22 ON MAGNETISM. 



one satellite is not diminished by the circumstance that 

 the same planet is acting also upon another satellite. 



(c) Use the apparatus of Figure 8 as a deflecting 

 apparatus, to deflect from its ordinary position a com- 

 pass-needle. Place the axis of Figure 8 in the direction 

 magnetic E. or- W. from the center of the compass: and 

 mount successively upon it one needle, two needles, 

 three needles. If the single needles continue in their 

 combined state each to exercise the same action as 

 when it is alone, so that the whole statical pull on the 

 compass-needle is successively represented by 1, 2, 3, 

 then the trigonometrical tangents of the angles of 

 deflection of the compass-needle will be in the succes- 

 sive proportions of 1, 2, 3. And the fact, in experiment, 

 is so. It follows from this that the statical force exerted 

 by the assemblage of needles is proportional to the sum 

 of the statical forces exerted by each single needle : that 

 is, it is proportional to the sum of the magnetic energies 

 of these needles. And therefore, the expression for the 

 statical force exerted must contain the sum of the 

 energies of the disturbing needles as factor. 



(This might have been inferred from the conclusion 

 of (6), or vice versd, by assuming the equality of statical 

 action and reaction. But in a matter of such funda- 

 mental importance, it appears well to establish each 

 proportion by independent experiment.) 



(d) Combining the results of (6) and (c), it will be 

 seen that the algebraical expression for the statical 



