52 



H. JACOBY, 



Then equations (2) give: 



8in B n,s 7 e cos Bn, s 



j, -+- rf n ^4 -+- ^ s sin ' r <*„€ — ^ sin i» ^ -+- £„,., — 0, 



. . (9). 



v 



. -+- p.d co — to cos 2? d £ — w sin B„ dr\ -+- L, n , = 



In these equations, the quantity d n A will allow for any possible 

 twisting of the telescope during the night, and for any error in fixing the 

 sidereal times of the several exposures. The quantity d n <a will remove the 

 effects of any changes of the scale value. The unknown quantities are there 



fore: 



u., v c , d£, dv\, dA, d co. 



Such a pair of equations is derivable from each exposure of each star. 

 Unfortunately they do not admit of a solution without making some assumpt- 



ion as to the unknowns d n ? and d n r\. This would be unnecessary if we 

 should adopt as known the right ascension and polar distance of one star. 

 But it is better that the results to be obtained from our trail plates should 

 be quite independent of determinations of star-places by other methods. 



Now let us remember that in equations (9) those derived from the 

 right ascensions must be multiplied by p s & sin 1" in order to make all 

 the equations of equal weight. Let us also write: 



C,,=^ wsin i"}*,** w, = j>, « sin l"w„ 



d„A' = w sin \" dA. 



n n 



Then equations (9) take the form: 



• • (9') 



u'-+-pd n A'-+-smB n d n \ — cos B„ . d. vj -i- C" = 



v, -+-P t d n w — cos B n d n % — sin B„ . d„ yj -+- £' . = 0, 



. . (10) 



in which d n % and d n -r\, as well as £' n § and '( n f are now expressed in seconds 



of arc. 



For convenience, we shall indicate by the subscript the mean of the 

 different values of any quantity, and by the symbol A„ the excess of the 



n th value over the mean of all the n values. Thus, for 



cos \ 8 = - (cos \ 6 -+- cos A 2 6 -*- . . . -#-cos A n 6), 



A n cos A n 6 = cos A n 8 — cos A n O, 



etc. etc. 



9 



$H3.-MaT. crp. 52. 12 



