The total of 159 skulls examined by me include 80 of _spinifer_, 50 of _ferox_, and 29 of _muticus_. There are no secondary sexual differences between skulls of corresponding size, except in _agassizi_-form skulls mentioned under the account of _T. s. asper_, and possibly in _ferox_. Most, and possibly all, of the skulls of _muticus_ having a basicranial length of 40.0 millimeters or more, and those of _spinifer_ exceeding 50.0 millimeters must represent females (by correlation of known maximum size of males with greatest width of head, which is, in turn, compared with the greatest width of skull and corresponding basicranial length). [Illustration: FIG. 15. Skulls of _Trionyx spinifer hartwegi_ (left, a-d, KU 2757), and _Trionyx muticus muticus_ (right, e-h, KU 1870). Dorsal views, a (× 1/2), e (× 3/4); occipital views, b (× 5/6), f (× 1); lateral views, c (× 1/2), g (× 3/4); ventral views, d (× 1/2), h (× 3/4). a., alveolar surface of upper jaw aq., articular surface of quadrate ex., exoccipital fp., fenestra postotica fm., foramen magnum if., intermaxillary foramen ic., internal choana mx., maxilla mxb., maxillary bridge oc., occipital condyle op., opisthotic ope., opisthotic-exoccipital spur opw., opisthotic wing pmx., premaxillaries (fused) pt., pterygoid q., quadrate qj., quadratojugal sq., squamosal s., supraoccipital spine tc., tympanic cavity ] Measurements used include basicranial length (occipital condyle to tip of upper jaw), greatest width (variable in position), greatest width of alveolar surface of maxilla (taken at level immediately posterior to anterior margin of internal choanae), greatest length of internal choanae, and least breadth of maxillary bridge (separating internal choanae and intermaxillary foramen). One ratio developed from the measurements was greatest length of internal choanae/least breadth of maxillary bridge, hereafter referred to as IC/MB. This ratio is discussed under the account of _T. s. asper_. _Greatest Width_ The position or level on the skull where the greatest width (Table 3) occurs is of some diagnostic value in distinguishing the skulls of _ferox_ from _spinifer_ and _muticus_. Skulls of _ferox_ usually are widest at the level of the quadratojugal (immediately in front of tympanic cavity), whereas skulls of _spinifer_ and _muticus_ usually are widest slightly more posteriorly at a level on the squamosal immediately behind the tympanic cavity. Occasionally the width at the level of the quadratojugal and squamosal is the same, or the greatest width of skull may be ventrad between the quadrates, which are slightly flared laterally. The latter condition possibly is most prevalent in _muticus_.