362 An Objective Study of Mathematical T7itelligenGe 
The nature of the correlation tables, and the form of the regression curves to 
which they gave rise, seemed to indicate that the number of boys examined (83) 
was sufficiently large to give fairly reliable results. On the other hand, the 
numbers furnished by separate school forms of average size (say 20) are certainly 
too small. Thus, the correlation coefficient between mathematics and classics was 
calculated for the Mathematical Eighth Form of the same school for Christmas, 
1907, and again for Christmas, 1908. The two values were 0-20 and 0-52 
respectively, showing a discrepancy of 160 % of the smaller value ! Similarly, 
the mathematics-classics coefficient for the Vllth, U. Vlth, and L. Vlth forms of 
the mathematical division investigated in this paper worked out as 0"23, 0'76, and 
— 0'25 respectively. This would seem to indicate that the results of Correlational 
Psychology hitherto obtained, where small numbers of cases have almost invariably 
been used, are utterly unreliable. In such cases the ordinary formulae for 
probable errors (the proofs of which rest on the assumption of a large number 
of observations) do not apply, and consequently no clear appreciation of the 
significance of the results is possible. 
APPENDIX I. 
A. Sample of questions in Geometry. 
1. (a) If two triangles have two angles and a side of one equal respectively 
to two angles and a side of the other, they will be equal in all respects. 
(6) ABGD is a square, perpendiculars BL and DN are drawn to any straight 
line through A. Prove that AL = BN. 
4. (a) The straight line from the centre of a circle, perpendicular to a chord, 
bisects the chord. 
(b) OP is the radius of a circle. On OP as diameter another circle is 
described. Prove that all chords of the larger circle drawn through P 
are bisected by the smaller circle. 
