334 CARNEGIE INSTITUTION OF WASHINGTON. 



days. The geographic positions for the dip and intensity results are then 

 more or less uncertain. In the case of declination-results, however, no such 

 uncertainty can well exist, for the sun or star that serves for the declination 

 observations usually permits at least fairly good determination of position. 



Observations for the determination of the amount of atmospheric refraction 

 have been made continuously on the Galilee and Carnegie, beginning with the 

 Galilee's third cruise. Two instruments are now being used on the Carnegie 

 in order to vary the conditions. The problem of measuring atmospheric 

 refraction at sea is a difficult one that has not yet been satisfactorily solved. 

 We can only say at present that the results obtained on the Galilee and Carnegie 

 do not indicate presence of any serious error in the ordinary nautical tables. 



The series of observations in atmospheric electricity obtained on the cruises 

 of the Galilee and Carnegie form one of the most important of recent contri- 

 butions to observational data. The observations consist in measurements of 

 potential-gradient, conductivity, and radioactive content of the atmosphere, 

 besides the usual meteorological observations. Perhaps the most important 

 result is a confirmation of the somewhat remarkable phenomenon that while 

 the conductivity over the ocean is as large as over land, or larger, the radio- 

 active content is much smaller. The values of the potential-gradient at sea 

 are of the same order of magnitude as those on land. 



The recurring series method of seeking hidden periodicities with applications. C. R. 

 Duvall. Read before Philosophical Society of Washington, January 30, 1915. 



The following is a brief outhne of the theory as advanced by Lagrange and 

 developed by G. N. Armstrong: 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 poly- 

 nomials 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 may be 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 sequence of sine terms satisfies a 

 scale of relation, and its general term may be determined, together with the 

 periods, amplitudes, and phases. 



Applications (see Annual Report for 1914, p. 319) to magnetic and sun-spot- 

 number data show 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. With regard to the 70-year period it is of interest that Professor 

 E. W. Brown has found an apparent common period of about 70 years in the 

 fluctuations in longitude of the Earth, Moon, and Mercury. He suggests 

 that there is a connection between these fluctuations and changes in the 

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



Latest annual values of the magnetic elements at observatories. J, A. Fleming and W, F. 

 WaUis. Terr. Mag., vol. 20, 131-135 (September 1915), 



A compilation of the most recent annual values of the magnetic elements at 

 observatories distributed over the Earth. 



The atmospheric-electric work of the Department of Terrestrial Magnetism, W, F. G, Swann. 

 Read before the Philosophical Society of Washington, January 30, 1915. 



The paper comprised a review of the developments made at the Department 

 of Terrestrial Magnetism in the instrumental methods of measurement during 

 the year 1913-14, and a discussion of the results obtained up to date, chiefly 

 in connection with the ocean work. 



