Dreyer — A Si'.rre// of the Spiral XehuJd Messier 33. 11 



The origin of the ^, -q system is a point (.:/, i)) sui:)posed to 

 represent fairly closely the centre of the plate. From the measures 

 we have tlie coordinates x and y, expressed in seconds of arc by 

 means of an approximate value of the screw-revolution (in this case 

 16"-37). AYe next compute the values of the followiug Cjuantities, 

 the indices 1 and 4 referring to the first pair of stars : 



tan = 

 tan 0, , = 



^ yi-l/i sin I//' 



F = ^cos(ii^ - 0), 

 Q = /xsin(i/. - 6). 



The coordinates of the '^central star," the origin of the x, i/ 

 system, referred to the standard axes through the point {A, B) are 

 then found by means of either of the reference stars by the formulae : 



I = 1-^(1 -f P)4- Q^, 

 =^ yj - y{l P) - Qx. 



The constants P, Q, E, y derived from the two pairs of reference 

 stars ought not to differ more inter se than the probable error in the 

 coordinates of the stars will account for ; otherwise the point B) 

 is not near enough to the centre of the plate, and it becomes necessary 

 to choose another point, and to try to obtain a better agreement. 



•(2) 



Xorth. 



(4)- 



•(1) 



I 



South. 



•(3) 



On the plate in question there are four reference stars very con- 

 veniently situated, forming a quadrilateral with the nebula inside it. 

 They all occur in Bessel's zones, but I have preferred only to make 

 use of recent observations. The star (2), as well as three others, 

 were kindly observed with the Dunsink Transit Circle by Mr. C. 

 Martin. The star-places from the Astronomische Gesellschaft zones 



