1878.] Mr Glaisher, On factor tables. 129 



urges Dase to calculate the next four millions, and expresses his 

 opinion of the value of the tables, I also quote: "In diesem 

 Vertrauen ist also in meinen Augen das zunachst Wlinschens- 

 werthe, dass auch die vier Millionen von 6000000 bis 10000000 

 bearbeitet werden, natiirlich unbeschadet kllnftiger noch weiterer 

 Fortsetzung, insofern Krafte zur Ausflihrung vorhanden sind. Sie 

 selbst besitzen mehrere dazu erforderliche Eigenschaften in beson- 

 derm Grade, eine ausgezeichnete Fertigkeit und Sicherheit in 

 Handhabung der arithmetischen Operationen, und, wie Sie schon 

 in mehreren Fallen bewahrt haben, eine unverwlistliche Beharr- 

 lichkeit und Ausdauer. SoUten Sie also durch Unterstlltzung 

 der begliterten, den wissenschaftlichen Bestrebungen freundlich 

 gesinnten Biirger Hirer Yaterstadt, oder auf andere Weise, in 

 den Stand gesetzt werden, sich solcher Arbeit zu unterziehen, so 

 konnte dies den Freunden der Aritlimetik nur angenehm sein." 

 He then points out that though the resolution of large numbers 

 into their factors is less frequently required than that of smaller 

 numbers, still this is counterbalanced by the fact that when the 

 resolution has to be performed, without the aid of tables, the work 

 is very much greater. With regard to the calculation, he mentions 

 Burckhardt's method as that which should be adopted, and con- 

 siders it important that the table should be printed from the cal- 

 culation itself, without copying. As for the arrangement, he says, 

 " Unbedingt halte ich hier die Einrichtung der Burckhardt'schen 

 Tafel fiir die beste." 



In 1862 the seventh million was published at Hamburg, the 

 title being " Factoren-Tafeln fiir alle Zahlen der siebenten 

 Million, oder genauer von 6000001 bis 7002000, mit den darin 

 vorkommenden Primzahlen. Von Zacharias Dase. Hamburg, 

 1862...." The arrangement is exactly the same as in Burckhardt, 

 there being 112 pages of tables. 



In the preface it is mentioned that Dase was induced by Gauss 

 to undertake the calculation of the tables, and then follows Gauss's 

 letter, of which a rt^sumd has just been given. After this it is 

 stated that about a year before (viz. in 1860), through the support 

 of patrons of science in Hamburg, Dase was enabled to devote 

 himself entirely to carrying out Gauss's project. On September 11 

 of that year (1861) Dase died suddenly, leaving the seventh million 

 complete, and the eighth million nearl}^ complete. He had also 

 determined a great part of the factors for the ninth and tenth 

 millions. Dr Eosenberg, of Hamburg, had undertaken the con- 

 tinuation of the work. The preface is dated November, 1861, and 

 is signed by the committee of the " Dase-Stiftung." There are six 

 names, including Professor C. A. F. Peters. 



The eighth million was issued in 1863 ; it is a continuation 

 of the seventh million, the pages being numbered 113 — 224, It 



