(324%) 
A+4dd Decl. D+ dD), and one in a direction at right angles to 
it, the latter will be 
m , h 
Tg = — sin (qe) + — sin (A+dA) sine, 
Q 0 
when « represents the small angle made by the direction towards 
the true Apex with the direction towards A + dA, D+ dD, or 
neglecting small quantities: 
m h 
Ty =F + — cos q.e + — sink. «. 
? e 
In order that [z?] may be a minimum 
m AP. 
E a cos q. € + ar sin h. a must be zero. 
dy 07 
a dA — aD dD, we obtain (dA 
and dD being independent quantities) : 
If we substitute for ¢ its value — 
m Ox ch 
lr om gag te . 
i h 
sin 2 2) = andr cong 3% pro sindsé] =o 
As, however, the motus peculiaris may be considered as an error 
of observation, which does not enter into the equations (4'), the 
equations of condition are reduced to: 
Lr] = 0 and =[F sin ot) = OF; he Saree) 
which shows that also the equation [¢?] = minimum leads to the 
] a 
right result; for, if — differs from zero, the conditions (C) and (C’) 
7 
I : ; 
are identical; if “= 0, (C’) assumes the indefinite form 
g 
15 
Proceedings Royal Acad. Amsterdam, Vol. IV. 
