May 19, 1911] 



SCIENCE 



?91 



an ordinary sphere m point four-space without 

 penetrating the surface of the sphere. ' ' 



Edward Kasner : ' ' The subdivision of curvi- 

 linear angles. ' ' 



E. D. Carmichael : ' ' The general theory of linear 

 g-differenee equations. ' ' 



E. D. Carmichael: "Note on multiply perfect 

 numbers. ' ' 



G. A. Miller : ' ' Isomorphisms of a group whose 

 order is a power of a prime. ' ' 



E. G. D. Eichardson : ' ' Theorems of oscillation 

 for two self -adjoint linear differential equations 

 of the second order with two parameters (second 

 paper)." 



J. B. Shaw: "Quaternion functions of three 

 parameters. ' ' 



J. E. Eowe: "The combinants of two binary 

 cubics and their geometrical interpretation on the 

 rational cubic curve. ' ' 



U. G. Mitchell: "Geometry and collineation 

 groups of the finite projective plane PG(2, 2^)." 



G. E. Wahlin: "The decomposition of rational 

 primes into ideal prime factors in the field 



fc( Vm)." 



L. G. Karpinski: "An Italian Algebra of the 

 fifteenth century." 



C. H. Sisam: "On hypereonical connexes in a 

 space of r dimensions. ' ' 



E. E. Boot: "Iterated limits of functions on 

 an abstract range." 



E. B. Van Vleek: "On the generalization of a 

 theorem of Poincare. ' ' 



E. B. Van Vleck: "On the classification of 

 collineations. ' ' 



A. E. Schweitzer : " On the philosophy of Grass- 

 mann 's extensive algebra. ' ' 



A. E. Schweitzer : "On the ' working hypothesis ' 

 in the logic of mathematics." 



W. B. Ford: "A set of sufficient conditions 

 that a function may have an asymptotic repre- 

 sentation in a given region." 



W. J. Montgomery: "The classification of 

 twisted curves of the fifth order. ' ' 



William Marshall : " On Hill 's differential equa- 

 tion in the theory of perturbations. ' ' 



H. Bateman : ' ' The fundamental equations of 

 the theory of electrons and the infinitesimal trans- 

 formation of an electromagnetic field into itself. ' ' 



N. J. Lennes: "Curves and surfaces in analysis 

 situs. ' ' 



N. J. Lennes: "Extension and application of a 

 theorem of Aseoli. ' ' 



L. I. Neikirk: "Substitution groups of an 

 infinite degree and their related functions. ' ' 



James Maclay : ' ' Parabolic curves. ' ' 



J. A. Nyberg: "Projective differential geom- 

 etry of rational cubic curves. ' ' 



E. B. Stouffer: "Invariants of linear differen- 

 tial equations with applications to ruled surfaces 

 in five-dimensional space. ' ' 



W. D. MacMillan: "A general existence the- 

 orem for periodic solutions of differential equa- 

 tions of a certain type. ' ' 



A. E. Crathorne: "The catenary with variable 

 end points." 



F. E. Moulton: "Periodic orbits of superior 

 planets. ' ' 



F. E. Moulton : "On the curves defined by cer- 

 tain differential equations." 



P. H. Safford: "An identical transformation of 

 the elliptic element in the Weierstrass form." 



W. H. Eoever : ' ' Southerly deviation of falling 

 bodies (third paper)." 



C. N. Moore : ' ' Convergence factors in double 

 series. ' ' 



L. E. Dickson: "On the negative discriminants 

 for which there is a single class of positive primi- 

 tive binary quadratic forms. ' ' 



L. E. Dickson: "On Format's 'descente in- 

 fijiie. ' " 



L. E. Dickson : "On perfect numbers and Ber- 

 noullian numbers. ' ' 



O. E. Glenn : ' ' On expressing a quantic in terms 

 of assigned powers of a given quantic. ' ' 



G. E. Clements : ' ' Implicit functions defined in 

 the neighborhood of a point where the Jacobian 

 determinant is zero. ' ' 



E. W. Marriott : ' ' Determination of the groups 

 of isomorphisms of the groups of order p*. " 



The summer meeting of the society will be held 

 at Vassar College on Tuesday and Wednesday, 

 September 12-13. F. N. Cole, 



Secretary 



THE AMERICAN PHILOSOPHICAL SOCIETY 



At the stated meeting of the society on April 

 7, Eear Admiral G. W. Melville (U. S. Navy, 

 retired) read a paper on "A Century of Steam 

 Navigation. ' ' 



The author said: In looking back over the his- 

 tory of the human race we are struck with the 

 fact that from time to time some genius brings 

 to light, or develops a principle which forever 

 after is a guide in our thinking. Such was Lord 

 Bacon 's exposition of inductive logic, which has 

 been the basis of all scientific advancement. 



Basing his argument on the above theory, the 

 admiral followed the growth of steam navigation 

 from the time of the inventions of James Watt, 

 down to the time of Fulton's first commercial 

 steamer Clermont, down to the time of the Lusi- 

 tania and Mauretania of to-day. 



He spoke of the varied improvements from that 

 time up to the present time, including the many 

 improvements, not only in ships and ship building 

 from the wooden hulls to the present steel hulls, 

 but the engines and boilers through their various 

 stages of improvements, commencing with a low 

 steam pressure of 10 pounds to the square inch 

 up to the present time of about 300 pounds pres- 

 sure per square inch. 



He traced through the various steps the great 

 evolution of steam ships from those of about 500 

 tons to those of 40,000 tons. Of necessity in a 

 short lecture of but 40 or 45 minutes, a very 



