_Lumbar Vertebræ._—The _lumbar_ region consists of those vertebræ of the trunk in front of the sacrum which bear no movable ribs. It may happen that, as the ribs decrease in size posteriorly (the last being sometimes more or less rudimentary), the step from the thoracic to the lumbar region may be gradual and rather undetermined in a given species; but most commonly this is not the case, and the distinction is as well defined here as in any other region. As a general rule there is a certain relation between the number of the thoracic and lumbar vertebræ, the whole number being tolerably constant in a given group of animals, and any increase of the one being at the expense of the other. Thus in all known Artiodactyle Ungulata there are 19 dorso-lumbar vertebræ; but these may consist of 12 dorsal and 7 lumbar vertebræ, or 13 dorsal and 6 lumbar, or 14 dorsal and 5 lumbar. The smallest number of dorso-lumbar vertebræ in mammals occurs in some Armadillos, which have but 14. The number found in Man, the higher Apes, and most Bats, viz. 17, is exceptionally low; 19 prevails in the Artiodactyla, nearly all Marsupials, and very many Rodents; 20 or 21 in Carnivora and most Insectivora; and 23 in Perissodactyla. The highest and quite exceptional numbers are in the Two-toed Sloth (_Cholœpus_) 27, and the Hyrax 30. The prevailing number of rib-bearing vertebræ is 12 or 13, any variation being generally in excess of these numbers. _Sacral Vertebræ._—The _sacral_ region offers more difficulties of definition. Taking the human “os sacrum” as a guide for comparison, it is generally defined as consisting of those vertebræ between the lumbar and caudal regions which are ankylosed together to form a single bone. It happens, however, that the number of such vertebræ varies in different individuals of the same or nearly allied species, especially as age advances, when a certain number of the tail vertebræ generally become incorporated with the true sacrum. Other suggested tests—as those vertebræ which have a distinct additional (pleurapophysial) centre of ossification between the body and the ilium, those to which the ilium is directly articulated, or those in front of the insertion of the ischiosacral ligaments—being equally unsatisfactory or unpractical, the old one of ankylosis, as it is found to prevail in the average condition of adults in each species, is used in the enumeration of the vertebræ in the following pages. The Cetacea, having no iliac bones, have no part of the vertebral column modified into a sacrum. [Illustration: FIG. 12.—Anterior surface of fourth caudal vertebræ of Porpoise (_Phocæna communis_). _s_, Spinous process; _m_, metapophysis; _t_, transverse process; _h_, chevron bone.]