100 REPORT — 18r3. 



[Faulhaber] 1631 ('Logarithmi'). Seven-figure logarithms of numbers 

 from 1 to 10,000, arranged in columns (three to the page), with charac- 

 teristics, xis there arc 3 coUimns, there are 99 logarithms on each page. The 

 printing is imperfect, the types having here and there become displaced, 

 so as to leave no mark. There are some errata on the last page, headed 

 " Typographus Lectori S." See above, Faulhaber, 1630 (' lugenieurs- 



Schul'). 



[Faulhaber] 1631 ('Canon'). Logarithmic sines, tangents, and secants 

 for every minute of the quadrant, to 10 places (semiquadrantally arranged); 

 no differences. Taken from Vlacq, 1628. The table is followed by 8 pages of 

 errata in the Frankfort 'lugenieurs-Schul,' in the logarithms of numbers, and in 

 the ' Canon.' Except perhaps Norwood, ] 631, this is the first reprint of 

 Vlacq's corrected ' Canon ' (1628), the previous writers haviug copied 

 GuNTER (1620). Rogg gives place and date as Nuremberg, 1637 ; but 

 the copy before us is not so. See above, Faulhaber, 1630 (' Ingenieurs- 

 Schul'). 



Filipowski, 1849. T. I. Antilogarithms. The numbers (to 7 figures) 

 are given answering to the logarithms as arguments, the range being frona 

 •00000 to 1-00000 at intervals of -00001. The arrangement is exactly the 

 same as in ordinary seven-figure tables of logarithms ; and the table occupies 

 201 pages. The proportional parts are given to hundredths (viz. 100 pro- 

 portional parts of each difference are given); and the change of figure in tho 

 middle of the line is denoted by two dots (thus, 0) placed over the fourth 

 figure of all numbers affected ; and when a final 5 has been increased it is 

 printed Y. The first 3 figures in the number arc alwaj-s separated by a 

 space from the block of figures. 



. T. II. Gaussian logarithms, arranged in a new way. Let A=log x and 

 X=log (.f-l- l)(so that 10^ =10^^ + 1), then on the first page of the table (p. 203 

 of the book) we have A given to 3 places for argument \ from \= -00000 to 

 •00449 (which last corresponds to A = 8-017), at intervals of -00001. On 

 the succeeding 16 pages we have ,\ as a tabular result for argument A from 

 A= 8-000 to 13-999, at intervals of -001, to 5 places. 



Since log (a + 6) =log b-\- log | ,- -|- 1 j, and 



log {a—b)=log 6-1- log (J-i), 



it is clear that the rules are very simple and uniform, viz. log a and log b 

 being given (6 < « suppose), we take log « — log 6 as argument, and enter 

 the table at the A or \ column, according as we want log a-\-b or log a — b, 

 and add the tabular result to log b. In this table also the notations 0, 

 V, &c. are used, as well as another in which a wavy line runs down by the 

 side of the logarithms whose leading figures have changed. This method of 

 marking is only possible when the tabular results appear one under the other. 

 The figures are throughout neat and clear, having heads and tails ; and the 

 copy before us is printed on green paper^ of a pleasant colour. In many 

 places there is a parsimony of figures, which we dislike extremely ; thus there 

 occur 44, 5, 6 as headings for 44, 45, 46, and or for 10 &c. A list of 36 

 errors affecting the first 8 figures of Dodson"s Canon (1742) is given, and in- 

 troduced by the remark, " The following is a list of errors as detected, by 

 means of our table, in the first 8 places of Dodson's Anti-Logarithmic Canon, 

 in addition to those corrected v.ith tlie author's own hand." These words im- 



