( 622 ) 



the foiiclusioii thai the resiiltiiit>- force and (lie resuliijjg couple are 

 for llie whole system. If the system consists of two j)arts .1 and /J, 

 we may express the same thing by saying that the total pondero- 

 motive action on one of these is e(pial and opposite to the total 

 action on the other. 



Of eonrse this \vill he e(pially Irne if, for a system whose slate 

 changes periodically, we ha\'e o]dy in aIcw the mean ponderomolix e 

 action dnring a fnll period. 



Tiiese theorems are nsefid whene\ei' the phenomena in one of ihe 

 parls, sav in .1, are not well ejiongh knox\Ji to permit a dii-ecl cal- 

 culation of the force acting on this part of the system. If llie |)heno- 

 mena in l> are less complicated, so that we encounter no diflicully 

 in determining the force oi- the couple acting on this part, the action 

 on .1 will he found at the same time. 



We mav apply this in the lirst place to well-known e.\[»erim(Mits 

 on electromagnetic rotations. 



Let us consider a cylindrical magnet, touched in two points 

 of its surface hy the ends of a conducting \\\vv IT. Let this wire 

 he Ihe seat of an electi'omotive htrce. prodncin.Li- a cui-rent that 

 Hows thi-ough ir and through part of the magiu't. The j)onderomotive 

 forces acting on the wire are known with certainty and may easily 

 he deduced from the fonnnla (\'I1) : they |H-oduce a couple, tending 

 to inrn the w ir(^ ahoiit the axis of the magnet. >\'illioiii enterijig into 

 anv s|»eculations concern iuii' the motion of the elecli-ons in its interior^ 

 we mav infei- that the mauiiel \vill he acted on hy an e(|iial couple 

 in the o|)posile direction. 



Of cour>e tiiis reasoning mii>t he jiiNtilie<l hy showing that the 

 siu-face-integral in (2J) is i-eally 0. if it is taken for a surface at 

 iidinite distance. This is readily seen to he the case, if we keep in 

 mind that, at great distances, the magnetic Unvv [jroduced l>y the 

 system varies inversely as the third power of the distance, aiul that 

 the inten>ih of the electric Held, if it exist at all, \\ ill cerlahdy c(mtain 

 no terms diminishing more slowly than the s(piare of the distance. 



§ 14. 1 shall choose as a second example some experiments, lately 

 made by Whitkhkad^j for the purpose of testing a consequence of 

 Maxwklt/s theory that has heen admitted hy many physicists and is 

 mia\-oidal)le in the theory of electrons, \ i/. that a ponderahle dielec- 

 tric, which is the seat of a variable dielectric displacement, and 

 therefore of a displacement-current, when placed in a magnetic 



h Whitehead, Ueber die magnehsche Wiikung clektrisclier Verscliiebung, Fliysi- 

 kalische Zeitsclir., 4, p. 229, 1903. 



