1878.] Mr Olaisher, On factor tables. 111 



editor, Bernoulli. At the date of publication of the volume (1785) 

 Bernoulli states that von Stamford was an Ingenieur-Hauptmann 

 at Potsdam, and had quite given up the pursuits that brought him 

 in connexion with Lambert. Rosenthal was a Berg-Commissarius 

 of Gotha, and had become known for his meteorological writings. 

 Felkel had been a master in the normal school at Vienna, and 

 before he began the construction of his factor table had printed 

 some mathematical writings. He was then (1785) director of the 

 Thun's poor-school in Bohemia. Hindenburg was professor at 

 Leipzig, and is the mathematician of that name so well known in 

 connexion with his writings on combinations and the combina- 

 torial analysis. The contents of the volume will be most readily 

 understood if I give a resume of the short correspondence of eleven 

 letters (30 pp.) between Lambert and von Stamford and Bosenthal. 

 On May 10, 1774, von Stamford writes to Lambert from Ilfeld, 

 near Nordhausen, to tell him that for six months he has been 

 calculating some hyperbolic logarithms to 20 decimal places, but 

 that he learns that Lambert already is in possession of them ; and 

 he asks Lambert to suggest to him some other piece of work. On 

 May 18 Lambert replies, and states that a friend of his at 

 Dresden [Ludwig Oberreit, an Oher-Finanz-Buchhalter'] had sent 

 him a few days previously a table of the prime factors of all 

 numbers, not divisible by 2, 3 or 5, from 1 to 72,000 and from 

 100,000 to 504,000. The calculator had intended to extend the 

 table to a million, but was prevented by a change of position 

 that deprived him of the requisite leisure. Lambert suggests that 

 yon Stamford should fill in the gap from 72,000 to 100,000, and 

 continue the table from 504,000 to 1,000,000 : such a table, he 

 adds, would be published by itself, and would form a moderately 

 large quarto volume^ Yon Stamford writes on May 24 ex- 

 pressing his willingness to undertake the completion of the table, 

 but asks if the portion from 72,000 to 100,000 is not contained in 

 Lambert's own table in the Zusdtze. 



On June 7 Lambert explains that his table only gives the 

 least factors, and also that a verification of it would be desirable. 

 The mode of calculation (which seems to be similar to that de- 

 scribed in the Beytrdge) is also explained. This is not worth re- 

 producing here, though it may be mentioned that the fact that 

 the concluding number (504,000) of the second part is seven times 

 the concluding number (72,000) of the first part is connected with 

 the mode of formation. 



Ten months afterwards, on April 2, 1775, von Stamford 

 writes that he has completed the filling in of the gap, so that the 

 table is complete to 504,000. He intends to leave his position as 

 master at Ilfeld, and to return to his former profession of engineer. 



^ This is in fact the extent and size of Chernac's Crihrum Arithmeticinn, (1811). 



