8 L. A. Bauer — Gravity Determinations at Sea. 



Hecker's final observation equation is of the following form : 



.in 



P+K+a i/f + bp+cr+ds+e(t-t o )+h=0. (5) 



I have substituted /3 for his quantity (Therm. — Bar. — com- 

 puted gravity reduction to 45° — correction due to speed and 

 course of vessel); it is the same as the quantity in equation 

 (1) after having had the correction c' applied to B. 



Te n = relation of the two zeros above + constant part 

 of other corrections. 



. - = correction to reduce the observations of boiling 

 point and readings of barometer to same 

 moment of time for any one set. 



bp = correction due to pumping, p, of barometer. 



or = " " " rolling of vessel. 



ds = " " " pitching " " 



e{t—t ) = " " " time changes in instruments 



supposed to progress linearly. 



fC, = constant which enters into the equation only for 

 deep sea observations, say for depths beginning 

 with about 2000 meters. 



There are thus in Hecker's complete equation seven unknowns, 

 7c n , a, b, c, d, e, and Jc„, which he determines by the method of 

 least squares. Substituting next in each observation equation, 

 of which there is one for each station, the derived values of 

 the unknowns, a residual quantity, v, is obtained, supposed to 

 be the gravity anomaly sought. 



To get a clear understanding as to the assumption implied in 

 his formula, let us suppose first that all the corrective terms 

 in (5) except Jc a and \, by a suitable scheme of observation 

 and in a calm sea, reduce to negligible quantities, then we 

 have for a shallow water station, s, 



/3, = — 7c n = constant, (6) 

 and for a deep water station, d, 



/3 a = — 7t' n — \ = constant, (7) 



or /3. v — /3 ( , — 7i' 2 = constant. (8) 



The same result (8) is obtained if we suppose, in passing 

 from s to d, the corrective terms for each station were the 

 same in magnitude and sign. But the difference /3s — /3d, 

 under the conditions supposed, when multiplied by 1'29 (see 

 equation 2) should be the difference in Ag at the two points, 

 which of course would not, in general, be a constant. In other 



