12 Preston — Radiating Phenomena in a Strong Magnetic Field. 



not resolved clear of each other, but until this resolution is effected it remains 

 possible that 5, C may be a triplet. These lines are all in the ultra-violet part 

 of the spectrum, and are weak, so that a prolonged exposure is necessary to bring 

 out all the details. When the double-image prism is not employed they 

 photograph as triplets, or rather as bands possessing three dense ribs ; but this 

 arises from the components of A overlapping the outer edges of B and C, while 

 B and C overlaj? each other a little, and thus form the middle rib of the triplet. 

 It appears, therefore, that if we can explain the production of the ordinary 

 quartet form (fig. 2) we are on the high road to the explanation of all the other 

 types of modification which the spectral lines suffer in the magnetic field. For 

 this purpose, therefore, let us consider briefly the investigation set forth in 

 Dr. Larmor's paper, already cited. In this investigation he considers the case 

 of a single ion describing an elliptic orbit under a central force directly 

 proportional to the distance. The influence of the magnetic field upon this 

 moving ion (supposed otherwise quite free from restraints) is such that its 

 elliptic orbit is forced into precession round a line drawn through its centre in 

 the direction of the lines of magnetic force. For the equations of motion of the 

 ion moving round the centre of force in the magnetic field are, as a first 

 approximation, the same as those which hold for a particle describing an elliptic 

 orbit under a central force when the orbit is forced to precess or revolve round a 

 line drawn through its centre in the direction of the lines of force. Thus the 

 equations which determine the motions of the ion are — 



X = - Qi'x + k [ny - mi) \ 



i/ = - Q^y + k {Iz -nx) • • • (1), 



s = - Qi^z + k {mx - ly) j 



where k is a quantity depending on the strength of the field, and the ratio of the 

 ionic charge to the inertia associated with it. While the equations of motion of 

 a particle describing an elliptic orbit under a central force while the orbit is forced 

 to precess with angular velocity w round a line whose direction cosines are /, m, n 

 are easily found by taking as axes of reference a system of moving axes which 

 revolve round /, »?, n with angular velocity &>, and are — 



X - - H'^x + 2(0 {ny - mz) + ijj'x - w'l {Ix + my + nz) \ 



i) = - Q'y + 2'" (''^ ~ "•^) "•■ '^^y ~ •"""* i^^ + '"y + '*^) r • • • ('^)> 

 z = - Qrz + 2(0 {mx - ///) + <v-z - w''n {Ix + my + nz) j 



and these agree with equations (1), when or is small enough to be neglected, and 

 if 2(1} be taken equal to k. 



If N be the frequency of revolution of the ion in its orbit, and if n be the 

 frequency of the precessional revolution, then the combined movement is 



