6 L. A. Iui a a- — Gravity Determinations at Sea. 



however, the first coefficient, 0*002044, he deduced empirically* 

 from a least-square discussion of nearly one-fourth of the 

 available pendulum observations, selecting undisturbed coast 

 and inland stations. Tins first coefficient gives for the ellip- 

 ticity of the earth, l/298 - 3 ; the value adopted in the 

 Smithsonian Meteorological Tables, 1907, is 0-002662 as 

 obtained by Professor Harkness in his work " The Solar 

 Parallax and its Related Constants, Washington, 1901." 

 For B = 760 mm , for example, the first corrective term for a 

 point on the equator would be, — 2 - 0095 mms for Helmert's 

 formula and -2'0231" ,ms for the Smithsonian Tables; the 

 second term for B = 760 mm and the equator amounts to 

 -f- 0-0053, so that the total correction, according to Helmert, 

 would be — 2 - 0042 rams . For the poles, the corrections would 

 be, +2-0095 and +2-0231 mms . In order, therefore, to detect 

 by ocean observations the difference between the two formulae, 

 it would be necessary to secure an accuracy of about - 01 m ' u 

 mercury or 0-015 n ' m acceleration or about 1/100,000 part of g. 

 This matter is mentioned here since one of the conclusions 

 drawn by Hecker from his ocean observations is that they 

 accord with Helmert's formula. 



But A and B are subject to various sources of error, partly 

 due to instrumental causes and observational errors and partly 

 due to motion of the vessel. Of the disturbances caused by the 

 vessel there are two which may readily be disposed of. First 

 that due to the possible attractive effect of the mass of the 

 vessel, since this even for a 100,000 ton vessel would only 

 be on the order of 1/1,000,000 of g, is negligible ; second, that 

 due to the course and speed of the vessel. Only the motion 

 in longitude counts — for a vessel sailing east along a certain 

 parallel the instruments aboard are being transported around 

 the axis of rotation of the Earth faster than is a fixed point 

 in the same parallel and the force of gravity aboard is accord- 

 ingly diminished and the mercury in the barometer made to 

 stand correspondingly higher than it would were the vessel not 

 moving. For a vessel sailing west, the effect is reversed. So 

 that if at a certain point on the earth gravity is measured aboard 

 a moving vehicle, once when moving eastwardly and next 

 moving westwardly at the same rate of speed, the values of 

 g at the two times would differ by twice an error, the exact 

 amount of which may be computed from the following 

 formula : 



* Helmert, F. E. Der norrnale Theil der Schwerkraft im Meeresniveau. 

 Sitzber. Akad. Wiss., Berlin, xiv, 1901. There is a misprint in Hecker's 

 publication of 1908 ; at top of. table, p. 226, Helmert's coefficient is given 

 as 0-00244 instead of 0-002644. 





