ON MATHEMATICAL TABL13S. 83 



The following is a list of references to § 4. 



Lists of Constants.— Bomos, 1747, T. XXVIL ; Galbeaith, 1827, T 

 LXIII. ; Hanischl, 1827, T. XI. ; [De Morgan], 1839 [T. V.] ; Fasley, 

 1840 [T. III.] ; MuLLER, 1844 [T. IV.] ; Shortrede (Tables), 1844, T. II. 

 MtLLER, 1844 [T. IV.] ; Eaper, 184G, T. V. ; Kohler, 1848 [T. III.] 

 Byrne, 1849 [T. III.] ; Bremiker, 1852, T. II. ; Willich, 1853, T. XX., &c. 

 Shanks, 1853 (constants to a great many places) ; Beemikee's Vega, 1857 

 HoiJEL, 1858, T. VIII. ; Hutton, 1858, T. XII. ; Galbeaith and Hatohton, 

 1860 [T. IV.] ; Wackerbaeth, 1867, T. IV., V., and XXI. ; Bruhns, 1870. 



Note. — Binomial-theorem coefHcients and coefficients of series-terms are 

 noticed under Interpolation Tables in § 3, ai't. 21. 



Art. 25. Miscellaneous Tables, figurate Numbers, Sfc. 



We have placed in this article tables which could not properly be 

 described under any one of the previous twenty-four heads. The list is not, 

 however, a long one, as we have frequently placed doubtful tables in the 

 article which most nearly applied to them. 



We may refer especially to Jonoourt's table of triangular numbers (de- 

 scribed below), which is perhaps unique. Eetshammer's commercial loga- 

 rithms and Montferriee's binary logarithms are described in § 3, art. 13, 

 Picarte's table to facilitate the performance of divisions is described in § 3, 

 art. 7. We may also particularly notice Degen's large table (§ 4) of "log 

 1-2. . . .x). There is a table of binomial-theorem coefficients in Eoijse (see 

 below) ; and other tables of the same kind are referred to under Interpolation 

 Tables in § 3, art. 21. Tables of endings of squares are noticed in § 3, 

 art. 4 ; and tables for the solution of cubic equations, viz, + {x — x^), in 

 § 3, art, 5. 



Browne, 1731, Pp. 6 and 7 are occupied by a table headed " Area of 



the circle in degrees and to the 10,000th part of a degree." CaUing ^ . a, 



> if B o 360 ' 



it gives a, 2a, 3a 100a, 200a, 300a, and 360a to 7 figures. There are 



also three other columns in which the results only differ by a change of 

 decimal point. 



Through a mistake in the printing in the copy before us, all the odd pages 

 are upside downi. 



Heilbronner, 1742. On pp. 922-924, the numbers from unity to 140, 

 72, and 100 are expressed in the scales whose radices are 3, 2, and 12 

 respectively. 



Joncourt, 1762 [T. I.]. A table of triangular numbers up to that of 



20,000, viz, ^''^"r^ ^' for all numbers from n = 1 to 20,000 (the table 



occupies 224 pp.). 



[T. II.] Cubes of numbers from 1 to 600. 



There are 36 pages of explanation &c., in which it is shown how [T. I,] 

 may be used in the extraction of square roots, &c, De Morgan refers to this 

 book as "De la Nature. . . .de Nombres trigonaux," 1762, so we suppose 

 some copies with the introduction &c. in French were published. The 

 Eoyal Society's copy has " Dec. 23, 1762," written in ink underj>.eath the 

 printed date. The book is handsomely printed. 



The Babbage Catalogue also gives the same work with an English title. 

 ' The Nature and Notable Use of the most simple trigonal numbers, with 



e2 



