558 REPORTS ON THE STATE OF SCIENCE. — 1916. 



6. Calculation of the value of Gravity from the readings of the Aneroid and 

 Mercury Barometers. 



The height of the mercury barometer reduced to 0° C. and corrected 

 for scale errors but not for latitude is given in the column headed Bg in 

 Table IV. 



As latitude has not been allowed for, the units are not true millibars. 



The corresponding atmospheric pressure is given in the same Table 

 under the heading p^, Pb, or pc, according to the method of reduction. 

 The value of gravity is found from the following equation: 



or 8g = 8p ^' 



Where Sg is tlie deviation from the value of gravity in latitude 45°. In 

 Table IV. the columns hg^, 8gu, 8gc, are calculated from the values p^, 

 Pb, and Pc, respectively. . ^ 



The application of corrections to these on account of the ship s motion 

 and the errors at land stations is discussed in later Sections. 



7. Correction for the Ship's Horizontal Motion. 



The ship's motion along the surface of the water involves a correction 

 for gravity equivalent to the extra centrifugal force upon the ship. 



The modification of the curvature of the ship's course relative to 

 the centre of the earth as she sails over the crests or hollows of ocean 

 swells operates as a pumping term and is treated in the same way. The 

 error is small if the swell is symmetrical and if the mean level of the 

 mercury be taken. 



The form in which the term is introduced in the present investigation 

 is 2 (i) I) cos /\ sin a, where a is the angle between the true north and south 

 line and the direction of the ship, w the angular velocity of the earth's 

 rotation, and X the latitude. It neglects the term involving the square of 

 the ship's velocity and the component of the ship's velocity in the 

 North-South direction. The appropriate correction for each observation 

 is included in Table IV. under the column headed m. 



The theoretical reasons for introducing this term were pointed out 

 by von Eotvos, but as its introduction appeared to cause the results 

 of Hecker's determinations of gravity at sea to diverge appreciably from 

 Helmert's formula doubt was cast upon the necessity for it.^ Voy- 

 ages on the Black Sea enabled Hecker^to test this point, and he found 

 that the barometric height differed by "08 mm. if the ship went east 

 instead of west, and therefore that it was necessary to include the term. 



A.ny uncertainty in measuring the velocity and direction of the ship 



2 Helmert, C. R. &''""-' Conference gfnfraU de V Association G^odisique Inter- 

 nationale, 1909, p. 22. 

 ' Loc. cit. 



