152 Sjjmmctt'ij of Egg and Symmetry of Embryo in the Frog 
separately it will be evident that, with the one exception just noticed, the former 
declines when the latter increases, and conversely. 
There is one other point that must be noticed. It is evident from Tables II. 
to V. that the dorsal lip appears in the great majority of cases on the same side 
of the egg as the grey crescent since in these observations the measurement was of 
the angle between the dorsal lip, or grey crescent, and the zero point. It may how- 
ever occur that these two structures appear on opposite sides of the egg, though 
this does not occur at all, or very little, when the axes are horizontal but the eggs 
spaced (IV.), and not very much when the eggs are spaced and the axes vertical 
(V.). It is under these conditions that the correlation between these two planes 
is highest. It must however be remembered that in calculating the coefficient the 
angles made by each of these planes with the First Furrow are compared, angles 
in which it is impossible, owing to the indistinguishability of the ends of the 
Furrow, to discriminate between any value and its supplement. 
Professor Pearson has however pointed out to me that since, any two of these 
angles being known, the third is directly obtainable; since in fact a — fi = <y where 
a, and 7 are the three angles, the three correlation coefficients ought also to be 
definitely related, namely, they should be the cosines of three angles which are 
together equal to 180°, and further the standard deviation being known of two 
angles and the value of the coefficient of correlation between them, the remaining 
standard deviation and coefficients should be obtainable by the formulae 
o"y" = o"a" + cr^- — 2cra o-p Pap , 
— a; ' 
CTaPaP — Crp 
pPy= ---- 
<7y 
In order however that 7 may always =a — /3, it is necessary that the angles 
should always be measured in the same sense, and this gives in certain cases a 
value for a (Plane of Symmetry and First Furrow) or for 7 (First Furrow and 
Sagittal Plane) which is greater than 90°. In working out the results already 
tabulated these cases had always been entered as less than 90°, that is, owing to 
the impossibility of distinguishing between the two ends of the First Furrow, the 
smaller of two supplementary values was always taken. For example : 
Let /3 (Plane of Symmetry and Sagittal Plane) be 100°, 
7 (First Furrow and Sagittal Plane) be — 30°, 
then a = fi + j= 130°, but was entered always as —50°. 
Hence the coefficients do not possess the magnitudes they should do to satisfy 
the equation. At the same time where ^ + y = nearly 180°, there is clearly a close 
relation between the First Furrow and the Symmetry Plane. After some discussion 
I have decided to adopt the following convention suggested by Professor Pearson. 
