1878.] Ml' Glaislier, On factor tables. 117 



the table, Hindenburg's apparatus is described in a book^ of 

 which the title is " Carl Friedrich Hindenburgs Beschreibung 

 einer ganz neuen Art, nach einem bekannten Gesetze fortgehende 

 Zahlen, durch Abzahlen oder Abmessen bequem und sicher zu 

 linden. Nebst Anwendung der Methode auf verschiedene Zahlen, 

 besonders auf eine darnach zu fertigende Factorentafel, mit einge- 

 streueten, die Zahlenberechnung uberhaupt betreffenden Anmer- 

 kungen. Nebst flinf Beylagen und einer Kupfertafel. Leipzig, 

 bey Siegfried Lebrecht Crusius. 1776." It consists of 6 + 120 pp. 

 and 9 diagram or folding sheets, containing drawings of the 

 apparatus and specimen tables^ The apparatus, as drawn, does 

 not seem to resemble Felkel's in appearance, being more compli- 

 cated, the bars used having squares cut out from them ; but I 

 have not read the book. Hindenburg intended that his table 

 should be of quarto size, similar to the Avignon edition of 

 Gardiner's logarithmic tables ; but afterwards, when he determined 

 to include all the factors, in accordance with Lambert's wish, the 

 title as advertised in the Leipziger Messverzeichniss ran " Factoren- 

 tafel, in welcher alle Primzahlen und alle einfache Theiler der 

 zusammengesetzteu, durch 2, 3, 5 nicht theilbaren Zahlen von 

 1 — 1000000 in bequemen, auf der Stelle verstandlichen Zeichen, 

 ausgesetzt, befindlich sind ; auf 100 grossen Folioseiten, nebst einer 

 Einleitung. Herausgegeben von C. F. Hindenburg. Leipzig, bey 

 S. C. {sic) Crusius" {Briefwechsel^ , v. pp. 177 — 178). In an ap- 

 pendix Bernoulli gives the following account of the causes that led 

 to the non-publication of the table. The first delay was caused 

 by Lambert's desire that all factors should be included ; Lambert 

 died; other difficulties occurred, some being due to the expense 

 of publication ; at length, at the beginning of 1782, all was going 

 well, but more difficulties arose, although the manuscript of the 

 first million, containing all the (prime) factors for each number, 

 with the list of primes, was quite complete. When at Leipzig in 

 September, 1784, Bernoulli himself saw the manuscript and the 

 beginning of the table printed very beautifully and clearly on 

 large royal folio sheets. " I must confess," he proceeds, " the 

 whole arrangement for finding the factors of composite numbers 

 pleased me very much ; it is very much simpler than I expected. 

 I convinced myself of this by several trials ; very quickly and at 

 a glance one can resolve into figures the symbols of the factors 



1 This is the work that Lambert tells Felkel he has received in his letter of 

 December 12, 1776. See end of § 8. 



" I may mention that the meaning of the anagram on the last page (p. 120) 

 of this work is explained in pp. 176, 177 of vol. v. of the Briefwechsel. 



3 In vol. I. (1781) of the Briefwechsel, pp. 367, 368, Bernoulli stated that the 

 first one or two millions of Hindenburg's calculation might soon be expected to 

 appear. 



9—2 



