80 



H. JACOBY, 



In these equations, A 2 a and A 3 tt denote the complete reductions from 

 eginning of the year to the instant of observation. We now have the 

 iities we have called Aa and Arc from the following: 



Aa = A^ -t- A 2 oc, A~ = \ x k -+- & %2 t. 



With these we can compute: 



u 



' = «+Aa, tr =s= -+- A it (34). 



We now approach the final step in the present discussion. As has been 

 stated above, the quantities u' and v will differ from zero on account of 

 various causes. To discuss these causes, let us put: 



* = correction required by the assumed constant of precession, n, 

 z = correction required by the assumed constant of aberration, 

 z z = correction required by the assumed constant of nutation. 



Also compute: 



t -t- t) cos (a ), $\ = (t — 1 -+- t) [sin (a ) cot (t: ) -t- cot e] , 



2 



2 



3 



3 



cos e cos O [tan e sin (ic ) — sin (a ) cos (t: )] -+- sin © cos (a ) cos (ir ), 

 cos i cos O cos (a ) cosec (ir ) — sin O sin (a ) cosec (tt ), 



sin (a ) cos £2 — 1.87 sin £ cos (a ) sin £2, 



cos (a ) cot (ir ) cos Q — 1 . 8 7 sin Q. [cos e. -h sin £ sin (a ) cot (ir )] . 



If we now finally let : 



Z = - (Tt) -H U, 



z\= — (a) -t- a, 



the following equations will hold: 





P'i *i h- p>, -t- p>, -*- / 4 — d' t A-+-u' t = 



5 



Such a pair of equations will be furnished by every star on every plate. 

 In these equations all the coefficients (3,, etc., are known, as well as the quan- 

 tities v and ti. We can therefore solve them by the method of least squares, 

 to find the most probable values of the unknowns g. , etc. It is of course 

 evident that it will be impossible to determine d A, because d t A and g 4 



always occur with the coefficient 



therefore be advisable 



t each equation containing d t A from the mean of all such equations aris- 

 from that star. This will remove z\ altogether, and substitute for the 

 nown d t A a new unknown {d Q A — d.A), which is determinable. Here 



CTp 



4o 



