76 Art. 9.-T. Terada: 



to tliat of tlie horizontal one: or less p^obal3h^ to a rotatory 

 oscillation of the kind considered in § 24, but in a horizontal 

 elliptical orbit instead of the vertical one. These will probably 

 remain the only admissible hypotheses, if the progressive nature 

 of the magnetic waves be ultimately denied Ijy the observations. 



The simplest ideal case conceivable of this kind is that 

 in which a linear current is subjected to a see-saw motion in the 

 vertical ptane, about its horizontal mean position. Referring 

 to the annexed figure," where .T^z-plane corresponds to the 

 earth's surface, let HH' be the mean position of tlie current j, 

 at the height A, and let it be vibrating about its mean position 

 in the vertical yz-^h\\\Q, as if it were a tangent to a string 

 subjected to a stationary vibration, at its node at H. Denote 



the frequency of vibration b}^ -fr . A is the point of observation 



at a distance x from the origin, and AD the perpendicular from 

 it to the current HT at time t. If AP represents the magnetic 

 field at A due to the current at t, it is perpendicular to AD 

 in the plane perpendicular to HT and of the magnitude 



2^ _ % 



if we denote by tl the inclination of HT to HH'. Let Q and 

 N be the feet uf the perpendiculars from P to 0:r and :r//-plane 

 respectively. Then, denoting the angle ^OAD by </', 



AQ= X =ÄPsiu ip. 



QN= - Y=PN sill tf, 



PQ=-Z=PN cos ä, 

 since the angle ^NPQ = ^. Put PN=ÄP cos é and tg (/>= '— • 

 Hence, we have for the fields of tlie thi'ce components: 



'liJlCOH 6 

 ;T- + //-COS-/^ 



2 /j;' bill ä 

 x' + h'-cos-d 



2?iccos ti 

 x^ + h'-cos-ä 



1) The coordinates axes are chosen lefthandid to correspond to our initial convention. 



^ 2///COS â 1 ^~ X 



X = --^ — - — - - lor rs -comx^onent, 



,. 2/j;'bili ä 4- T^ , 



— 1= —^^ _^ tor h-component, 



Z = ^ _^ ;^ lor L pwara-coiiiponeiit. 



