Decembeb 7, 1906.] 



SCIENCE. 



717 



bureau and such field work as is paid for 

 by the association. 



The principal work of the central bu- 

 reau, under the direction of Dr. F. R. Hel- 

 mert, may be summarized as follows: 



Relative gravity determinations in vari- 

 ous countries have been furthered by spe- 

 cial examinations in detail of apparatus to 

 be used for this purpose and by instructing 

 the observers. 



Professor Borrass has been occupied in 

 studying the existing relative gravity de- 

 terminations with a view to their proper 

 combination in a gravity net extending 

 over the globe. 



A systematic study of deviations of the 

 vertical in Europe has been continued by 

 Professor Borsch, and progress has been 

 made in the publication of the results. 



A systematic study by Dr. Helmert of 

 the curvature of the geoid along certain 

 meridians and parallels, in countries where 

 there is extended triangulation, has been 

 nearly completed. 



The determination by Dr. Kiihnen and 

 Dr. Furtwangler of the absolute value of 

 gravity at Potsdam which has been in prog- 

 ress for several years has been completed 

 and the final results are now being printed. 

 In these determinations, five different pen- 

 dulums have been used at Potsdam and a 

 very extensive series of observations have 

 been made with great care. It was found 

 that the general experience of the past was 

 repeated and that systematic differences, 

 much too large to be accounted for as 

 errors of observation, were found between 

 the results from different pendulums. In 

 trying to account for the large residual 

 furnished by one of the five pendulums, 

 which was of peculiar form, the suspicion 

 arose that possibly the stem of this pendu- 

 lum was subject to flexure, as the pendu- 

 lum took various positions during each 

 swing. Accordingly, a mathematical the- 

 ory of such a possible flexure was developed 



fully for the first time. The effect of the 

 flexure upon the value of gravity given by 

 each of the five pendulums was then com- 

 puted, using this mathematical theory 

 which expresses the effect in terms of the 

 modulus of elasticity of the material com- 

 posing the stem, the dimensions of the 

 stem, and the masses of different portions 

 of the pendulum. The corrections brought 

 the results into closer agreement. The 

 same theory was, with similar success, ap- 

 plied to six other series of pendulum ob- 

 servations made at various times and at 

 places connected with Potsdam by accurate 

 relative determinations of gravity. In 

 these series, pendulums of various designs 

 have been used. The adopted value of 

 gravity at Potsdam is a simple mean of the 

 seven values, one of these being the value 

 observed at Potsdam. The adopted mean 

 differs by one part in 25,000 from the 

 Potsdam determination. Helmert states 

 that he believes the possible error of the 

 adopted mean to be less than one part in 

 100,000. The total range of the seven 

 values is one part in 33,000. 



Two of the seven values depend upon 

 observations made with the Bessel ball and 

 wire pendulums. For these the complete 

 theory developed by Bessel for taking ac- 

 count of the flexure of the wire was used 

 without modification. 



The gravity determinations at sea by 

 Dr. Hecker, already referred to, were made 

 under the direction of the central bureau 

 and paid for by the association. 



The principal field work, supported by 

 the association, is the determination of the 

 latitude variation. For the latitude obser- 

 vations and the necessary computations of 

 them, made at the central bureau, the ex- 

 penditure has been, on an average, $14,000 

 per year, during the past three years, more 

 than two thirds of the total expenditure of 

 the association. From 1899 to date, obser- 

 vations have been made continuously at 



