94 REPORT — 1873. 



Croswell) 1791. T. I. Log secants, half log secants, and half log sines, viz. 

 log sec X, ^ log sec x and ^ log sin x, to every minute of the quadrant, to seven 

 places, the last two being separated by a comma for the convenience of those 

 who outy requii-e five places ; semiqiiadrantally arranged : no differences. The 

 table, as headed in the book, implies that the tabular results are natural ; 

 but they are as above. 



T. V. Proportional logarithms for every second to 3°, to 4 places : the 

 same as T. 74 of Rapek. 



T. XIll. Small table to convert arc into time. The other tables are 

 nautical. 



De Decker, 1626. T. I. Ten-figure logarithms of numbers to 10,000, 

 with characteristics and differences. 



T. II. Logarithmic sines and tangents, to seven decimals, for every minute, 

 from GuNTER 1620 (§ 3, art. 15). 



These tables were always assigned to Vlacq till, in the course of the pre- 

 paration of this Report, it came to light that De Decker was the author, Vlacq 

 having only rendered some assistance. For the history of them, as well as 

 for their connexion with ' Tables des Logarithmes pour les nombres d'un a 

 10,000 composes par Henry Brigge,' Gouda, 1626, and the tables in Wells's 

 ' Sciographia,' 1635, see Phil. Mag., October and December (Supp. No.), 1872, 

 and May, 1873. 



Degen, 1824. T. I. Log ^^ (1 . 2 . 3 . . . . .r) is given from .v = 1 to x= 1 200, 

 to 18 places. The complement of the logarithms from 100 is also added if the 

 characteristic be less than 100 — if not, the complement from 1000 or 10,000 ; 

 thus log (1.2.... 69)= 98-233. . . . , and the complement is 1-766 . . . . ; log 



(1.2 70) =100-078 , and the complement is 899-921 The first 



portion of this table is reprinted by De Morgan, to 6 places, in the ' Ency- 

 clopasdia Metropolitana ' (§ 3, art. 25). 



T. II. The first hundred multiples of the modulus -434 . . . , to 30 places. 



T. III. The first nine multiples of log 2, log 3, log 5, log 0, log 7, log 11, 

 log 12, log 13, log 14, log 15, log 17, log 18, log 19, log 21, log 22, log 23, log 24, 

 log 26, log 28, and log 29 (Briggian). 



The other tables consist of formulge &:c. There is a full introduction. 



[De Morgan] 1839. [T. I.] Five-figure logarithms to 10,000 (arranged 

 consecutively, and not as in seven-figure tables), with differences, and degrees 

 corresponding to the first number in each column. 



[T. II.] Logarithms from 1001 to 1100, to 7 places. 



[T. III.] Log sines, cosines, tangents, and cotangents to every minute, to 

 5 places, with differences. 



[T. IV.] Log sines for every second of the first nine minutes, and also for 

 every tenth of a minute in the first degree. 



[T. v.] A small table of constants ; most of them taken from Babbage. 



[T. YL] Log (1 . 2. 3. . . .a'), from a:=6 to .r=25, at intervals of unity, 

 and thence to 265, at intervals of 5, these last three tables being also to 5 



places. 



The tables are beautifully printed, and are practically free from error. 

 Prof. Wackerbarth states ('Monthly Notices of the Royal Astronomical 

 Society,' April 1867) that he finds the only error in the work to be among 

 the constants on p. 213, line 5, where 2-718281829 should be 2-718281828, 

 the following figure being 4. 



There is no name on the titlepage ; but it is well known that the tables 

 were prepared by De Morgan, and they are always spoken of by his name. 

 They were examined by Mr. Farley of the Nautical- Almanac Office. 



