83 REPORT — 1873. 



Mr. Beverley made some improvements in Tatior's Sexagesimal Table 

 (§ 3, art. 9), and devised a plan to introduce them into Taylor's table without 

 reprinting it. He accordingly made application to the Board of Admiralty to 

 be allovred to do so in the copies that remained unsold ; but this was refused. 

 He then offered to purchase all the unsold copies of Htjtton's ' Products ' 

 and Taylor's tables, in order to introduce his improvements ; but his applica- 

 tion was refused after the terms had been agreed upon, because he asked for 

 six months' credit. In the Appendix he complains that " the immense 

 labour that the calculation of his tables required him to exert had then ruined 

 his constitution, and brought him to the verge of a prematui-e grave." It is 

 to be presumed tliat the Admiralty had some grounds for their refusal ; but 

 it is certain that no use has been made of Hutton or Taylor since the time of 

 Mr. Beverley's application. No pains at any time seem to have been taken 

 to circulate or make known any of the books published by the Board of 

 Longitude, so that none of them have ever come into general use. 



Mr. Beverley died in 1834, at the age of 39 ; and the present work was 

 published after his death, as it contains a notice of his life by " J. B.", and 

 evident traces of revision. He often refers to his Taylor's Sexagesimal Table, 

 but no doubt it was never published. We have seen 'The Book of Formulae 

 &c., Cirencester, 1838,' by the same author ; but it contains no tables. 



Borda and Delambre, An IX. (1800 or 1801). [T. I.] Seven-figure 

 logarithms of numbers from 10,000, to 100,000, with differences and pro- 

 portional parts for aU. The line is broken when a change takes place in 

 the middle of it. It may be remarked that while in all modern tables 

 of logaritlims of numbers three figures are common to the block, and 

 four only are given in the columns, in this table there are but two leading 

 fig-ures, and five are found in the columns, so that the lines are broken in 

 very few instances. [T. II.] Eleven-figure logarithms of numbers to 1000, 

 and from 100,000 to 102,000 (the latter vsdth differences). 



[T. III.] Log sines, cosines, tangents, and cotangents for centesimal argu- 

 ments, viz. from 0' to 10", at intervals of 10", and from 0' to 50", at in- 

 tervals of 10' to 11 places, without differences (", ', " being used to denote 

 .centesimal degrees (or grades as they are sometimes called), minutes, and 

 seconds). 



[T. IV.] Hyperbolic logarithms of numbers from 1 to 1000 to 11 places. 



[T. v.] Log differences of sines for every 1", 2", . . . 10" throughout the 

 quadrant, and the same for tangents for 1" and 2", to 7 places, viz. log 



sin 2" -log sin 1", log sin 3" -log sin 2" throughout the quadrant of 



100", logsin 4"-log sin 2", log sin 6"— log sin 4" throughout the quadrant, 

 &c. It is to be noticed, however, that in this mode of description of the 

 table log sin 0" must be treated throughout as instead of — oo ; for facing 

 1" we have given log sin 1" (not log sin 1"— log sin 0") in the first column; 

 jand facing 2" in the second we have log sin 2" &c. 



[T. VL] A great centesimal table, gi\'ing log sines, cosines, tangents, co- 

 tangents, secants, and cosecants from 0" to 3", at intervals of 10" (with full 

 proportional parts for every second), thence to 50" at intervals of 1\ with 

 full proportional parts for every 10"). 



A page of tables for converting sexagesimals into centesimals &c., com- 

 pletes the work, which is a thick small-sized quarto, with clearly printed 

 and not too heavy pages. After the printing of the work Prony asked 

 Delambre to examine the Tables du Cadastre (Avhich are to every 10" 

 throughout. the quadrant to 12 places ; but see § 3, art. 13) ; and this gave 

 Delambre the opportunity of reading them with Borda's table of sines and 



