ON MATHEMATICAL TABLES. 3 



any one that is of value in relation to mathematics as a science will be in- 

 cluded, although it may have been calculated for merely commercial purposes 

 and published under a name that would apparently exclude it from this Report. 

 ]\[auy tables of compound interest are valuable when viewed as tables of powers; 

 and many navigation tables calculated merelj^ for the use of the sailor, and pub- 

 lished under titles that would imply that they were of a merely technical cha- 

 racter, are in reality trigonometrical tables under a disguised form. 



From the above remarks it will be found in most cases very easy to decide 

 whether a table is included in the scope of this Report or not. A few of course 

 come on the boundary ; and then there is some little difficulty in drawing the 

 line fairly. Of this kind are tables for the expression of hours and minutes as 

 decimals of a day, &c. ; most of these it has been thought better to include. 



It was necessary as a preliminary to form a classification of mathematical 

 (numerical) tables ; and the following classification was drawn up by Prof. 

 Cayley and adopted by the Committee. 



A. Auxiliary for non-logarithmic computations. 



1. Multii:)lication. 



2. Quarter-squares. 



3. Squares, cubes, and higher powers, and reciprocals. 



B. Logarithmic and circular. 



4. Logarithms (Briggian) and antilogarithms (do.) ; addition and sub- 



traction logarithms, &c. 



5. Circular functions (sines, cosines, (fee), natural, and lengths of circular 



arcs. 



6. Circular functions (sines, cosines, &c.), logarithmic. 



C. Exponential. 



7. Hyperbolic logarithms. 



8. Do. antilogarithms (e^) and h . Itan (45°-\-i(j)), and hyperbolic sines, 



cosines, «fcc., natural and logarithmic. 



D. Algebraic constants. 



9. Accurate integer or fractional values. Bernoulli's Nos., A'' 0'"^, &c. 



Binomial coefficients. 

 10. Decimal values auxiliary to the calculation of scries. 



E. 11. Transcendental constants, e, tt, y, &c., and their powers and functions. 



F. Aritbmological. 



1 2. Divisors and prime numbers. Prime roots. The Canon arithmeticus &c.' 



13. The Pellian equation, 



14. Partitions. 



15. Quadratic forms a--\-h^, &c., and partition of numbers into scjuarcs, 



cubes, and biquadratcs. 

 10. Binary, ternary, &c. quadratic and higher forms. 



17. Complex theories. 



G. Transcendental functions. 



18. Elliptic. 



19. Gamma. 



20. Sine-integral, cosine-integral, and exponential-integral, 



21. Bcsscl's and allied functions. 



22. Planetary coefficients for given -,. • 



23. Logarithmic transcendental. 



24. Miscellaneous. 



b2 



