284 Prof. Tyndall on the Nature of the Force by which 



lanced by a suitable counterpoise, iv ; let the north pole of the 

 earth be towards N. Supposing the beam to occupy a position 

 oblique to the magnetic meridian, as in the figure, the end /, or 

 the marked end, of the needle is solicited towards N by a force 

 (j), and the tendency of this force to produce rotation in the 

 direction of the arrow is expressed by the product of </> into the 

 perpendicular drawn fi'om the axis of rotation upon the direc- 

 tion of the force. Setting this distance = d, we have the mo- 

 ment of in the dii'ection stated, 



= (f>d. 



The end h of the needle is repelled by the earth's magnetic pole 

 with a force 0' : calling the distance of the direction of this latter 

 force from the axis of rotation d', we have the moment of <})' in 

 a direction opposed to the arrow, 



= (f>'d'. 



Now as the length of the needle may be considered a vanishing 

 quantity, as compared with its distance from the terrestrial pole, 

 we have practically 



<f> = ^', 

 and consequently 



(f>d<'(}>'d'. 



The tendency to turn the lever in a direction opposed to the 

 arrow is therefore predominant ; the lever will obey this ten- 

 dency, and move until the needle finds itself in the magnetic 

 meridian : when this position is attained, the predominance 

 spoken of evidently ceases, and the system will be in equili- 

 brium. Experiment perfectly corroborates this theoretic deducr 

 tion. 



In this case, the centre of gravity of the needle recedes fi-om 

 the north magnetic pole as if it were repelled by the latter ; but 

 it is evident that the recession is not due either to the attraction 

 or repulsion of the needle considered as a whole, but simply to 

 the mechanical advantage possessed by the force (f>', on account 

 of its greater distance from the axis of rotation. If the force 

 acting upon every particle of the needle were purely attractive, 

 it is evident that no such recession could take place. Supposing, 

 then, that we were simply acquainted with the fact, that the end 

 /of the needle is attracted by the terrestrial pole, and that we 

 were wholly ignorafit of the action of the said pole upon the end 

 h, the experiment here described would lead us infallibly to the 

 conclusion that the end h must be repelled. For if it were 

 attracted, or even if it were neither attracted nor repelled, the 

 motion of the bar must be towards the pole N instead of in the 

 opposite direction. 



