ON MATHEMATICAL TABLES. 65 



The cliief tables in which the angle is divided completely centesimaUy are 

 Callet 1853, BoRDA and Delambre, and Hobert and Ideler. 



For the meaning of S and T (Delambre's tables), see § 3, art. 13, near the 

 end of the introductory remarks. 



Gunter, 1620. Log sines and tangents for every minute of the quadrant 

 (semiquadrantally arranged) to 7 places. This is the first (Briggian) loga- 

 rithmic trigonometrical canon calculated or published. The book is ex- 

 tremely scarce ; and we have only seen one copy of it, viz. that in the British 

 Museum, where it is bound up with Briggs's ' Logarithmorum Chilias Prima.' 

 There is engraved on the titlepage a diagram of a spherical triangle, S P Z. 

 De Morgan (who had never seen a copy) says that it also contains logarithms 

 of numbers as far as 1000 ; but this is not correct. The British-Museum copy 

 has written in ink on the titlepage, " Eadius autem verus est 10,000,000,000." 

 This has reference to the fact that the logarithm of the radius is taken 

 to bo 10, and is true in one sense, but not in the usual one, which 

 is that, this being the radius, the sines &c. are true to the nearest unit. 

 Custom has veiy properly decided to consider the radius of a logarithmic 

 canon the same as what would be the radius of the resulting natural canon 

 if the logarithms were replaced by their numbers. We have not seen the 

 second edition, in which no doubt the logarithms of numbers mentioned 

 by De Morgan were added ; or it is just possible that some copies of 

 Briggs's ' Chilias ' (1617) were issued with the ' Canon,' both being bound 

 together in the copy we have seen, and that this has given rise to the 

 assertion. Gunter's ' Canon ' was also issued under an English title, ' A 

 Canon of Triangles,' &c. (Bodleian Catalogue) : see Phil. Mag. (Suppl. No.) 

 Dec. 1872. For a life of Gunter, see Ward's ' Lives of the Professors of 

 Gresham College,' pp. 71-81. 



Briggs, 1633 (' Trigonometria Britannica '). Natural sines (to 15 

 places) and tangents and secants (to 10 places), also log sines (to 14 

 places) and tangents (to 10 places), at intervals of a hundredth of a degree 

 from 0° to 45°, with interscript differences for aU the functions. The 

 division of the degree is thus centesimal; but the corresponding argu- 

 ments in minutes and seconds are also given, the intervals so expressed 

 being 36". 



This table was calculated by Briggs ; but he did not live to publish it. The 

 trigonometry is by Gellibrand. 



Gunter, 1673. At the end of the work is given a table of log sines and 

 tangents for every minute of the quadrant to 7 places, followed by seven- 

 figure logarithms of numbers to 10,000. 



The table of log sines &c. is printed as it appeared in Gxjnter's ' Canon 

 Triangulorum,' 1620, as the last figures in very many instances differ from 

 the correct values, which were first given by Vlacq in the ' Arithmetica ' &c. 

 (1628). 



This is the fifth edition of Gunter's works; but we remember to have seen 

 it stated somewhere that the works themselves (separate) were regarded 

 as the first edition in this enumeration. 



Berthoud, 1775. At the end of the ' Recueil des Tables n^cessaires 

 pour trouver la longitude en mer,' is a table of log sines to every minute of 

 the quadrant to 6 places (pp. 25-34). 



Callet, 1827 (* Log Sines &c.'). Log sines and tangents for every second 

 to 5°, and log sines, cosines, tangents, and cotangents from 0° to 45°, at 

 intervals of ten seconds, with differences, all to seven places. 



1873. s 



