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



extends from 7,002,001 to 8,010,000. There is a short preface by 

 Dr Rosenberg, who edited the work. 



The ninth million was published in 1865, the title page describ- 

 ing it as "von Zacharias Dase, und erganzt von Dr H. Rosenberg." 

 The page-numbers run from 225 to 334, and the table extends 

 from 8,010,001 to 9,000,000. In a very short preface, signed "Das 

 Comite der Dase-Stiftung," it is stated that the tenth million is 

 near completion. 



§ 18. The tenth million has not been published. In the 

 " Bericht erstattet vom Vorstande der Mathematischen Gesell- 

 schaft in Hamburg," dated March 4, 1878, it is stated that the 

 Dase committee were unable to publish this million for want of 

 means. Further enquiries showed that the manuscript of the 

 tenth million was in the possession of the widow of Dr Rosenberg. 

 On examination it was found that the manuscript was begun by 

 Dase, and that it had been completely finished by Rosenberg. 

 Mrs Rosenberg was willing to give the manuscript to the society, 

 either for publication or for presentation to a public library. It is 

 added that the society were unable to obtain the publication of 

 the table. In a letter to myself, dated Hamburg, May 28, 1878, 

 Dr H. Schubert informs me that a few weeks before the manu- 

 script was presented to the Berlin Academy. 



§ 19. The manuscript of the fourth, fifth, and sixth millions, 

 presented to the Berlin Academy by Crelle\ and which Gauss 

 refers to in his two letters, has not been printed, so that there is a 

 gap from the third to the seventh million. Clearly it is very 

 important that this gap should be filled up ; and my father, feel- 

 ing the improbability of the publication of the Berlin manuscript 

 after so long a time, commenced the preliminary work necessary for 

 the calculation of the fourth million at the beginning of last year. 

 In reply to a letter from Professor Cayley, asking if there was any 

 chance of the publication of the manuscript. Professor Kummer, 

 the secretary of the mathematical section of the Academy, re- 

 plied, in a letter dated April 29, 1877, that the manuscript^ had 

 been examined on a former occasion and found to be so inaccurate 

 that " the Academy was convinced that the publication would 

 never be advisable." Under these circumstances my father, with 

 the assistance of two computers, at once commenced the actual 

 calculation, which has been steadily continued without interrup- 

 tion. At the time of writing this (June, 1878) the fourth million 

 is completely finished and ready for press ; and all the numbers 

 corresponding to least factors between 211 and 523, for the fifth 



^ Gauss only states that the manuscript was presented by Crelle to the 

 Academy, but Prof. Kummer speaks of the tables as calculated by Crelle. 

 2 More strictly the portion from 3,000,000 to 4,039,500. 



