(67) 
By the equations (3) we find: 
} 
Pa 0, aa = 0, wm (ed) A, 
@ 
by (1): 
1 
§=0, n= ——(%+i?H, C=9, 
@~ 
and by (2): 
ee Seat ME eV, 
@~ 
Hence 
H= a 
v? oe 
Le ri nch af 
@ 
and 
fae 2 is a3 Z 9 V. 
oF + Hi) 
Consequently, the two first of the equations (4) become 
1 if igh 
— + l =) U— — v= 
( Te i va ya 
and 
uJ it a R Zz 2 
aa, fet) rar eB fife 5 ( za ss V —= 0, 
Ve uy wv @*? + v* (z + iP 
or, if we introduce the quantities 4, #', etc, 
Ge EHD SH kREV SOS. … (24) 
(x +4)? 
o? + v2 (a + i)? 
(2+ t dH —IA)VLiLRI U— g2. 9? v?V=0 (25) 
These equations correspond to the two last of PorNcARÉ's formulae 
(6), and if we were to follow his mode of reasoning, we should say 
that, in virtue of (24), U must be a small quantity of the order k 
so that the second term in (25) becomes of the order of h*. We 
should then omit this last term; all influence of the magnetic fieid 
would thereby disappear from (25). 
There is however an error in this reasoning, because, as I shall 
now show, the coefficient of U in (24) may become of the same 
order as that of V. 
