Sixty-two Stars about r^ Cassiopeise. 385 



Logarithms for these plates 

 only. 



n = a sill t: 

 m = n cos t: 



P = sec f) = [0.265487] 



Q = [4-685575 ] tan osec n = [5.1408 ] 



R = [8.89403„ ]taii2 rJsec = [9.5390„ ] 



S = [8.89403 ] sec o (i 4- 3 tan 2 fj) = [0.0727 ] 



T = [4.384545^] tan d = [4.5743,, ] 



U = [8.59300,, ] (i + 3 tan 2 d) = [9-5o62„ ] 



^^ = [3-57960n ] sec tan 0(1 - 3 tan^ d) = [4.94800,,] 

 ^= [3-57960 ] sec o tan r7(2 +3 tan 2 §) = [4.99804 ] 



«' — o. =Pn + Qnm — En'-^ -f Snm^ + Vn^m + Wnm^ 



>/ 



o' — d = m - r«2 + Un^m 



where a and ~ are the final corrected mean distance and position 

 angle respectiveh' of the star whose «' and o' are desired. It was 

 fonnd also that the terms in V and W were not needed since they 

 are so nearh' equal and have contrary' signs. 



But since these values of «' — a and o' — do not take into ac- 

 count the proper motion of the reference star which in this case 

 is considerable, but are onh* the mean of man}- measures taken 

 on widely differing dates regarding r^ Cassiopeire as fixed in the 

 position given on page 382, I have given in column 3, Table VI., 

 the mean epoch at which these values of «' — a and o' — o truly 

 represent the mean coordinates of the diff'erent stars referred to 

 7^ Cassiopeia 1872.0 as the origin, that thus they may be cor- 

 rected for the interval between this mean epoch and 1872.0 by 

 any assumed or computed proper motion of rj in the same manner 

 as when dealing with other star catalogues. 



In the last column is given the Bonn Durchmusterung number, 

 and in column tAvo the magnitudes from the same for so many 

 of the stars as I have been able to identify. 



Using the difterences of right ascension and declination of 

 Table YI., and the given position of -/^ Cassiopeije, we get the 

 right ascensions and declinations of Table Til., good for 1872.0, 

 save with regard to proper motion as mentioned above. 



In column two is given the number of plates on which 

 the star is found, but it may be well to state that the given posi- 



