26 THE AMERICAN NATURALIST. [VoL. XXXV. 
divides about one-third of the distance from the anterior 
end. The normal leg of the left side is connected with the 
more ventral and mesal of the two parts, as would be natural 
from its position. The dorsal part is apparently free from the 
pubis. The distal extremity of the tibio-fibula appears to have 
three terminal enlargements instead of the normal two. Three 
bones of about the same size replace the normal astragalus and 
caleaneum. Eight bony elements align themselves in the posi- 
tion of the metatarsals, one group of six, with two very much 
smaller ones at some distance. Three phalanges arise from the 
terminal metatarsal of the more strongly developed end and 
one from the next metatarsal. This structure certainly bears 
out Bateson's statement : * In the enormous majority of poly- 
melians the extra repetition consists of parts of a complemen- 
tary pair." 
Case III (Figs. 2, 10, 11, 12) is another young Rana hale- 
cina Dum. and Bibr, in the anatomical collection of the 
University of Chicago, which from an accompanying note 
seems likely to have been found in the immediate vicinity. 
The coloration of the body is somewhat abnormal, in that the 
. Spots are smaller and more numerous than is usual. Directly 
ventral to the right fore leg, which is slightly displaced dorsally, 
and is smaller than the normal leg of the other side, is a pe- 
duncle from which two legs arise. These are each about the 
size of the left normal leg and distinctly larger than the normal 
leg of the right side. Each of the supernumerary legs seems 
normal in its parts and has the usual blotches. The ulnar aspects 
face each other. The skiagraph reveals two fused bones in 
the cone-shaped projection (indicated by asterisk) between the 
supernumerary legs. It seems to me that we must regard each 
of the halves of the outgrowth as again double, the internal 
member of each pair having developed from pressure and. 
Juxtaposition into these two fused bones in the cone-shaped 
projection. This seems likely from the analogy in abnormali- 
ties of crustacean appendages, such as that shown in Fig. 182, 
IV, in Bateson's Materials Jor the Study of Variation, which is 
taken from Maggi. In the cases cited of duplicity of append- 
ages already of a double nature, the two median elements fuse 
