( 225 ) 
are equal to zero. The same holds for stars in the same great 
circle passing through the assumed Antapex at distances of 2) and 
180—A, from that point. Hence, when the stars are equally scat- 
tered over the heavens 
sin Ay cos Ag Ee | and sin Ay cos Ay EAN fl 
When the stars are unequally distributed, these two values will 
1 5 e_O h / 
yet be small with regard to sin? Ay Moreover — dA and — dD 
? 8 
as : h : 
are smal] quantities with regard to —, when the error in the assumed 
Q 
Apex is small. If however after a first calculation it would appear that 
dA and dD were not so small that we could neglect the quantities 
of the second order, the calculation must be repeated with more 
accurate values of A, and Do; in this case the two last terms of 
h 
the normal equations may be neglected with regard to foie? LA | 
4 
We then obtain: 
fi h h [vo sin do] 
eT eae It Wa GY ia ee 
[vo sin A] = [sin? Ag] ; or b [ea Jo] 
If this value of — differs from zero, it may be substituted in 
Q 
the equations (B), and then the determination of dA and dD depends 
on the solution of: 
[ro ($4) vin 2,| = (oe in? | B dA + 
[GOED een Ber) “2 
zo (52) sin | = IGG gt | cee dA + 
(GD) eert) aan) dP, 
B) 
If we have started from the correct Apex, dA and dD are both 
