84 REPORT — 1873. 



two additional tables, &c., translated from the Latin of E. de Joncourt by 

 the author's self.' 



Phillips, 1829. This is not properly a table at all. Names and an 

 abbreviated way of writing them are suggested for all numbers up to 9 

 followed by 4000 figures, the chief peculiarity of the system being that 1000 

 is called ten hundred, and 10,000 a thousand, and so on. The only 

 explanation of the object of the table is contained in the curiously untrue 

 remark that, by adopting the author's names, " we obtain a clearer view of 

 calculations which are generally called inconceivable only because we have 

 hitherto adopted no terms to express and hmit them." On Sir R. Phillips, 

 and the value of his works, see De Morgan's 'Budget of Paradoxes' (1872), 

 pp. 143-145. 



D. Galbraith, 1838. A piece contains 4, 5. . . .56 squares, and the 

 table is to show the number of dozens in any number of pieces up to 100, 



&c. It contains ^ for x = 4, 5 56, and y = 1, 2, 3 100, 200, 



300, 400, and 500, the value of x being constant over any one page : thus 

 X = 15, 1/ = 65, we have given 81-3 for jL (15 x 65) = 81j'^y . The table was 

 calculated to give the number of handkerchiefs in any number of pieces, «S:c. 



De Morgan, 1843. Degen's table (§ 4) of log (1, 2. . . .w) is reprinted 

 to six places by De Morgan at the end of his article on " Probabilities " in 

 the ' Encyclopaedia Metropolitana.' The last figure is not corrected : the 

 table occupies pp. 486-490. 



Rouse (no date). The tables, which are neither elaborate nor very nume- 

 rous, are not of sufficient mathematical value to render it necessary to do more 

 than give a general idea of their contents. In the body of the work are a num- 

 ber of small tables of this kind : — A and B (of equal skill) play 21 games ; and 

 the odds in favour of A's winning 1,2.... 20, 21 are given as tabular results. 

 Similar tables are given for 20, 19 .... 2 games played. Then we have the 

 same when the odds in favour of A are 6 to 5, 5 to 4, 5 to 3, &c., — the 

 maximum number of games, however, being six. On a folding sheet at the 

 end is given the number of ways in which 1, 2, 3. . . .60 points can be 

 thrown with 1, 2. . . .10 dice, and also the number of ways iu which 52 

 cards can be combined into 4 hands in any given manner (thus, 5 diamonds, 

 4 hearts, 3 spades, and 1 club can be obtained in 3421322190 ways); the 

 factor and the result when the suits are not specified are also given. The 

 mode of formation of the table is obvious. 



On a folding sheet at the beginning of the book is given (a + 6)" at 

 full length hrn = l,2.... 30. 



The following is a list of miscellaneous tables contained in works that are 

 described in § 4. For greater convenience a brief description of the contents 

 of each table is appended to the reference to it. 



Figurate Numbers. — Lambert, 1798, T. XXXVII. 



Hyperbolic Antilogarithms {viz. powers of e) and their Briggian logarithms, 

 — ScHULZE, 1778 [T. I.] ; Vega, 1797, Vol. II. T. III. ; Lambert, 1798, T, 

 XI. ; Hulsse's Vega, T. VII. ; Kohler, 1848, T. III. ; Shoetrede, 1844 

 [T. XL], III. ; Hutton, 1858, T. XII. ; Callet, 1853 [T. II.], III. 



Miscellaneous. — Sharp, 1717 [T. I.] | multiples of j); Dodson, 1747, 



T. XX. (combinations), T. XXIII. (permutations), T. XXXV. (seconds in any 

 number of minutes less than 2°) ; Schulze, 1778 (Pythagorean triangles) ; 

 Maseres, 1795 (miiltiples of primes); Vega, 1797, Vol. II. [T. VII.] and 

 [T. VIII.] (piling of shot) ; Lambert, 1798, T. II. (multiples of primes), T. 



