176 Symmetry oj Egg and Symmetry of Embryo in the Frog 
axis and yet not towards that point in the axis at which the fertilization spindle is 
to be developed (this point is pretty constant and about half-way between the 
animal pole and the centre of the egg). The funnel need not, however, even be 
directed towards the axis. Hence, the meridian of the ' copulation ' path may make 
an angle with that of the 'penetration' path. As a matter of fact, I have not always 
in the Frog succeeded in detecting a ' copulation ' path. It is generally most in 
evidence when, as in Fig. 5 C, the penetration path is turned away from the axis, 
and it is always, parallel to the furrow. In no case that I have observed did the 
penetration path under these circumstances make a greater angle than 30° with 
the First Furrow, and in all cases but one, the angle was less than 15°. We shall 
find that it will be necessary to divide the eggs into three classes according as the 
sperm-path is included in or parallel to the furrow (Fig. 5 A, B), inclined towards 
the furrow (Fig. 5 D) or away from it (Fig. 5 C) : in the last case the path does 
not of course lie in a meridional plane at all. 
The data necessary for the calculation of these angles are, the perpendicular 
distance, in the section in which it occurs, of the sperm-entrance point from the 
furrow, and the distance from the foot of this perpendicular to the middle point of 
the furrow in the same section; similar measurements for the inner end of the 
sperm-path (' penetration ' path) ; the distances (the number of sections of known 
thickness) between the sections in which occur the entrance point, the inner end 
of the path and the centre of the egg ; and lastly, the length of the egg radius. 
With the help of a little Trigonometry the value of the angles may then be found. 
Let us now consider the measurements. The distributions and correlations for 
Plane of Symmetry and First Furrow, Sperm-entrance Meridian and First Furrow, 
Sperm-entrance Meridian and Plane of Symmetry, Sperm-sphere Meridian and 
First Furrow, and Sperm-sphere Meridian and Plane of Symmetry will be found 
in Tables XXVI. to XXXI. There is a summary of results in Tables XXXII. and 
XXXIII. 
(1) The Plane of Symmetry and the First Furrow. 
I tabulate these merely for the purpose of comparison with previous results. 
I. When the eggs are close and the axes horizontal (XXVI. a, a\ a") the 
standard deviation is cr = 45-99 + 2-00 but there is clearly a tendency for the 
Furrow to be not only in but at right angles to the other plane. This is what 
occurred in the original series of eggs examined (described in the previous paper, 
and tabulated above in Table L). The value of a was there 48-33 + 1-14. The 
values of the standard deviation have also been calculated about 0° and about 90° 
separately; they come to o- = 18-63° + 1-39 and o- = 21-48° + 1-60 respectively, as 
compared with o- = 18-70° + 0-60 and o- = 23-29° ± 0-86 found before (Table I.). 
The agreement is, I think, sufficiently close. 
II. When the eggs are spaced and the axes vertical, the standard deviation 
works out at o- = 25-34° ± r63. This is not so near to the values obtained previ- 
