54 BEPOiiT — 1873. 



works he has seen. Of seven-figure tables we have found Babbage as con- 

 venient as any, and it is nearly free from error ; Callet and Htjtton are also 

 much used ; Shortrede and Sang are both conspicuous for giving the multii^les 

 of the differences instead of proportional parts ; the latter work also extends 

 to 200,000 instead of 100,000 as usual. Of five-figure tables De Morgan's 

 (Useful-Knowledge Society) tables are considered the best, and arc practically 

 free from error. We cannot, however, here particularize the advantages of 

 the different tables, which must be gathered from their full descriptions. 

 Some of them have, of course, been merely included on account of their his- 

 torical value. We may here mention that the subject of errors in these tables 

 will be considered in a subsequent Report. 



Vega (p. iii of the Introduction to the ' Thesaurus,' 1794) says that Ylacq's 

 ' Arithmetica ' (1628) and ' Trigonometria ' (1633) were printed at Pekin in 

 1721, under the title " Magnus Canon Logarithmorum, tum pro sinibus ac 

 tangeutibus ad singula dena secunda, tum pro numeris absolutis ab unitate ad 

 100,000. Typis sinensibus in Aula Pckinonsi, jussu Impcratoris cxcusus, 

 1721 " (three volumes folio, on Chinese paper), and that a copy had been 

 offered him for sale two years previously (1792). Montucla (' Histoire,' 

 vol. iii. p. 358) says, the name of the Emperor in question was Kang-hi. 



Rogg also (p. 408) confirms Yega, extracting the title from Brunet's 

 * Manuel du Libraire.' 



In the preface to his tables (1849) Mr. Filipowski concludes by a sneering 

 remark on the Chinese, saying that Mr. Babbage proved, " as had long been 

 suspected, from what source those original inventors had derived their 

 logai'ithms ; " and we have noticed this tendency to ridicule the Chinese in 

 this matter as detected plagiarists in others. In point of fact there is no more 

 plagiarism than when Babbage or Callet publishes a table of logaritlims with- 

 out the name of Ylacq on the titlepage. The first publication in China, we 

 infer from Rogg, merely professed to be a reprint of Vlacq ; and if logarithms 

 came into general use, it is natural that they would be published, as with us, 

 without the original calculator's name. The fault is with those who form 

 preconceived opinions on subjects they have not investigated. 



A Turkish table of logarithms is described in § 4. A small table of 

 logarithms to base 2 is noticed below, imder Montferrier, 1840. 



We may mention a little book, ' Instruction clcmentaire et pratique sur 

 I'usage des Tables de Logarithmes,' by Prony (Paris, 1834, 12mo), which 

 explains the manner of using of tables of logarithms &c., adapted to Callet, 



In many seven-figure tables of logarithms of numbers the values of S and T 

 are given at the top of each page, with Y, the variation of each, for the purpose 



of deducing log sines and tangents. S and T are the values of log — —, and 

 loo- - — L for the number of seconds denoted by certain numbers (sometimes 



° X 



only the first, sometimes every tenth) in the number-column on each page. 



Thus, in Callet, 1853, on the page of Avhich the first number is 67200, 



^ , sin 6720" _, ^ , tan 6720" ... ,, ,„ ,, ... . 



S=log ,,„ .,-, and T=log — ^.-o,-, , while the Ys are the variations of 

 ° b/20 5720 



each for 10". To find then, say, log sin 1° 52' 12"-7, or log sin 6732"-7, we 

 have 8=4-6854980, and log 6732-7 = 3-8281893, whence, by addition, we 

 have 8-5136873; but Y for^lO" is -2-29 ; whence the variation for 12"-7 

 is —3, and the log sine required is 8-5136870. Tables of S and T are fre- 

 quently called, after their inventor, Delambre's tables. 

 It is only since the completion of this Report, and therefore too late to 



