ON MATIIliMATlCAL TAULJiS. 59 



We know of only two errors : viz., in log 52943 the last figure should bo 

 5 instead of 6 ; and in log 102467 the last two figures should be 02 instead of 

 92. The occurrence of the former of these errors is very remarkable, as the 

 logarithm is correct in Vega (folio, 1794), with which the table was read 

 twice (sec Sang, 'Athenaeum,' June 8, 1872, and Glaisher, 'AthensBum,' 

 June 15, 1872, or ' Journal of the Institute of Actuaries,' July 1872 and 

 January 1873). The latter is given in Gould's (American) 'Astronomical 

 Journal,' vol. iv. p. 48. 



Copies of the book were printed on papers of different colours — yellow, 

 brown, green, ifec, as it was considered (no doubt justly) that black on a 

 white ground fatigues the eye more than any other combination *. Yellow 

 or light brown seem the colours most preferred by computers, green not being 

 very satisfactory. 



In the preface to his tables (1849), Mr. Filipowski writes : — " Babbage's 

 ' Tables of Logarithms,' which probably are the most accurate of all ; for, by 

 the aid of his ingenious calculating machine, he was enabled to detect a 

 variety of errors in former tables." This is untrue. 



[Scheutz, 1857.] Five-figure logarithms, from 1000 to 10,000, calcu- 

 lated and printed by Scheutz's calculating machine : specimens of a 

 few other tables are added. A history and description of the machine &c. 

 is given. 



Sang, 1859. Pive-figure logarithms, from 1000 to 10,000, arranged as 

 in a seven-figure table ; no differences. 



Gray, 1865. The table in this tract is rather an auxiliary table to 

 facilitate the calculation of logarithms to twelve places, than a table itself. 

 The tables at the end of the work (see p. 2 of the Introduction) give 

 log(l + -001n), log (l + -00rn), log (1 + -O0r70> from «==0 to k=999, at 

 intervals of unity, to twelve places. The use of the sequantities in the cal- 

 culation of logarithms is well-known (see, e.g.. Introduction to Shokteede's 

 Tables, vol. i. 1849). Pages 43-55 are occupied with the history of the 

 metliod, and will be found valuable and interesting. The rest of the book 

 is devoted to explanations &c. 



Weddle's method of calculating the logarithms of numbers by resolving 

 them into the reciprocals of series of factors of the form 1 — •!";•, r being a 

 digit, and then using a subsidiary table of the logarithms of these factors, is 

 fidly explained, as also are some improved methods of Mr. Gray's own, 

 depending substantially on the same principle ; and aU arc illustrated with 

 full numerical examples. The whole constitutes the most complete account 

 of the simplest and best of the known methods for the calculation of isolated 

 logarithms that we have met with ; and any one engaged on work of this 

 kind would do well to consult it. Of course for calculating a table, the 

 method of differences, as Mr. Gray remai'ks, is the best. A portion of this 

 tract appeared in the * Mechanics' Magazine ' for 1848 ; and the whole is 

 reprinted from the ' Assurance Magazine and Journal of the Institute of 

 Actuaries.' 



Pineto, 1871. This work consists of three tables ; the first (Table 

 auxiliaire) contains a series of factors by which the numbers whose logarithms 

 are required are to bo multiplied to bring them within the range of 

 Table 2, and occupies three pages. It also gives the logarithms of the 

 reciprocals of the factors to twelve places. Table 1 merely gives logarithms 

 to 1000, to ten places. Table 2 gives logarithms from 1,000,000 to 1,011,000 



* " Of all the things that are meant to bo read, a blaek monumental inscription on white 

 marble in a bright light is about the most difficult." — Do Morgan. 



