44 Motion of a System of Bodies. 



whether we invert the motion of the plate, or make the magnet re- 

 volve in opposite directions. 



When the magnet is suspended directly over the centre of the re- 

 volving plate, (and which is called its concentric position,) it receives 

 no impulse; because the voltaic currents thus generated, lie in planes 

 passing through the magnetic axis of N, and those of the same de- 

 nomination meet at the centre. The counter currents that thus arise 

 upon opposite sides of the magnetic pole, exactly neutralize each other. 



Art. IV. — Motion of a System of Bodies ; 



by Prof. Theodore Strong. 



Continued from Vol. xxv, p. 289. 



Again, supposing T, T', &c. to denote the same things as before, 

 we have Qx - Py= ( - xQ- ~xPjr=Tr, for- XQ= the force Q 



y 



when resolved at right angles to r, and xP= the force P resolved 



x y Qx — Py 



at right angles to r,and "XQ-- XP=- — ~ — = the resultant of 



x y 

 the forces -xQ, - XP, since they act in contrary directions; in the 



xd^v vd 2 x 



same way Qx' — P'y' »TV, and So on ; hence we have — jTr 



z'd 2 y'-~y'd 2 x 

 Tr, ~^j~ 2 — =TV, &c. ; .".it may be shown in the very 



same way as at p. 43, that if we multiply these equations by m, m\ 

 &lc. respectively, we shall have, (by adding the products,) the equa- 



zd 2 y — yd 2 z\ 

 tion Sm( ^ 2 j =SmTr, which is independent of the recipro- 

 cal actions of the bodies m, m', he, ; by restoring the values of Tr, 

 TV, &c. we have the first of (18) ; and in a similar way may the se- 

 cond and third be found. Let h denote the distance of m from the 

 origin of the coordinates, then if m is acted upon by any force mF in 

 the direction of the straight line h 9 we shall have F for the force which 



acts on a unit of m in that direction j .'.by resolving F in the direc- 



x y 

 tions of the axes of x and y, we have yXF,txF for the parts of P 



and Q respectively which arise from F, .\ by considering these forces 



