36 REPoiiT — 1873. 



The primes of each hundred are separated, which for some purposes would 

 be an advantage. 



LiMBERT states (Introd. ad ' Supplemental &c., 1798) that Kruger received 

 this table from Peter Jaeger. 



Felkel, 1776. Table of all simple factors of numbers to 144,000, the 

 tabular results being obtained from three tables. Thus Table A gives primes 

 to 20,.353 ; these occupy one page, along the top line of which run the Greek 

 letters o, /3 . . . . and down the left-hand column four alphabets consecutivel}-, 

 viz. small italic, small German, capital italic, and capital Gorman (there 

 being 100 lines); and any prime given on this page is henceforth in the book 

 denoted by its coordinates, so to speak : thus 9839 would be printed yu^i, &e. 

 The principal table occupies 24 pp. ; and then Table B occupies one page at 

 the end. Suppose it required to find the factors of 1.38, .593. The middle 

 table is entered at 138 and Table E at 593. In tlie latter we find as result 

 " g line 20," so that we know that the compartment under ^ in the 20th line of 

 the block 138, refers to the number in question. In this compartment is printed 

 e, g, (3x, which, interpreted by Table A, gives 7, 13, and 1523 as the factors. 

 There are a few details that have been omitted in this description ; the last 

 three figures are written in the compartment wherever there is room for 

 them. 



On the titlepage is a large engraving of a student (no doubt a portrait of 

 Felkel) turning in contempt from a disordered cabinet of military books to 

 another neatly arranged, containing Euler, Newton, Maclaurin, Bernoulli, 

 Boscovich, &c., and holding in his hand the works of Lambert ; with mottoes 

 " Bella odi, Pacem diligo, vera soqiior," &c. above. It will be seen that this 

 table is entirely superseded by Chernac and Burckhardt. In the arrangement 

 of the latter the table would only have occupied 16 much smaller pages, 

 and its use would have required no explauation ; but on account of the rarity 

 of the work, it has been thought worth while to describe at some length 

 what is certainly the most remarkable-looking table we have seen. 



De Morgan states that " Murhard mentions the first part of a table (by 

 A. Pelkel) of the factors of all numbers not divisible by 2, 3 or 5 from 1 to a 

 hundred millions, Vienna (1776)." On referring to Murhard we find such is 

 the case, " 100,000,000 " being an obvious misprint for " 10,000,000 ; " wo 

 have seen Murhard's error reproduced by other writers. 



Of Felkel's table Gauss (in the letter prefixed to Base's Seventh Million) 

 says : " Felkel hatte die Tafel im Mauuscripte bis 2 Millionen fertig und der 

 Druck war bis 408,000 fortgeschritten, daun aber sistirt, und die ganze 

 Anflage wurde vernichtet bis auf wenige Exeraplare des bis 336,000 geheuden 

 Theils, woven die hicsige Bibliothek eines besitzt." The copy of Felkel in 

 the Eoyal Society's Library, which extends to 144,000, is that which has 

 been described above. Felkel's table is also referred to by Hobert and 

 Ideler in the introduction to their work (see § 4). 



Felkel was editor of the Latin edition (Lisbon, 179S) of Lambert's 

 'Zusiitze' (the ' Supplemcnta' &c., see § 4) ; and he has there given, in the 

 ' Introductio Interpretis ' and at the end, some account of his life and the work 

 he accomplished and hoped to accomplish with regard to the theory of numbers. 

 He commenced the study of mathematics when of a somewhat advanced age ; 

 and he speaks in the warmest terms of Lambert, with whom he was in cor- 

 respondence, and from whom he derived much assistance. This accounts for 

 Lambert being the book open before the student in the engraving described 

 above. 



In a note on p. siv of the Introductio to the ' Supplemental he (Felkel) 



