No. 431.) PAIRED LIMBS OF THE VERTEBRATES. 841 
upon the general problem of limb migration. He was, how- 
ever, unable to carry out his plans, and he generously turned 
over to me his measurements for use in the present paper. 
DETAILS OF DATA. 
Straight specimens were selected for measurement. Gravity 
center was determined in terms of the total length ! by balancing 
the specimen either on a knife-edge or within the delicate tips 
of curved forceps. By this simple method the limit of error was 
found to be surprisingly small, estimated by repeated tests at 
about r per cent. In the measurements individual variations 
are taken into account, since it was found that a more advanced 
embryo is sometimes smaller in size and variable slightly in 
proportions, and in preparing the table of averages as plotted 
in Fig. 1 this source of error has been largely counterbalanced 
by the use of guide points representing the average of several 
(usually four) successive individuals. All measurements are 
computed in percentage of the total length of the specimen, and 
are estimated from the snout tip. The landmarks whose rela- 
tive position is computed are indicated graphically in the present 
Fig. 1,2.¢., anterior margins of pectoral, of ventral, and of dorsal 
fins, and posterior margins of pectorals and ventrals. Of the 
latter margin the functional (dermal) one is alone considered. 
THE RESULT OF THIS ANALYSIS. 
The center of gravity is found to shift forward (about 
5 per cent of the total length) in the earlier embryos (embryos 
from 27 mm. to about 6mm.), in later stages (up to embryos 
of 200 mm.) backward to the extent of about 8 per cent of the 
total length. In well-grown specimens the position of the 
gravity center remains practically unchanged. 
The pectoral fin undergoes conspicuous changes: from the 
time it can be distinctly differentiated from the ventrals it 
1 The transverse plane in which the center occurs was alone determined; its 
more accurate position within this plane has evidently no bearing upon the present 
problem. 
