310 ON THE DIRECT MAGNETIC INFLUENCE OF THE SUN 



the horizontal parts of the disturbing forces, viz., X sin + Fcos 0, 

 acting eastward, and Z cos X + (X cos - F sin 0) sin X, acting 

 northward, in the direction of the magnetic meridian. We have 

 thus 



ZcosX + (XcosO - Fsin0)sinX 



) 



=i jsin0 (2P sinS + Q siaX cosS) + cos0 (2P sin X cos 8 - Q sing) 



- R cosX cosS ; 

 and at the equator, 



Ajff= jp jsing(2P sin0 - Q cos0) - R cosSJ. 



Lastly, if V denote the vertical component of the earth's mag- 

 netic force, we have 



Fsin0)cosX 



= \(2P cos0 + Q sin0) cosX + R sinX ; 



a result which, as might have been anticipated, is independent 

 of the magnetic declination. At the equator 



A V = jR- 3 (2P cos0 + Q sin0). 



From the foregoing we learn : 



1. That the effect of a distant magnetic body on each of the 

 three elements of the earth's magnetic force consists of two parts, 

 one of which is constant throughout the day, while the other varies 

 with the hour-angle of the luminary. 



2. Each of these parts varies inversely as the cube of the dis- 

 tance of the magnetic body. 



3. The variable part will give rise to a diurnal inequality, hav- 

 ing one maximum and one minimum in the day, and subject to the 

 condition 



A 9 + A^ = 0. 



The third of these laws does not hold, with respect either to the 

 solar-diurnal or to the lunar-diurnal variation. Thus, in the solar- 

 diurnal variation of the declination, the changes of position of the 



