118 REPORT— 1873. 



John Newton, 1658. [T. I.] Logarithms to 1000, to 8 places, and 

 logarithms from 10,000 to 100,000, also to 8 places. A column is added to 

 each page containing the logarithms of the differences, to 5 places. 



[T. II.] Log sines and tangents (semiquadrantaUy arranged) for every 

 centesimal minute (viz. nine-thousandth part of a^-ight angle), to 8 places, 

 with differences. 



[T. III.] Log sines and tangents for the first three degrees of the quadrant, 

 to 5 places, the interval being the one thousandth part of a degree. Loga- 

 rithms of the differences to 8 places are added. 



The trigonometrical tables are thus of the kind introduced by Briggs, and 

 are partly centesimal (see § 3, art. 15, p. 64). This is the only extensive 

 eight-figure table that has been published ; and it is also remarkable on 

 account of the logarithms of the differences, instead of the differences, being 

 given. It seems worth consideration whether, in the event of a republication 

 of Vlacq, 1628, it would not be advantageous to replace the differences by 

 their logarithms. It is usually most convenient, if many logarithms are to 

 be taken out at one time, to interpolate for the last five figures in a ten- 

 figure table by means of an ordinary seven-figure table ; but in other cases 

 recourse is generally had to simple division, and the natural differences are 

 best. The table would occupy too much space if both the diflerences and 

 their logarithms were added ; and there is not much chance of two publi- 

 cations ever being made, one with natural, and the other with logarithmic, 

 differences. If the choice had to be made, the decision would probably be in 

 favour of the simple differences as they are, though a good deal might be 

 ■urged on the other side. 



A few errata are given at the end of the address to the reader, and a great 

 many more on the last page ; the tables, however, reproduce nearly all 

 Viacq's errors, which affect the first 8 places (see ' Monthly IS'otices of the 

 Boy. Ast. Soc' March 1873), This was the first table in which the arrange- 

 ment, now universal in seven-figure tables (viz. with the fifth figures run- 

 ning horizontally along the top line of the page), was used. The change of 

 the third figure in the line is not noted. 



The title of this work being the ' Trigonometria Britannica ' (printed 

 * Britanica ' on the titlepage), it is often confounded with Beiggs's work of 

 this name, Gouda, 1633 (§ 3, art. 15), from which it is derived. Also, as 

 GeUibrand's name appears on the titlepage it is sometimes attributed to 

 him in catalogues. 



In the Cambridge Univei-sity Library is a copy of this book, in which the 

 titlepage and introduction are absent, "the first page being the titlepage to 

 the tables, so that the work is anonymous. Whether some copies of the tables 

 alone were published, or Avhether the copy in question is imperfect, we do not 

 know. 



Norie, 1836. T. XXIII. Log sines, tangents, and secants to every quar- 

 ter-point, to 7 places. 



T. XXIV. Six-figure logarithms of numbers to 10,000, with difterences. 



T. XXV. Log sines and tangents to every ten seconds to 2°, and log sines, 

 tangents, and secants for every minute of the quadrant, to 6 jilaces, with 

 differences. 



T. XXVI. Xatural sines for every minute of the quadrant, to 6 places. 



T. XXVII.-XXIX. To find the latitude by double altitudes and the 

 elapsed time. Log i clap, time, middle time, and rising (for explanation of 

 these terms see T. XVI. of Maskelyne, § 4) arc given at intervals of 5^ 

 the two former to 6';, .and the last to <>, to 5 places, with proportional 



