( 362 ) 
Hence each star gives two equations of condition between h, A 
and D, expressing that the observed proper motions projected on two 
mutually perpendicular directions are equal to the projections on 
those same directions of the parallactic proper motions. Arry chooses 
for the two directions the parallel and the declination circle. 
To get a clear insight into the character of AtRy’s solution it 
is preferable however to choose for these directions the direction of 
the star towards the Antapex and the great circle through the star 
at right angles to the former. 
Doing this his equations of condition get the form 
(16) >< == 
and 
19 x= bate). : 
Q 
So we can say that by Arry’s method A, D and h are deter- 
mined in such a way that all the equations (16) and (17) are 
satisfied in the best way possible. Now as Arry and every one 
who has applied his method, have solved these equations by least 
squares, this determination comes in reality to the choosing of 4, 
D and k in such a way that both 
(18) Er? minimum 
a en en 
(19) = 5 sin i—v) minimum. 
OQ 
The former of these does not contain the unknown quantity / 
and only leads to a determination of A and D. The second gives 
the three unknown quantities, so that we arrive at two independent 
determinations of A and D and one of h. I will here discuss the 
two conditions (18) and (19) separately. 
11. The condition = t*? minimum. 
The minimum conditions are (with the aid of (6)): 
oF pee 
(20) Srv =0 
0x 
ee 
(21) 22 5D 
For stars all situated at the same point of the sky, they are reduced 
to this one 
(jr 207 =0 
