706 
MR, G. F. C. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
When xp = 0 so that the normal is along the direction of motion, the normal 
pull is KE 0 2 /87t, or 27rcr 2 /K, and is independent of j8. 
When xjj = 77 / 2 , so that the tangent plane is parallel to the direction of motion, 
the normal pull is KE 0 2 (1 — #/u 2 )/8 tt, vanishing when the speed of light is reached, 
i.e., when u — v. 
Now for all real values of /3 the denominator is positive. Thus, if /3 is large 
enough, the normal pull, N, may be negative over a certain range of values of xp. 
For a given value of /3, as xp increases from 0 to 7 t/2 , N changes from positive 
to negative and from negative to positive again as xp passes through the values 
given by 
2/T cos 4 xp — cos 2 xp (/3 -f /3 : ) + 1 — /3 = 0, 
or 
cos~ t// = — {1 + /3i \//3 2 + 10/3 — 7}. 
The value of xfj given by this is not real till 
£ 2 + 10/3 - 7 = 0, 
i.e., till /3 = — 5 fi- \/32 = ‘6568542 (/3 must be positive). 
The value of xp corresponding to this value of /3 is 37° 25' 45 ,, ‘4. Thus, if an 
electrified sphere is in motion along its polar axis, the normal pull is positive all over 
it till /3 = '6568542, or u/v — ‘810465. At this speed the pull vanishes at the points 
whose co-latitude is 37° 25' 45 ,, ‘4. As the speed increases, there are two lines 
of latitude along which the pull vanishes, and between which the pull is negative. 
Tf xp x denote the value \jj where the pull changes from positive to negative, and xp 2 the 
value where it changes from negative to positive, then the values of xp x and xp 2 are 
given in the following table :— 
A 
ujv. 
fi- 
Yor 
•6568542 
•810465 
0 
37 
/ a 
25 45'4 
0 
37 
1 11 
25 45'4 
■7 
•8567 
22 
13 
53 
18 
•75 
•8660 
15 
41 
60 
42 
•8 
•8944 
11 
6 
66 
15 
•85 
•9220 
7 
42 
71 
2 
•9 
•9487 
4 
42 
75 
33 
•95 
•9747 
2 
8 
80 
25 
1-00 
1-00 
0 
0 
90 
0 
When u = v, we have already seen that N vanishes when xp = 7r/2, so that there 
is then no real change from a negative value to a positive one. Now when xp = 0, 
N is always positive whatever the value of ujv ; thus when u = v, N changes from 
positive to negative for an infinitely small increase in xp. 
