572 



SCIENCE. 



[N. S. Vol. I. No. 21. 



earth's crust. It has given rise to many 

 diverse opinions, and the apparent anoma- 

 lies in the force of gravity have been so 

 great with various methods of reduction as 

 to necessitate the rejection of certain classes 

 of stations even in the most elaborate dis- 

 cussions, as those of Clarke and Helmert. 

 Three methods of reduction were applied to 

 these stations, and the effect of latitude was 

 eliminated by comparison with a theoret- 

 ical formula based on Clarke's figure of the 

 the earth. In each of these methods cor- 

 rection was made for the elevation above 

 sea level and for topographical irregularities 

 near the station, and they differ only in the 

 allowance made for surface attraction, as 

 follows : 



1. Bougner's reduction. The vertical at- 

 traction of the entire mass above sea level 

 was subtracted. With this method the re- 

 sults show a large defect of gravity on the 

 western mountains and plateaus, closely 

 proportional to the average elevation, but 

 having no relation to the altitude of the 

 particular point of observation or to dis- 

 tance from the ocean. 



2. Elevation reduction. Ko correction 

 was made for attraction. The defect of 

 gravity in general disappears, but there are 

 large residuals in the mountainous regions, 

 gravity being in excess at stations above 

 the average level of the surrounding coun- 

 try, and in defect at those below. The 

 size of the residuals is nearly proportional to 

 the difference in elevation between the sta- 

 tion and the average level. 



3. Faye's reduction. On the theory that 

 the surface of the earth is in general in a 

 condition corresponding to hydrostatic 

 equilibriun, M. Faye proposed that no cor- 

 rection be made for the attraction of the 

 average mass above sea level, but that ac- 

 count be taken of local deviations fi-om the 

 average level, as, for instance, the attraction 

 of a mountain on a station at its summit. 

 Developing this idea we may consider that 



all general continental elevations are com- 

 pensated by a lack of densitj- or other 

 cause below sea level, but that local irregu-^ 

 larities of surface are not so compensated, 

 but are maintained by the partial rigidity 

 of the earth's crust. The measure of this 

 lack of compensation will be the attrac- 

 tion of a plain whose thickness is the differ- 

 ence in elevation between the station and 

 the average surrounding countrj'. The lat- 

 ter was estimated within an arbitrarily 

 adopted radius of 100 miles of each point, 

 and the correction applied, positive for 

 stations below the average and negative for 

 those above.* With this reduction aU the 

 large residuals' disappear. For the four- 

 teen stations (in mountainous regions) 

 where it was applied, the sums of the re- 

 siduals are : with Bougner's reduction 2.577 

 dynes, with elevation reduction 0.677 dynes, 

 with Faye's reduction 0.175 dj-nes, indica- 

 ting a decided advantage for the latter. 



A similar discussion made of former 

 Coast and Geodetic Survey observations on 

 oceanic islands and coasts shows that the 

 excess of gravity that has been found on 

 islands with Bougner's reduction largely 

 disappears on the application of Faye's idea, 

 subtracting the attraction of islands con- 

 sidered as displacing sea water. The resid- 

 uals with Bougner's reduction are probably 

 a measure of the lack of densltj' below sea 

 level, and with the elevation reduction a 

 measure of the lack of compensation. The 

 general conclusion is that the so-called 

 anomalies of gravitj' may be largelj' ac- 

 counted for on general principles, and that 

 the value of these measurements in connec- 

 tion with the problems of geodesy and the 

 intimately related questions of terrestrial 

 phj'sics will be proportionately enhanced. 



By comparing the values of g measured 

 on the summit and near the base of Pike's 

 Peak the value 5.63 was deduced for the 



*Mr. Gibert independently applied this method 

 o£ reduction, usins a radius of 30 miles. 



