

 from this letter has been made in a note to § 8. The correspondence 

 relates chiefly to Felkel's machine and to Hindenburg's apparatus, 

 which are found to be essentially the same^. This of course must 

 be the case to some extent with all mechanical appliances for 

 constructing factor tables. From what has been said in § 1 it is 

 clear that the fundamental principle must be the same, but 

 considerable modifications may be introduced in details, and 

 these may be of great importance in facilitating the formation of 



^ The machine is fully explained in an appendix by Bernoulli {Briefwechsel, v, 

 pp. 232—234). 



2 Briefwechsel, v. p. 155 (note). 



