58 



H. JACOBY, 



Then if we write for brevity: 



*"» = cos A n G d' n Z — cos A n 8 d' | — sin A n d' f], 



V n = cos A n 6 d' n yj -+- sin A n d' f — cos A n 6 d' Y] , J . . . (25) 

 / n = A n 2 cos o A n 0— cosA n 0A o 6 2 



we obtain readily: 



A n 6cos A n 6 Tl — A n cosA n e Yo — sinA n 6 T ; 



/; T2 -sinA n 6A ^ T ' 2 -4-...-r n = 



K e cos o A „ e Y i — A » c° s A „ 9 y'o -+* sin A „ 9 Yo 



(26) 



f n y 2 -f- sin a„ e a e 2 Ta -*- . . . -x' n = o 



The first of these equations involves the quantities y' and A o 2 Y' 2 with 



coefficient, and the second is subject 



with 



regard to y and A 6 2 y 2 . If we prefer to avoid this, we can do so by intro- 

 ducing two new unknowns G and G\ defined by the equations: 



G = T ' -t- A 2 T ' 2 , G' = To -*-A o 2 T2 . 



If we then put: 



/"„' = fn - \ «» 4„ A, V, 



equations (26) become: 



A n 6 cos A n 6 Yl — A„ cos A n 8 G' — sin A n G 



f„'Y 2 -»-. • • — x "„ = ° 



A n 6 cos A n 8 -f\ — A n cos A n 6 G-+- sin A n 6 G' 



. . (27) 



Cy' 2 -*- - • • — ^,, = 



A solution of these equations, or some modification of them, by least 

 squares will make known the values of the y's. Equations (24) will then 

 furnish us with d x and d y. These being substituted in equations (16), 

 will give the values of: 



u s -+- p s d A' and v s -+- p s d w. 



Then, with the help of equations (15) and (8) we again obtain a series 

 of polar right ascensions which all differ from the truth by the same con- 

 stant, and a system of polar distances which all differ from the truth by a 

 constant factor. This result is no longer subject to the condition that the 

 telescope did not move, but only to the condition that it moved in accord- 

 ance with the curve represented by equations (22). 



*H3.-MaT. OTp. 58. l8 



