432 



Reports on Special Researches 



taken as constant because of the small size of the areas liere involved. In order to reduce the obser- 

 vations to a common date, corresponding to the mean date of all the tracks, another unknown w, the 

 secular-variation term, is included in the above equation, and also x, the most probable correction 

 to the approximate mean value Eq, of the element in question at the point (/)o, Xq- We have finally 

 for the observation equation 



E = Et+x+yA((>+zA\+wM (1) 



in which At is the date of observations minus the adopted mean date. In the practical application 

 of this method the weights assigned to the various results in the Tables of Results (see pp. 97-104 

 and 261-287) have been applied. 



d. The values of x, y, and z have sometimes been determined from the data of one track only, or 

 both tracks separately, from the equation 



E = Ef,+x+yA<t>+zA\ 



(2) 



The values of the magnetic elements for some point, usually the mean position of one group, have 

 then been calculated from the x, y, z, and the mean value and mean position of the other group. The 

 values for the different epochs thus become strictly comparable. 



The methods a and h are temporary expedients to obtain approximate values expedi- 

 tiously. The method c is to be preferred, since it has the advantages of combining observa- 

 tions by weights, of exhibiting discordant results, also of indicating thereby whether the 

 groups cover too large an area for the assumption of Unear changes ; as it involves consider- 

 ably more time and labor, its general application, however, must be deferred to a later date. 

 Chief assistance in the determination of the present values of the annual changes was ren- 

 dered by Computer C. C. Ennis. 



An inspection of the preliminary values of the annual changes in Tables 96-98 

 shows that the quantities are of the same general order of magnitude as disclosed by 

 observations on land. As already stated, the discussion of the values is deferred until 

 additional data have been obtained. The annual changes for the declination and inclina- 

 tion are invariably referred to the north-seeking end of the magnetic needle. Thus 6' W 

 means that the north-seeking end of the compass moved to the west at the average annual 

 rate of 6' during the period shown in the third column of the tables; 1' N means that the 

 north-seeking end of the dip needle moved downwards at the average annual rate of 1' 

 during the period in the third column. 



Preliminary Average Annual Changes in the Magnetic Elements Determined From 

 THE Galilee and the Carnegie Observations, 1905-1916. 



Table 96. — Average Annual Changes for the Indian Ocean.' 



'The first three entries of the table are derived from the intersections of the tracks of the Carnegie in 1911 with those 

 of the Gauss (the vessel of the German Antarctic Expedition, 1902 and 1903); see Terr. Mag., v. 16, p. 136, 1911. 

 'Two groups only. 



