No. 2.] THE STUDY OF VARIATION. 463 
Section III. 
Why does the variation tend towards forward rather than 
backward homeeosis ? 
Bateson says ‘the attempt to apply to numerical variations 
the conception of variation as an oscillation about oze mean is 
not easy, difficulty arising especially in regard to the choice of 
a unit for the estimation of divergence; ... to judge from the 
scanty indications available, it seems that in cases of numerical 
change, variations to numbers greater than the normal number 
and to numbers less than it, are not generally of equal fre- 
quency. Probably no one would expect that they should be 
Soi) (9450571). 
It has already been noted that in 28% of the one hundred 
salamanders examined, the sacral ribs are borne on the XX 
vertebra, while in not a single specimen are they symmetrically 
borne on the XVIII. Most certainly numerical variations to- 
wards a greater number, than the normal, of pre-sacral vertebrze 
are more frequent than variations towards a smaller number. 
The positions of the oblique or unsymmetrical sacra also 
indicate pre-sacral increase. In only one case among the 
eight examples is the territory of the XVIII vertebra invaded 
(Plate A, Spec. 62), and this invasion marks the only en- 
croachment upon the domain of this vertebra in a total of 127 
specimens examined by Parker and myself,—an interesting 
fact when it is considered that the XX vertebra, no further 
removed morphologically, presents a total of 35 invasions. 
Of course the easiest way of disposing of this question is to 
look upon the variation as atavistic. The “ancestral type” 
was possessed of a larger number of pre-sacral vertebrz, and the 
“mud-puppy ” of to-day, by its anatomical variations, kindly 
indicates, in approximately 35% of its representatives, the 
character of its quasi-progenitor. 
But if 35% of the present individuals tend towards pre-sacral 
multiplication, z.e., tend to assume ancestral characters, we must 
not deny to these potentially progenitorial individuals the same 
tendency to vary that is possessed by their young, z.c., 35% of 
the thirty-five should have an added increase of the pre-sacral 
