the components of the molecular rotation are first found, viz.,

Then the potentials L, M, N of distributions of matter of densities $/2, 1/2, (/27 respectively throughout the ellipsoid are determined.

N = 0,

where

Then

du

a2+u c+u (a+u)" (c2+u)1

is the parameter of the confocal ellipsoid through x, y, z.

To obtain the corresponding expressions inside the ellipsoid it is

which, with a suitable value of k, gives the potential of the irrotational motion outside the ellipsoid moving parallel to the axis of z with velocity Z.

ƏN ƏM ƏL ƏN ƏM ƏL
Əy Əz' Əz Əx' dx dy

are not re

But inside the ellipsoid spectively equal to the values of u, v, w from which the investigation commenced.

VOL. LV.

R

7. The expressions

0

ƏN ƏM ƏL ƏN ƏM ƏL

ду дх ду

by dz' az ax' day cannot be taken by themselves to represent the velocities inside and outside the ellipsoid, for, though they would furnish continuous values of the velocities at the surface of the ellipsoid, they would not make the pressure continuous.

V. "Researches on the Structure, Organisation, and Classification of the Fossil Reptilia. Part IX. Section 1. On the Therosuchia." By H. G. SEELEY, F.R.S. Received January 8, 1894.

(Abstract.)

This paper discusses the classification of reputed Permian and Triassic Reptilia which have been referred to the Anomodontia as Theriodonts.

Lycosaurus, as the genus placed first on the Sir R. Owen's list, is accepted as the type of the Theriodontia. The species Lycosaurus curvimola is regarded as the type of the genus, being the only species in which its characters are fully shown. Galesaurus planiceps, which was the type of the Cynodontia, is probably distinct from Nythosaurus larvatus, and from Sir R. Owen's second type of Galesaurus planiceps of 1887, which is referred to as Thrinaxodon liorhinus. Elurosaurus felinus agrees with Galesaurus in having a transverse development of bones of the palate, regarded as palatine and transverse, which abut toward the inner side of the lower jaw. The palate in this genus is found to be covered with groups of small teeth with conical crowns,

which are unknown in Lycosaurus. The palate of Lycosaurus curvimola is found and described in the type specimen. It shows a transverse development of the palatine arch abutting against the lower jaw, behind which is a long compressed sphenoidal keel flanked by narrow pterygoid bones. The occipital condyles do not appear to be prominently developed in Lycosaurus. The genus is regarded as the type of a division of the Theriodontia, defined by having the molar teeth pointed and without cusps. A snout from Tamboer, named Pristerognathus polyodon, is referred to this group. It is characterised by six incisor teeth in each premaxillary bone and three incisor teeth in each ramus of the mandible, followed by canine teeth and small molars of Lycosaurian type.

Professor Cope's definition of the Theriodontia as distinguished from the Anomodontia by characters of the post-orbital arch is regarded as unsupported by evidence. The author would limit the Theriodontia to animals which conform to Sir R. Owen's original definition based on the dentition (1876), and have temporal vacuities and a small quadrate bone. It would then include the Lycosauria, with type Lycosaurus curvimola; the Cynodontia, with Cynognathus crateronotus (n.sp.) and Thrinaxodon liorhinus as types; and a group of South African Reptiles named Gomphodontia, based upon new genera Gomphognathus and Trirachodon, which have the molar teeth with flattened cuspidate crowns more or less worn with use. The palate is formed on the type of Lycosaurus in these Theriodontia.

Gorgonops is closely allied to Theriodonts in its dentition (though no molar teeth are known). The skull is closed behind as in Kistecephalus, and the temporal vacuities are roofed. It appears to show a palate formed on the same plan as in Theriodontia so far as its transverse development is concerned, but it has not any hard palate extending above the posterior nares as in Theriodontia. It is regarded as the type of a distinct group, named Gorgonopsia.

The Pareiasauria have the same transverse palatine arch, abutting against the lower jaw, but not developed downward to the same extent, as in Theriodontia. Its hard palate appears to be carried back behind the teeth, so that the posterior nares are further back than in the Theriodontia. It differs from the Theriodontia in the slight development of the coronoid process of the lower jaw, and in having the temporal vacuities roofed; and from the Gorgonopsia in having the skull open behind, and in having no canine teeth.

