OSBORN — ZOOLOGIC AND PALiEONTOLOGIC RESEARCH 
5 
II. Intensive study of the evolution of the living and fossil ungulate 
skull and skeleton and of the teeth by the means of indices (measure- 
ments of a single bone or tooth) and of ratios (comparative measure- 
ments of two bones or of teeth and bones). This has been especially 
the work of Osborn and of Gregory on the titanotheres and of Osborn 
on the horses. In the limbs, Cope (1889)^^ adumbrated this idea. 
In 1900 Osborn^® worked out the angulation, which was developed by 
Gaudry (1906).^® R. C. Osburn (1906) a student of Osborn, applied 
the idea in aquatic adaptation. Matthew (1909)^^ took up the limb- 
ratios of Carnivora in relation to weight and speed. 
III. Phylogenetic intergradations of skeletal and tooth form as 
observed in the finely intergrading ascending and descending geologic 
stages of evolution. This has been the work of Osborn, Scott, Matthew, 
Granger, and Gidley in this country, and of Deperet in France. 
IV. Application of the principles of mechanics to the muscles and 
evolution of the proportions of the limbs. This has been chiefly the 
work of Osborn and of Gregory. Gregory, especially, has developed 
the mathematical aspect of this subject -and the means of restoring the 
musculature of extinct mammals.^® 
This method has been partly anticipated by the physical anthro- 
pologists, also by the leading students of animal motion. This extended 
investigation by Osborn and Gregory in perissodactyls, compared 
with amblypods and proboscideans, opens up principles which apply 
equally to all quadrupeds and bipeds, reptilian, avian, mammalian. 
V. Substitution of a vertical phylogenetic or phyletic classification 
for the horizontal geographic classification of Linnaeus, Flower, and 
Cope. Osborn, especially, has worked out this system of classification 
Cope, E. D. The Mechanical Causes of the Development of the Hard Parts 
of the Mammalia. Journ. of Morphology, vol. Ill, pp. 137-290, 1889. 
15 Osborn, H. F. The Angulation of the Limbs of Proboscidea, Dinocerata, 
and Other Quadrupeds, in Adaptation to Weight. Amer. Nat., vol. XXXIV, 
pp. 89-94, 1900. 
15 Gaudry, Albert. Fossiles de Patagonie. Les Attitudes de quelques Ani- 
maux. Ann. de Paleontologie, tome I, pp. 1-42, 1906. 
1^ Osburn, R. C. Adaptive Modifications of the Limb Skeleton in Aquatic 
Reptiles and Mammals. Ann. N. Y. Acad. Sci., vol. XVI, no. 9, part III, pp. 
447-482, March 1, 1906. 
15 Matthew, W. D. The Carnivora and Insectivora of the Bridger Basin, Mid- 
dle Eocene. Mem. Amer. Mus. Nat. Hist., vol. IX, part VI, 1909. 
15 Gregory, W. K. Notes on the Principles of Quadrupedal Locomotion and 
of the Mechanism of the Limbs in Hoofed Animals. Ann. N. Y. Acad. Sci., vol. 
XXII, pp. 267-294, 1912. 
