184 OBSERVATIONS ON NEBULiE 



24. A correction remains to be noticed, which is due to difference of refrac- 

 tion in any two stars whose apparent differences of R. A. and Decl. have been 

 measured. This becomes of considerable importance from the construction of 

 the observatory, which was such as to limit the range of the telescope to com- 

 paratively low altitudes, for the stars of the nebulae were observable only during 

 the last two or three hours of their diurnal circles. The altitude of the object 

 at the time of observation was therefore noted; at first, roughly, by means of a 

 rude quadrant, or by estimation from the bearing of the telescope; afterwards, 

 when the importance of this correction was fully known, and especially in the 

 Nebula Cygni, where the distances measured were considerable, by recording 

 the sidereal time of observation, from which the hour angle, and thence the 

 altitude of the object is easily deduced. The altitude being known, the ob- 

 served measures were corrected for refraction by the following equations: 

 If A' and D' = the observed differences of R. A. and Decl. between any two 

 stars in the field, reckoned with their usual signs, and in 

 minutes of space, 

 and A and D = the true differences, " " " " " " , 

 ' r = difference of refraction for 1' at the known altitude, always 

 positive, 

 V — the angle of variation of the hour circle in the field of view, 

 reckoned from the vertical around to the right hand, 

 and 8 = the declination of the nebula, 

 we have these three equations: 



(1.) D = B' + r !>• cos\ V. 

 (2.) A = A' -f- 2 r D' sin. v cos. v sec. 8. 

 (3.) A = A' - r A' sinl v. 

 The first two are applicable to observed differences of Decl. and R. A. be- 

 tween two stars in the field of view; the last to observed passages of a single 

 star between two wires, in determining the value of the scale. These equa- 

 tions are not such as they would be for an instrument mounted equatorially : 

 they express the condition, that the stars in the field shall, at all altitudes, run 

 on a parallel to one of the wires, which was, in the present instance, the only 

 practicable mode of conducting observation. 



For the three nebulae observed the values of r cosl v (eq. 1,) and 2 r sin. v. 

 cos. V sec. 8 (eq. 2) were calculated for every observable degree of altitude, and 



