1183 
~ SY ee é 5 ‘ ad 
€, = = (qa + qa’) cos Aar ua sin 2a vy sin Un wz + m — 
: dar’ 
m denoting the electrical moment of the vibrator. 
From this expression follows : 
dE, 0). 05, ’ oo hey * , 
== —- —~ |— 0%: = 2 (qa + qe) cos 2xuxsin An vy sin 2x we 
dt Ov dz 
i a dm 
Anr® dt 
and in connection with (2) and with equations of the form 
ve = c(vy — wf): 
Det (q+rp) at (q' + rp’) a} cos 2ar ua sin 2a vy sin Ln we = 
a dm 
aca (7) 
The divergence of the vector in the lefthand member of this 
equation is zero, and so also that of the vector in the righthand 
member. We can therefore represent it by: 
= — OY, — 
= (oa + Ga’) cos 2a ua sin 20 vy sin Ln we. 
Equation (7) being satisfied identically in 2, y and z, we have 
girmp=o GIP SOE In veer GN 
Differentiating these equations respectively with regard to q and 
q we get: 
dg 06 0g do! 
RE se Sea CAG He eN (a 
0g 0g dg’ 0¢ 
If we treat the expressions for the components of 5 in the equa- 
tions (2) in the same way, we find: 
Pr == 9 pl — vg = 0 . . . . . (8a) 
and 
dp Op’ 
EE ae (9a) 
Op Op 
and therefore : 
7. Op\ A dy. dy: 
(it) ip En arl Oe 
0g Op p dg Op 0g 
When g is known, we can substitute in (10) the values for 
q and p from (8) and (8a) and so we get a relation which the 
coefficients o as functions of g and p must satisfy. The- value of the 
os on the other hand depends upon the value of @ as a function 
jp dm 
of x, y, and z and upon the velocities (*. 
in equation (7) ) which 
77 
Proceedings Royal Acad. Amsterdam. Vol. XV, 
