110 Transactions of the Royal Society of South Africa. 
Perhaps it may be necessary to note another point of view which has 
been taken up with regard to this question of the origin of paired limbs. It 
is pointed out that in development it is the mesodermal elements which 
seem to take the initiative, that in the origin of the skeletal elements the 
successive appearance of parts is from within outwards, and that a mere 
epidermal fold cannot be looked on as the actual origin of limbs, for the 
real structure of a fin begins only when the supporting mesodermal cartila- 
ginous elements appear. With regard to the first two points, it is true that 
ontogeny is often a valuable guide in tracing the rise of an organ, but not an 
infallible one, and with regard to the last, the finished organ is often 
totally different from its initial phases, as for instance in the case of the 
axial skeleton of vertebrates. Besides, it is difficult to imagine that an 
external organ of locomotion originated entirely from an internal structure. 
It seems, therefore, quite legitimate to discuss the origin of paired fins apart 
from that of the radials or girdles. 
Reviewing the position as a whole with regard to the origin of unpaired 
fins, apart from the question of the source of their secondary supporting 
structures, the following hypothesis has been proposed: (1) The external 
valvular flaps of the gill septum and (2) external gills attached to the gill 
septum ; (3) longitudinal lateral folds of the body conjectures from certain 
evidences to have been present in some primitive fishes ; (4) longitudinal 
lateral folds such as occur in Amjphioxus ; (5) unpaired fins. 
The only one of these which seems entirely exclusive of the others is the 
last, for which there is little or no evidence. What is suggested is that the 
paired limbs of fishes arose as modifications of the external gill flaps, called 
here for convenience valvular opercula, which appeared as separate active 
external organs in co-ordination with muscular pharyngeal inspiration and 
expiration, and that these opercula in their turn may have originated as 
segmental differentiations of a supra-branchial lateral fold, originally used 
in raising and sustaining the body in the water, and which now appears in 
ontogeny as more or less disconnected longitudinal folds. This is not 
opposed to the hypothesis that external gills which are vascularised gill 
septa may have given rise to the paired limbs of Amphibia and terrestrial 
animals. 
Much more could probably be said in elaboration of the supposed oper- 
cular origin of paired limbs. Thus a specially pleasing feature, and there- 
fore perhaps to be regarded with caution, is that it appears to account for 
the absence of paired limbs in the Cyclostomes which have a branchial arch 
skeleton but no opercula, and shows that this negative feature is not secondary 
but essentially connected with one of the three fundamental characters of 
the Chordata, namely pharyngeal respiration by gill slits : in fact the phylum 
could be divided into two sub-phyla on the basis of its pharyngeal 
respiratory system and its derivatives (paired limbs) thus : 
