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TRANSACTIONS OF THE AMERICAN PHILOSOPHICAL SOCIETY 



My studies on the body-forms of fishes (1928), which were based primarily on measure- 

 ments made on the Jrcturus expedition of the New York Zoological Society, set forth the 

 various ways in which the form of the cephalic and post-cephalic parts of the whole fish 

 are correlated with each other and tend in norma lateralis to conform to a superposed kite- 

 shaped frame of reference. 



Stream-lining of the head, back and belly may be the resultant of growth along various 

 "metabolic gradients" in the three principal axes of length, height and thickness. The 

 kite-shaped figure results from the location of the peak of the vertical gradient somewhere in 



Fig. 295. The "entering angle" and the "run." A. Long-bodied fish [Aldrovandia macrochir). B. Deep-bodied fish 

 (Xesurus punctalus). P, prosthion; A, apex; G, gasterion; O, opisthion. 



the first third of the long diameter of the body. Hence as a rule the "entering angle" 

 (which is determined at least in part by the shape of the head) is greater than that of the 

 "run," or tapering part of the body (Fig. 295). The stream-lining of the body as a whole 

 largely depends upon the contours of the surface bones and of the skin but the neurocranium 

 and backbone must form an adequate support for the whole stream-lined shield. 



Ceteris paribus, the detailed proportions of any given skull element will be in direct 

 geometrical relations to tendencies that affect larger areas. Thus Fig. 295 shows that the 

 slope of the cranial roof tends to vary directly with the height of the apex of the back; while 

 Fig. 296 indicates that the slope of the cranial roof tends to vary inversely with the distance 

 from the tip of the snout to the apex, projected on the horizontal. 



Differential growth rates — Intrinsic and extrinsic. — In the individual development of 

 anguilliform fishes the fastest growth increments have obviously been along the antero- 



