GEOLOGY: W. BOWIE 
177 
ada, India and in Europe, which had been reduced by the isostatic or 
Hayford method, the best gravity formula deduced is 
70 = 978.039 (1 + 0.005294 sin^ 0 - 0.000007 sin^ 2 (^) 
in which 70 is the value of gravity in dynes at sea level, at the latitude, 
and the first term, 978.039, is the value of gravity at the equator. 
From the constant 0.005294 a reciprocal of the flattening of the earth 
of 297.4 was derived. 
The well known formula 
Ch = -0.0003086 3^ 
was used to correct the value of gravity for the distance above sea level. 
H is the elevation of the station in meters. 
If we assume that the best known value of the equatorial radius of 
the earth is 6,378,388 meters,^ then the polar semi-diameter is 6,356,941 
meters. The difference is 21,447 meters or 13.3 miles. 
The results of the investigations of the Coast and Geodetic Survey 
make it possible to compute the value of gravity for stations in the 
United States, and possibly also in any other country, with an average 
uncertainty in the result of about 0 . 020 dyne or one part in 50,000. 
Further work on the gravimetric survey of the United States will 
enable us to obtain better values of the shape of the earth, and for the 
constants of the gravity formula, and will no doubt lead to important 
discoveries regarding the distributions of densities in the outer por- 
tions of the earth and especially within the outer ten miles. 
1 Washington, D. C, U. S. Commerce Dept. Coast ^ Geod. Surv., Rep., 1891, Appendix 
No. 15; Ibid., 1893, Appendix No. 12; Ibid., 1910, Appendix No. 6. 
2 London, Phil. Trans. R. Soc, 149, 1859, (745); Button, C. E., Washington, D. C, Bull. 
Wash. Phil. Soc, 11, 1889, (51-64). 
3 Hayford, J. F., U. S. Commerce Dept. Coast & Geod. Surv., The figure of the earth and 
isostasy from measurements in the United States, 1909; Supplementary investigation in 
1909 of the figure of the earth and isostasy, 1909. 
4 Hayford, J. F., and Bowie, W., U. S. Commerce Dept. Coast Geod. Surv., Sp. Pub.y 
No. 10, 1912; Bowie, W., Ihid., No. 12, 1912. 
s Bowie, W., Ibid., No. 40, 1916. 
* This, according to the latest investigation, is the most probable depth (see 
7 Barrel!, J., Chicago, III, J. Geol. Univ. Chic, 22, 1914, (215). 
8 See Hayford, loc. cit., Note 3, 1909, (54). 