The Endothiodont type is believed to show the transverse descending palatal arch between the rami of the mandible. Pristerodon is regarded as possibly Endothiodont; and Endothiodon uniseries is made the type of a genus Esoterodon. A small skull from Molteno Pass, Cryptocynodon simus (n.sp.), is regarded as an Endothiodont with imperfectly-developed canine teeth. The Endothiodontia have

no incisor teeth, have the hard palate imperfectly developed, and no coronoid process to the lower jaw.

Another South African group is regarded as indicated by Delphinognathus, Tapinocephalus, and a new genus named Dinocephalus, which has the largest tusks known in any South African genus, associated with small molars. In the typical genera the skull bones are very thick and the temporal vacuities small. Elurosaurus is probably to be placed in this group. It is referred to as Dinocephalia.

Thus there is a series of groups of South African Reptilia which appear to agree in having a palate which has some resemblances to Mammals but approximates to Sphenodon, Lizards, and Crocodiles. All these sub-orders are combined as the Therosuchia. In this order or group may be included the Deuterosauria from the Permian rocks of Russia.

The Deuterosauria is distinguished from the Theriodontia by having palato-nares which open by oval vacuities on a concave surface instead of behind a hard palate. The transverse palatine arch is not developed downward. The sphenoidal region is at an angle with the palate, and in the same plane with the occiput.

Finally, the names given by Professor Cope to allied American types are examined. It appears that the Theromora as hitherto used is a synonym of the Anomodontia, though it might be conveniently limited to the American types, which appear to be distinct from those of Africa and Europe. But it is not possible to use either that name or the names Pelycosauria or Cotylosauria till the characters of the groups they indicate are adequately defined by good characters. The relation of the Therosuchia to other Anomodontia is shown in the following grouping.

ANOMODONTIA.
THEROSUCHIA.

Pareiasauria.

Procolophonia.

Gorgonopsia.

Dinocephalia.

Deuterosauria.

Lycosauria.

Theriodontia. Cynodontia.

Gomphodontia.

Endothiodontia.

[Theromora.]

THEROCHELONIA.

Dicynodontia.

Kistecephalia.

MESOSAURIA.

VI. "Researches on the Structure, Organisation, and Classification of the Fossil Reptilia. Part IX. Section 2. On the Reputed Mammals from the Karroo Formation of Cape Colony." By H. G. SEELEY, F.R.S. Received January 4, 1894.

(Abstract.)

The author re-examines the remains of Theriodesmus, and contests the interpretation of the carpus given by Professor Bardeleben, producing specimens of South African Reptiles in which there is a single bone beneath the radius, as in Theriodesmus. This character is shown in a small skeleton, at present undescribed, which the author obtained from Klipfontein, Fraserberg, which he regards as referable to a new genus. Other evidence is produced supporting the interpretation of three bones in the proximal row in the carpus, in a specimen from Lady Frere. The author then compares the forelimb of Theriodesmus with that of Pareiasaurus, which was obtained subsequently, and arrives at the conclusion that the types of limb are too closely related to be referred to different orders of animals, and therefore that Theriodesmus must be transferred from the Mammalia to the Therosuchia.

The skull described as Tritylodon longævus is examined, and its close resemblance to the skulls of new Theriodonts is pointed out. The author believes that it shows evidence of possessing both prefrontal and post-frontal bones, which were situate as in Theriodonts, and circumscribed the orbits in the same way; so that, although the post-frontal bones appear to have met in the median line to form a crest, at the back of the frontal, there is no other character in the skull by which it can be distinguished from the skull of a Theriodont. It therefore appears to be reptilian, and thus would make known divided roots to the molar teeth in Reptilia, and a more complicated type of crown than in any Theriodont yet known.

VII. "Researches on the Structure, Organisation, and Classification of the Fossil Reptilia. Part IX. Section 3. On Diademodon." By H. G. SEELEY, F.R.S. Received January 12, 1894.

(Abstract.)

The author describes fragments of jaws and teeth from Upper Karroo strata at Wonderboom and Aliwal North, collected by R. D. Kannemeyer and Alfred Brown. They may possibly belong to more