468 



TABLES 495-512.— GEOMAGNETISM * 1! 



TABLE 495.— ELEMENTS OF THE EARTH'S MAGNETIC FIELD 



The elements commonly used to describe the natural geomagnetic field are : 



Remarks 

 Bearing of magnetic north with respect 



to geographic north, counted positive 



from north around by east 

 Positive when Z has downward direction 

 Positive regardless of direction 

 Referred to geographic north 

 Referred to geographic east 

 Positive when downward 

 Positive regardless of direction 



For a given time and place, the field is completely described by specifying the values of 

 three magnetic elements, provided they include one from the group D, X, Y, and one from 

 the group, /, Z, F. The ways in which the magnetic elements are interrelated may be 

 seen from figure 20 and the formulas below. The formulas in the right-hand group are 



Fig. 20. — Interrelation of the magnetic elements. 



obtained from the others by differentiation; they are useful when dealing with small incre- 

 ments, such as those which describe annual and daily changes and minor local anomalies 

 of the geomagnetic field. The formulas pertaining to values of AD and Al are expressed 

 in minutes of arc. 



X = HcosD 

 Y = H sin D 

 F = X tan D 

 H 



VX 2 + Y 2 

 H = F cos / 

 Z = H tan / 

 Z = F sin / 



AX = cos D AH — H sin D sin 1' AD 

 AY = sin D AH + H cos D sin 1' AD 

 AF = cos I AH + sin / AZ 

 H AZ — Z AH 



Al = 



H 2 sec* / sin 1' 



A/=(|-f) 



sin 21 



F= VH 2 + Z 2 



2 sin 1' 

 AZ = tan/ AH 4 1 sec 2 / A/ sin 1' 



F= VX 2 + Y 2 + Z 2 



* Prepared by E. H. Vestine, Carnegie Institution of Washington, and David G. Knapp, U. S. Coast 

 and Geodetic Survey. 



158 For references, see bibliography following Table 511, p. 501. 



(continued) 

 SMITHSONIAN PHYSICAL TABLES 



