122 CARNEGIE INSTITUTION OF WASHINGTON. 



inaccessible, aud scattered through several volumes. The tenth 

 volume has never been published heretofore. The work is therefore 

 an improvement and extension of existing tables. 



E.J. Wilczynski, Berkeley, Cal. Grant No. 135. For investigation 



of ruled surf aces , etc. (Dr. Wilczj'nski is a research as.sociate of 



the Carnegie Institution.) $1,800. 



Abstract of Report. — As the results of Professor Wilczjmski's work 



either have been published in the mathematical journals or else are 



to appear shortly, it seems unnecessary to give any detailed account 



of them. The following list gives the titles and places of publication: 



1. A fundamental theorem in the theory of ruled surfaces. Mathematische 



Annalen, vol. 58, pp. 249-256. 



2. Studies in the general theorj^ of ruled surfaces. Trans. Am. Math. Soc, vol. 



5, pp. 226-252. 



3. Invariants of a system of linear partial differential equations and the theory 



of congenences of rays. To appear in Am. Jour, of Math., October, 1904 

 (36 pages). 



4. On ruled surfaces whose fiecuode curve intersects everj^ generator in two coin- 



cident points. To appear in Trans. Am. Math. Soc, October, 1904 (6 pages). 



5. General theory of curves on ruled surfaces. Offered to Trans. Am. Math. 



Soc. (about 15 pages). 



6. General projective theory of space curves. Offered to Trans. Am. Math. 



Soc. (about 40 pages) 



7. The general projective theory of space curves and ruled surfaces. Read at 



the Heidelberg International Congress of Mathematicians, and to be 

 printed in its proceedings (about 6 pages). 



One remark of a general nature may properly be made here. The 

 general character of these investigations places them at the begin- 

 ning of a new kind of geometry, a projective geometry, which does 

 not confine itself to the consideration of algebraic cases, as has 

 hitherto been the case, but which proves theorems of a more gen- 

 eral nature by the use of differential equations, resembling in that 

 respect the general theory of surfaces. It differs from this latter 

 theory, however, in being a projective and not a metrical theory. In 

 this general, projective, infinitesimal geometry, the theory of curves 

 and ruled surfaces are merely the first chapters. The larger field 

 promises to be of absorbing interest and importance. 



PALEONTOLOGY. 



Oliver P. Hay, American Museum of Natural History, New York, 

 N. Y. Grant No. 118. For f^tonog rap king the fossil chelonia 

 of North America. (For first report see Year Book No. 2, p. 

 xxxvii.) $3,000. 



Abstract of Report. — The work of monographing the fossil turtles 

 of North America has been diligently pursued during the present 



