108 
Transactions of the Royal Society of South Africa. 
(1) The gill septa with their skeletal elements of the apparently primitive 
Cyclostomes and Elasmobranchs are fixed, not projecting beyond the surface, 
and therefore not likely to give rise to external organs like paired limbs. 
This may be admitted in the case of the Cyclostomata, but it is just these which 
have no paired limbs. In the case of the Elasmobranchs the opercula are 
external organs and are well developed in Chladoselachidae and Holo- 
cephali. 
(2) Another objection to the origin of pectoral fins from vertical folds is 
that it has been observed in most cases examined that when they arise as 
folds of the body these are more or less longitudinal in direction, and it is 
only subsequently that they assume a vertical position, and that by rotation 
sometimes in one direction, sometimes in another. This certainly does not 
corroborate this vertical fold origin, but it may be noted that the position of 
the developing paired limb has not been investigated in many kinds of fish, 
and that the paired limbs of Elasmobranchs are not necessarily primitive in 
this respect. In this group and that of the Dipnoi, indeed, the endo- 
skeletal elements seem rather to be taking the place of the primitive fin. In 
some Achirus and in the larval form of a very large South African sole 
(Synapturs microlepis) the rudiments of the pectoral have been observed to 
be vertical in position. 
In this connection, however, another theory of the origin of paired limbs 
which has been much discussed may be noted, namely, that they arise from 
a longitudinal lateral fold, not such as Balfour supposed to have occurred in 
primitive fishes, but as it arises in the formation of the metapleural folds in 
Amphioxus (Thatcher, etc.) These folds now function as a protective 
covering for the external opening of the gill slits. Evolution of organs 
is often in the direction of a reduction in numbers in co-ordination with the 
elaboration of a few, and it is not impossible that with muscular pharyngeal 
in place of the more primitive ciliary respiration the fold may have become 
differentiated into valvular opercular flaps for the remaining gill opening. 
This suggestion is very speculative as is also this theory itself, but it is 
mentioned as a possibility which might indicate that the origin of paired limbs 
in ontogeny as longitudinal folds which only later become vertical folds is 
not so inconsistent with their derivation from opercula as appears. 
(3) It is objected that transverse folds across the body, such as the 
opercula, would rather tend to arrest than to assist in the forward movement 
of a swimming fish, but it is just for this purpose that paired fins are frequently 
used, as may.be observed in the commonest types of fish in life. With 
the shortened and deep body assumed by the vertebrates in taking to 
a free-swimming life there is no such provision for the checking of the 
forward movement as is found in the more elongate bodies, in which advance 
or retreat can be effected by a reversal of the undulatory movement of the 
body and paired fins are necessary for this purpose. This is confirmed by 
