348 plDcker on the theory of diamagnetism. 



them the even powers of a must disappear. Retaining, there- 

 fore, the first power only of a, we neglect only the third, and 

 those higher than the third. We thus obtain 



sin (<^ + a) = sin <^ + a cos ^, 

 cos (</) + «)= cos + a sin</); 



and if, for the sake of brevity, we set 



/•2 + c2-2rccos</)='CP2=m2 .... (5). 

 and develope, we have 



{r^ + c^--2rccos (<^ + a)}~^=(m^4:2acr sin 0)"^ 



Substituting these values, the expression (3) passes into the 

 following : — 



and may also be written in the following form : 



_?^^P^+(^ + ^)cos^. 3} . . . (6) 



The expression (3) therefore gives the moment of rotation 

 produced by the action of the pole P upon the little needle of 

 soft iron. The corresponding moment of the pole Q, is 



?fg!L^P<^-(^+^>os^-3}, ... (7) 



where, for the sake of shortness, we have set 

 ?'^ + c^ + 2rc cos <f) = 7?2'^. 



This expression is obtained immediately from the foregoing, 

 when, as in paragraph 15, c is exchanged for d, and the sign of 

 fi and cos </> is at the same time altered. 



19. If the lever CC be caused to rotate in the horizontal plane 

 around the point O, then the momenta (6) and (7) change with 

 the angle (f>. These also change with r, that is, when the little 

 iron bar, while remaining at right angles to the lever, is placed 

 at different distances from the centre of rotation O. If we re- 

 gard r and (f> as variable quantities, by which they will obtain 

 the significance of polar coordinates, we can calculate the mo- 

 ments of an inertia for all points of a straight line, consisting of 

 infinitely small magnets, which are all at right angles to the 



