( nm } 



Let us put 

 Then 



SO tliat the amplitude factor is now known in all cases in whicli the 

 harmonic of the second order is a zonal one whose pole coincides 

 with that of the other harmonic or is 90° distant from it. All other 

 cases may be reduced to these two by suitable decomposition of the 

 harmonics. In this way I find the values of the amplitude factors 

 inscribed in the following table ; the letters x, y, z again serve to 

 indicate the direction of the secondary vibration. 



■^xy ^ x'y' ^ xz ^ yz J^ zz 



Yx +^Uy.{l) -^Uy.{^) +3/4^(z) -\y.{y.\ 



Yy +=^/4^(x) +^Uy.{y) +3/4;i(z) -hy{i) 



^z +V4;^(x) +3/4x(y) +;.(z) 



§ 14. In the magnetic field there are three modes of motion of 

 the first order, whose frequencies are 



«] + w'l , «1 — n'l , «1 (17) 



We shall call the amplitudes of the variable pi (§ 8) in the first 

 two motions, and that of the variable ;?3 in the last one 



Then there are five motions of the second order, having the 

 frequencies 



?io -|- n\ , Jig — n\ , «2 -j" \ 'ï'z ) ''2 — è "'2 ) "2 • • (^^) 



Let 



respectively be the amplitudes of pi (§ 9) for the two first motions, 

 of P3 for the third and fourth, and of ^^5 for the last vibration. 



We shall now take as an example the combination of the first 

 of the vibrations (17) with the first of (18). 



The motion of the second order consists in a Y„,- and a F.v'^- 

 vibration for which we may respectively write 



