proceedings: geological society 139 



Mr. C. R. DuvALL then presented a paper, illustrated by lantern 

 slides, on The recurring-series metliod of seeking hidden periodicities loith 

 applications. A generating function in the form of a general rational 

 proper fraction in x may be developed into a power series in two ways. 

 In the first, the coefficients satisfy a scale of relation, and in the second 

 the general coefficient is in the form of a sum of products of polynomials 

 by powers. Both processes being uniquely reversible, a general form is 

 determined of a sequence of numbers satisfying a scale of relation. 

 A sum of sine terms is transformed into a sum of powers; a particular 

 case of a sum of products of polynomials by powers. Hence, any 

 sequence of numbers which may be represented by a sum of sine terms, 

 satisfies a scale of relation, and its general term may be determined 

 and the periods, amplitudes, and phrases. Results of applications to 

 magnetic and sun-spot-number data were given, showing a striking 

 agreement in the two phenomena of three periods of about 11.4, 22, and 

 70 years, with some indications of a fourth period of 6 to 8 years. 

 Prof. E. W. Brow^n's diagram of fluctuations in the longitude of the 

 Moon, Earth, and Mercury, all compared with the sun-spot curve, 

 gave indications of a common period of about 70 years, and suggested 

 a connection between these fluctuations and changes in the Earth's 

 magnetic field, all possibly due to changes in the Sun's magnetic field. 

 The paper was discussed by Mr. Bauer, who gave a brief account of 

 recent work of others, particularly of Schuster and Michelson; Mr. 

 Sosman asked whether any groupings had been taken for periods asso- 

 ciated with that of the rotation of the Sun; Messrs. Humphreys and 

 Abbot made reference to the inaccuracy of data sometimes published. 



J. A. Fleming, Secretary. 



THE GEOLOGICAL SOCIETY OF WASHINGTON 



The 289th meeting was held in the lecture room of the Cosmos 

 Club, on January 13, 1915. 



informal communications 



H. M. Eakin, Effect of the earth's rotation as a deflecting force in 

 stream erosion. In 1909 the^ speaker gave a paper before the Geologi- 

 cal Society of Washington in which rotational deflection was discussed 

 as to its source, its variations with latitude and velocity, and its ex- 

 pression in torsional flow and selective lateral erosion in alluvial streams 

 as compared with that of the more familiar centrifugal force developed 

 on stream bends. It was shown that above latitude 60° N. a straight 

 stream has the same tendency to greater erosion on its right bank due 

 to rotational deflection as that directed to the ouier bank by centrif- 

 ugal force on a bend with a 6-mile radius of curvature. This meas- 

 ure of the erosional effect of rotational deflection lead to the conclu- 

 sions: That this force is sufficient to cause lateral migration of large 

 streams in high latitudes; that the Yukon River, in Alaska, has thus 

 migrated to the right side of its valley throughout the lower 800 miles 



