( 372 ) 
mation, the same for stars in various parts of the sky, we shall see 
at once that the effect of taking the mean for various parts of the 
sky in such a zone of constant À,, is this, that the different v’s will 
become equal with some approximation, whilst moreover for such a 
zone, as indeed for the whole sky, 7 andp become small quantities. 
If therefore we introduce into the equations (31) of Airy: 
À == constant 
(37) | Uy = U = constant 
| 
they will become de 
[Gat (DE) 
—, [0x 9% Ox — [—0% 
isa op) Ar | tan) IE ele 
These equations are identically the same as those into which our 
equations (14) are transformed, if in these too we introduce the 
values (37). 
So zones of the same 4 will furnish approximately the same 
results if treated according to both methods. Hence the combination 
of all these partial solutions will certainly not lead to strongly 
deviating results. 
A still closer correspondence may be expected between the results 
of ARGELANDER’s method and the results of the second form of that 
proposed by us, when by taking means, all the angles are first 
made small. 
For if we neglect quantities of the order. 
pda, pel npe 
we may write in the second member of the equations (34) po = sin po, 
so that those equations become, if here again we take a zone of 
constant À,, 
