611] REPORT OF THE COMMITTEE ON MATHEMATICAL TABLES. 499 
And the like further complication presents itself in the part III. of the same 
table, X = 28 (not, as it happens, in part II., nor of course in the concluding part IV., 
which is a mere enumeration of real primes). Thus III. (1), we have congruences^ 
(mod. p 3 ), 
p = % v = -%> P = %, Vn — + 12, &c.; 
and having actual prime factors, 
p 
59 
101 
and having ideal prime factors, their third powers actual, 
P f 3 (v) 
2 I-t;, 
3 1 - 277,; 
as regards these last the signification being 
2 3 = (1 — 77„) (1 — 77,), 77o + 77, = — 1, 77o77, = 6 (as is at once verified), 
3 3 = (1 — 277 0 ) (1 — 277,) ; 
but the simple numbers 2, 3 are neither of them of the form (a + brj 0 ) (a + 677,). 
f(v) 
5 - 2t7, 
1 - 477,; 
Contents of Report 1875 on Mathematical Tables. 
7. Tables F. Arithmological. 
Page 
Art. I. Divisors and Prime Numbers ...... 462 
II. Prime Roots. The Canon Arithmeticus, Quadratic residues 471 
III. The Pellian Equation . . . . . . . . 477 
IV. Partitions .......... 480 
V. Quadratic forms a 2 + b' 2 &c., and Partitions of Numbers into 
squares, cubes, and biquadrates ..... 484 
VI. Binary, Ternary, &c. quadratic and higher forms . . . 486 
VII. Complex Theories ......... 493 
63—2