9.2 REPORT— 1873. 



The order of the columns is sine, tangent, difference for sine, difference for 

 tangent, cosine ; but this arrangement only holds up to 5", when differences 

 are added for the cosine also. A change in the figiu-e at the toj) of the 

 column is denoted in the column by a line subscript under all the figures of 

 the firsf^^ logarithm affected, which arrests the eye at once. 



[T. VII.J Natural and log sines (to 15 places) for every 10' (ten minutes 

 centesimal) of the quadrant. It is as well here to note that in the log sine 

 and cosine columns only nine figures are given, as the preceding figures are 

 olitainable from [T. VI. J ; two, however, are common to both : thus from 

 [T. VI.] we find log sin 10'=7-1961197, and in [T. VII.] we have given, 

 corresponding to log sin 10^ 969843372; so that log sin 10'=7-19611969 

 843372. It will therefore be noticed that the log sines are in strictness 

 given to 14 (and not 15) places. Further, it appears that the last figure 

 has not been, or at all events not been always, corrected; for log sin 50"= 



log -^ = -34948500216800940...., and the logarithm in [T. VII.] ends 



with the figures 6800. This is the only one we have examined. 



At the end of [T. VII.] is given a page of tables to connect decimals of a 

 right angle with degrees, minutes, and seconds, ikc. 



[T. VIII.] consists of proportional-part tables, and occupies 10 pp. : by 

 means of them any number less than 10,000 can be multiijlied by a single 

 digit with great ease ; the use of this in interpolation is evident. A full 

 explanation is given on pp. 32-36 of the Introduction to the work. 



[T. IX.] Log sines and tangents for every second of the first five degrees, 

 to seven places, without differences (sexagesimal). 



[T. X.] Log sines and tangents for every ten seconds of the quadrant, to 

 seven places, with differences (sexagesimal). 



[T. XL] Logistic logarithms, viz. log 3600" — log x" from x = 0" to 

 a- = 5280" = 1° 28'; 3600" = 1°. 



The other tables have reference to Boi'da's method for the determination 

 of the longitude at sea. 



On the whole, this is the most complete and practically useful collection 

 of logarithms for the general computer that has been published. In one not 

 very thick octavo volume, 11 important tables are given ; the type is very 

 clear and distinct, though rather small. In the logarithms of numbers an 

 attempt has been made to give rather too much on the page ; but for general 

 usefulness this collection of tables is almost unique. 



The introduction, of 118 pp., is the worst portion of the work ; it is badlj' 

 arranged, confused, and, worst of all, has no index ; so that it is very hard to 

 find the explanation of any table required, if it is explained at all. On 

 p. 112 the value of e is given; but the figures after the 8th group of five 



are erroneous, and should be 47093 69995 95749 66967 6 (see Erit. 



Assoc. Report, 1871, Transactions of Sections, p. 16). 



On pp. 12 and 13 of the introduction are two tables that deserve notice ; 

 the first gives the square, 4th, IGth .... 2''°th roots of 10 to about 28 significant 

 figures (leaving out of consideration the ciphers that follow the 1 in the 

 higher powers). The second gives powers of '5 as far as the 60th. 



With regard to errors, an important list is given by Lefort in the ' Comptes 

 Uendus,' vol. xliv. p. 1100 (1857) ; and these of course apply to the later 

 iirages. Manj^ errors of importance, as also some information as to the 

 sources whence CaUet derived his tables, are given. See also Gauss in Zach's 

 ' Monatliche Correspondonz,' November 1802 (or 'Werke,' t. iii. p. 241), for 

 four errata, and Gernerth's paper (referred to at the end of the introductory 



