108 REPORT— 1873. 



This tabic is followed by 2 pages of tables for the conversion of centesimals 

 into sexagesimals &c. 



T. V. All prime divisors of numbers to 102,000 (multiples of 2, 3, and 5 

 excluded), and primes from 102,000 to 400,313. 



T. VI. Hyperbolic logarithms of numbers to 1000, and of primes from 

 1000 to 10,000, to 8 places. This is followed by powers of 2, 3, and 5 to the 

 45th, 36th, and 27tb respectively. 



T. VII. Powers of e and their logarithms, viz. e' and log ^^e^, from .r=*01 

 to .r=10 at intervals of "Ol, to 7 figures and 7 places respectively. 



T. VIII. Square and cube roots of numbers to 10,000, to 12 and 7 places 



respectivelj''. The table is followed by a page of coefficients, such as ^ — ~\ 



1 1.3 



5 — T~7;) 9~~i — -■> <i^c., to 10 places, and their logarithms to 7 places. 



T. IX. Power-tables. A, the first 11 powers of numbers from -01 to 1*00 

 at intervals of -Ol, to 8 places. B, the first 9 powers of numbers from 1 to 100. 

 C, squares and cubes from 1 to 1000. D, the first hundred powers of I'Ol, 1-02, 

 1-025, 1-0275, 1-03, 1-0325, 1-035, 1-0375, 1-04, 1-045, 1-05, 1-06, to 6 places. 

 E, the first hundred powers of the reciprocals of these numbers, to 7 places, 

 r, the sums of the powers in D : this table therefore gives x-\-x'^ ■\- . . . ..r" 



(-fe?) 



for the values of x written down under D, and for n = 1, 2, 3, . 



100. G stands in the same relation to E thatF does to D. The tables from 

 D to G Avere calculated for their use in computing interest &c. 



T. XII. An extended table of Gaussian logarithms. It gives B from A = 

 •000 to A= 2-000 at intervals of -001, from A = 2-00 to A = 3-39 at intervals of 

 •01, and thence to A = 5-0 at intervals of -1, to 5 places. There are also given, be- 

 sides, other quantities for the same arguments, viz. C (=:A + B), D (=B4-C), 

 E ( = A-|-C), and F (=B— A), all to 5 places, with difierences and propor- 

 tional parts (of two kinds) for B and C. 



^( ^ W Cc(oO^—\'\ ( X Of 



T. XIII. Interpolation table, viz. '-^^-^ — -, . . ^— — , o ft > ^^°™ 



a; = '01 to .r=l-00 at intervals of -01, to 7 places ; then follows a page of 

 constants. There are, besides, mortality tables, very complete tables of mea- 

 sures and weights of different countries, &c. The table of 12-place square 

 roots was published' here for the first time : it was calculated by Hensel in 

 1804. The seven-place cube roots, the chord-table, and the new columns of 

 the Gaussian table were calculated by Dr. Michaelis, of Leipzig. The author 

 draws attention to the fact that the last figures in T. VIII. and XII. are given 

 correctly. 



It is a matter of sufficient interestto note here that, though the work is called 

 an edition of Vega, it contains one error from which the other tables known by 

 the name of Vega and published subsequently to his folio of 1794 were free. 

 In Vlacq (1628), log 52943 was printed 7238085868 instead of 7238085468, 

 and the error was first pointed out and corrected by Vega in his folio of 1794. 

 All the seven-figure tables, therefore, from 1628 to 1794 (and several of the 

 subsequent tables also), have 7238086 instead of 7238085 ; but Vega's smaU 

 editions (the ' Manuale ' and ' Tabuloe ') have the logarithms correctly printed. 

 In Hulsse's edition, however, the error is reproduced afresh, and the last figure 

 is printed 6. It follows therefore either that Hiilsse did not reprint Vega's 

 table, or that, if he did, he noticed the discrepancy, and decided in favour of 

 tlie erroneous value. The slight suspicion thus cast on these tables is unfor- 



