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The pterygoid ridge in this group is not very strongly marked, and 
gradually dies away upon the lamina enclosing the alisphenoid canal ; 
the pterygoid processes have considerable antero-posterior extent, and 
the true pterygoid bones are reduced to mere ribands. On the other 
hand, in the Artiodactyla, the pterygoid ridge, continued from the in- 
ferior root of the zygoma, terminates abruptly, with a free process in 
the Ruminants ; while in the Hogs and other allied forms, it is from 
this process that a laterally projecting plate extends down on the outer 
side of the pterygoid process, forming a pterygoid fossa in a manner 
different from all other mammalia, and very characteristic of these 
Non-ruminant Artiodactyles. The temporal bone in the Perissodactyla 
also furnishes characters in the back of the zygoma, which gently 
slopes away to its origin, and in the association of a distinctly marked 
eminentia articularis with a rather large and more or less thickened 
and mammilliform post-articular process. The principal differences 
in the occipital bone I pointed out in my former paper, and notwith- 
standing the marked difference between the Hog and the Ruminant, 
I must observe that they agree in the flatness and squareness of the 
basal portion, while in the Perissodactyla it is transversely convex, 
being rounded off on each side into the great foramen lacerum. 
I mentioned in a note appended to my former communication, an 
idea which occurred to me just before that paper went to press, that 
a further distinction between the two groups might be found in the 
structure of the premolar teeth. I have found, on investigation, that 
the character will not always admit of being rigidly applied, since in 
some genera of Perissodactyla, as the Lophiodon to which I there 
alluded, the posterior lobes of the premolars are not so completely 
developed as they are in the true molars; and on the other hand, in 
some of the Artiodactyla, as the Peccary, they advance a little beyond 
the rudimentary condition in which they are usually found, though 
never attaining an equal development with the others. The character 
will however in most cases enable us to distinguish ; and in the course 
of the observations I was thus led to make, I have discovered another 
more important one, which I will next proceed to explain. 
If we consider as an entire molar tooth that which has four prin- 
cipal tubercles, the molars of the lower jaw must be said to be placed 
each in advance of its homologue in the upper jaw to the extent of a 
quarter of a tooth, so that the premolars, which in most cases repre- 
sent but half molars, alternate with their opposing teeth above. 
It is in accordance with this universal law, that the last lower milk 
molar in the Artiodactyle division of the Ungulata has three pair of 
lobes ; not, as has been imagined, that it may pretypify the last true 
molar, which in the same group is usually also six-lobed. The last 
lower true molar, being placed like the rest, a quarter of a tooth in 
advance of its four-lobed opponent, the pair of tubercles that are added 
to it behind play against the posterior surface of the hindmost pair of 
lobes of the upper tooth ; but in the last lower milk molar it is the 
anterior pair of cusps that are supernumerary, since they close between 
the two pair of principal tubercles of the penultimate upper milk 
tooth, which like the last one has-the form of a true molar; while 
