L. A. Bauer —Gravity Determinations at Sea. 9 



words /3 is composed of two distinct quantities, one, Ag. repre- 

 senting the gravity anomaly and the other the various sources 

 of error, E, and so we have : 



* - vk + E ' 



or /3-£§q-E=0. (9) 



Comparing this equation with Keeker's (5), it must be evi- 

 dent that his corrective terms include the effects of the very 

 quantities — the A^'s — to be determined. Since he applies the 

 method of least squares to his equation, Hecker must assume 

 that during a cruise the local gravity anomalies, i.e., the 

 Ag's, partake of the nature of accidental errors — that they 

 either balance out in the long run or oscillate about a mean 

 constant value, which enters into the constant terms of (5). 

 But is not the proving whether such distributions of gravity 

 anomalies exist, or do not exist, the very purpose of gravity 

 surveys \ 



Furthermore, since Hecker adjusts each cruise by itself, then 

 by the theory of least squares alone, the sum of his residuals 

 or outstanding gravity anomalies must reduce to zero, or prac- 

 tically so, because of the presence of the constant terms in (5); 

 hence his average computed fi lor the cruise must be theoreti- 

 cally equal to his average observed /3, or in other words, the 

 average gravity anomaly of a whole cruise would he zero. It 

 must be evident then that as Hecker derives his unknowns they 

 are not true values but are affected by the gravity anomalies 

 over the areas for which the adjustment is made. They might 

 be different, for example, for a cruise from New York to 

 Liverpool than for one from Hamburg to Rio de Janeiro, even 

 though all conditions lemained precisely the same except that 

 of difference in route followed. Manifestly then Hecker's 

 method of adjustment is open to grave objections and it is a 

 question as to how much of his resulting conclusions may not 

 already be contained in his fundamental assumptions. Let us 

 hope that the variations in the gravity anomalies at sea about 

 an average value will be found to be of a sufficiently accidental 

 nature to vitiate Hecker's main conclusions ! 



Strictly speaking, the values of the unknowns entering into 

 equation (5) can only be derived from stations where there 

 exist accurate gravity observations from which the anomaly 

 Ag can be derived. This means, however, restriction to shore 

 and harbor observation, but these are the very observations 

 which above all Hecker has been unable to reduce satisfactorily 



