Impulsive Motion of Electrified Systems. 141 



speeds. To facilitate the use of Legendre's tables'* for E 



and F, we put n- 



= sin y. 











Motion along Axis. 



Itotiou perpe 



ndicular to Axis. 



7- 



, 



17 U . 



m t /m Q . 



U/Uo- 



mtlm . 



o 



10 



•1736 



1-0001 



10154 



1-0001 



1-0106 



20 



•3420 



10019 



1-0642 



1-0016 



1-0366 



30 



•5000 



1-0104 



1-1547 



1-0085 



1-0860 



40 



•6428 



1-0357 



1-3054 



1 0278 



1-K.27 



50 



•7660 



1-0992 



1-5557 



1 0712 



1-2772 



60 



•8660 



1-2500 



2-0000 



11590 



1-4502 



70 



•9397 



1-6329 



2-9238 



1-3317 



1-7291 



80 



•9848 



2-9662 



5-7588 



1-7068 



2 2631 



85 



•9062 



5-7804 



11-4737 



2-1263 



2-8320 



We notice that, as n increases, both U/U and m t /m in- 

 crease more rapidly when the motion is along the axis of the 

 disk than when it is perpendicular to the axis. For some 

 value of n between *8660 and '9397 the value of m t jm Q for 

 motion along the axis becomes three halves of the value of 

 ni f /m for motion perpendicular to the axis, and then the 

 magnetic energy for motion along the axis becomes equal to 

 that for motion perpendicular to the axis. 



The ' ; longitudinal mass/'' mi, is easily found. For 

 we have f 



dF = E F dE _ E-F 



dn n(l — /r) n ' dn n 



and thus 



mi= 2 ± (1 \=1£(1\= 2U <» (l + tt*)E-(l-tt»)F 



du\u J v 2 dn\n J v 2 ' irn^il — n 2 ) 



§ 29. Momentum and energy of a system of revolution 

 moving slowly in any direction. — -When a system which is 

 symmetrical round an axis, and is also symmetrical with respect 

 to a plane normal to that axis, moves either along or at right 

 angles to its axis, its electromagnetic momentum is in the 

 direction of motion, but the amounts of momentum are 

 different in the two cases. If, however, the axis makes any 

 angle other than or \tt with the direction of motion,, the 

 momentum has a component at right angles to that direction 

 as well as one parallel to it. 



A general investigation would be difficult, but we can easily 



* Legendre, Traite des Fonctions.Ellijitiques, vol. ii. 



t A, Caley, u Elementary Treatise ou Elliptic Functions/' chapter 3. 



