250 Prof. J. J. Thomson on the 
: on epee ver 
peers / 10 18 Soe 


e* 
sa’ 

g=—0a/ 20-726 +’. 
When k=2, 
9 
= 
e e e 
Gxt. 2) 31-94—.— my } = 2103 i 
(6 Ba mg )(31 24 Bp ) =( 103 303 2maq ) ; 


By applying the usual methods we find that all the roots of 
this equation are real, so that the steady motion of the five 
particles is stable for displacements in the plane of the 
orbit. 
Let us now consider displacements at right angles to the | 
plane of the orbit. When £=0 the frequency equation is 
ve? - 
Be —— mq =(); 
the solution of which is 
Saye 
IN al 
When k=1, the frequency equation is 

5 2 
mo*?—mq*=0, 
hence 
q=o. 
When k=2, the frequency equation is 
ve ee : 
pr 1942 os —mg =e 
or 19°42 oo? ve 19:49 ide | 29 
11 EaeRe Kee ee 
AD SAG 3 
oe whe ss —mg=9 
Hence, in order that the equilibrium may be stable, 
8:42 ve ve 
2 
@ must be > ——~—, >:433 —.. 
L9AZ 0" mb° 
Thus the five corpuscles are unstable when in one plane 
unless the angular velocity exceeds a certain value; the 
arrangement is stable, however, when the angular velocity 
is large. 
