( 230 ) 
ee (54) dA. vy (34). dD 
which equation, in contradiction to that used by Airy, is indepen- 
dent from the existence of a parallactic solar motion ; therefore I hold 
myself authorized to consider Arry’s transformed equations (B) as 
corresponding more closely to the fundamental hypothesis than 
those of KAPTEYN. 
a h 2 
7. The condition (v — — sin 1) |= minimum, may again serve 
O df 
N 
en h 
to eliminate — from the equations (2). 
) 
As the position of the Apex and the amount of the solar motion 
are mutually independent, we consider: 
3 ‘ / 2 
10. the relation which exists between (ev zon ) | and the 
4 
position of the Apex. 
If we augment the right ascension and the declination with dA 
and dD, we get uv, for v, and A) =A + dÀ for A. 
Now 
h m 
Q 
i 
sin A and vp = — cos (q +e) + | sinh ena 
Q Q 
me 
U == — cos g + 
Q 
or: 
m m , he. 
Up = — cosg — — sing.e + — sin À, 
Q eg Q 
h ] ] 
while — sin Ay == — sind aa — cos A ae 
0 Q 0 
Hence: 
9- 
] 1 2 5 i = 
(eo == di sin ho) | = ie cos q — ae sin ae ees cos À d.) le 
v Q ? Ee 
Ae m 2 
In order that (ev — —sin i) | or (= cos 1) | may really be a 
g g i 
minimum 
ee 
| cos g = sing econ g. — cos d @,] must be 0. 
¢? Q 
Q 
