( 361 ) 
The second of these equations is derived in quite the same way 
as the first. 
9, Derivation of the Apex from condition (II). 
The maximum conditions are: 
as a GOE +. See Oe 
ee er Zing satya Os 
in which we put: 
sinp = sinpy + Cos po ($4 DA a), dA +- cos py ($4) ap 
a = (54), + (<4), a+ (5545) de 
The first of the equations thus becomes: 
dA = cos po sin hol $4 )5 + sin py sind (55). | zi 
4+dD= jens Po sin À 65). En + sin Po sin ee 
= — & sin po sin dy eS : 
0 
Here again, for quite similar reasons as in the equations of the 
preceding article, the terms with sin po in the coefficient of dA and 
dD may be neglected, they being of the order of dA and dD. The 
equation is thus reduced to the former of the two following ones 
(the second is found in the same way as the first): 
wa |cospo sin (55) | dA + Gazz sin nl 5) (4) dD= — sin po sin NEN 
| coe sin (35) GE) | dA + |coepo sin (55) dD=— |sin po sin (35) 
10. Airy's method. 
In his derivation of the position of the Apex and the amount of 
the linear proper motion of the sun, Airy starts from the idea, that 
the peculiar proper motions having no preference for any particular 
directions, may be treated entirely as errors of observation. 
