342 ANNALS NEW YORK ACADEMY OF SCIENCES 



specific characters and sharply distinguish members of different phyla. 

 For example, in the cross between the horse (E. cab alius) and the ass 

 {E. asinus) , it is found that the cephalic indices are transmitted as pure 

 non-blending characters. 



Among the most significant indices are the following: (1) the cephalic, 

 which is obtained by dividing the total or basilar length of the skull 

 by the zygomatic breadth; (2) the cranial, which is obtained by divid- 

 ing the basilar length by the postorbital length of the skull; (3) the 

 facial, obtained by dividing the basilar length by the preorbital length 

 of the skull, etc. The horses show proopic dolichocephaly, or elongation 

 of the face, and a static condition of the cranium, while the titanotheres, 

 in contrast, show opisthopic dolichocephaly, or elongation of the cranium, 

 and abbreviation of the face. Like the phyletic differences of proportion 

 between the horse and the ass, these differences are most exactly ex- 

 pressed by the method of indices. 



The application of the ratio method to the limbs of the hoofed mam- 

 mals has again produced most surprising results. It is found that mam- 

 mals of different phyla adapted either to "weight" or to "speed" con- 

 verge respectively toward typical "weight" or "speed" ratios, which are 

 obtained by dividing the length of the lower segments, tibia and radius, 

 respectively, by the upper segments, femur and humerus, metacarpus 

 and metatarsus, respectively. These ''weight ratios" and "speed ratios" 

 are far more significant as regards function and phyletic change than 

 the actual or direct measurements. 



Dr. Lucas exhibited lantern slides illustrating some interesting pic- 

 tures from old works on whaling and showing the methods practiced by 

 the early Japanese, European and American whalers. 



The Section then adjourned. "William K. Gregory, 



Secretary. 



SECTION OF ASTRONOMY, PHYSICS AND CHEMISTRY. 



22 January, 1912. 



Section met at 8 :15 p. m., Vice-President Campbell presiding. 

 The minutes of the last meeting were read and approved. 

 Dr. F. M. Pedersen of the College of the City of New York was then 

 elected Secretary of the Section for the year 1912. 

 The following programme was offered : 



C. C. Trowbridge, Recent Discoveries Concerning a Chemically 



Active Modification of Nitrogen. 

 William Campbell, Some Notes on Iron and Steel. 



The Section then adjourned. F. M. Pedersen, Secretary. 



