( 56 ) 
— bee dM, 0° Me 1 0? Mar} { Ne t 7 
a dr? Ow dy Ow dz cae ye jer UV" fg, ELC. . ( ) 
where q is a constant coefficient. 
If the ion experiences a resistance, proportional to the velocity, 
we must introduce a term 
on the right-hand side of (6), and in the case of a magnetic field 
with the magnetic force (A, B, C), there will be a term 
e(c dy ZB dz rE 
dt dt 
Hence, the equations (7) will change into 
ee eh ¢ aM, 1 ( ‚oM, EN 
q dé dt 
Ne ot? N e? dt TAN 
9 Ë Me 0° My 3? Mz ] 0° Mo. 
ay? | 
de? de dy Ow dz vO; 
ete. 
§ 4. The above formulae may be put in a form better known 
in the theory of electro-magnetism and admitting of direct compa- 
rison with the equations of Vorer. We shall arrive at it, if we 
observe that there will be a magnetic force , which may be decom- 
posed into two parts, the one 5, being produced by the vibrations 
of the ions, and the other 92 belonging to the same state of motion 
as (fo Joy Mo) 
The components of the first of these parts are found to be ') 
ONS 0? My 0 Mer ARAI 5 io 07 My OM (9) 
Hi. = == a Sd ly =a mee a pe ee ay ; 
ole adt ) dek UT Ted Soa De 
and those of {3 satisfy the equations 
Ne, § 124. 
