350 



MR WILLIAM SWAN ON OBSERVATIONS 





porting it rests, or ZO, the torsion-fibre by which it is suspended. We may 

 then suppose the magnetic axis to be transferred parallel to itself, until it passes 

 through 0, without altering the direction which the freely suspended magnet 

 will assume ; and, in like manner, the observed direction of the magnet will 

 remain unchanged, although we suppose the optical axis of the collimator at- 

 tached to it to be transferred parallel to itself, until it passes through 0. Let 

 AA' represent the direction of the magnetic, and BB' that of the optical axis, and 

 let a spherical surface described about meet the lines OA, OB, OZ, in the points 

 A, B, Z ; then the circle Z N z will be the plane of the magnetic meridian, and the 

 spherical angle AZB, or the arc NC of the horizontal circle NESW, will measure 

 the horizontal angle between the optical axis of the collimator and that plane. 

 It is obvious, also, that we may include the cases of the ordinary compass-needle 

 or of the magnet with an attached mirror, if in the one case, we conceive OB to be 

 the axis of figure of the needle ; or if in the other, we suppose that a pencil of rays 

 proceeding from the fixed scale along a given line, such as NO, and falling on the 

 mirror at 0, is reflected to B. 



If now, when the verniers of the theodolite employed to observe the magnet 

 indicate zero, the optical axis of the theodolite-telescope is in a plane parallel to 

 the plane ZOD, the arc DN will be the true, and DC the apparent reading for 

 the magnetic meridian. 



Hence, if the arcs DN, DC, and NC, be represented by $ <\ and #. we shall 

 have the apparent reading for the magnetic meridian, 



8 1 = 8 + (p. 



Next, let z, instead of Z, be taken as the point of suspension, the angles AOB, 

 AOZ, BOZ, all remaining unchanged, then the magnet will be in precisely the 

 position which it would occupy if the whole figure revolved about the line NS, 

 until z coincided with Z. 



If then a 0, b represent the new positions of AO, BO, we shall have 



aZb = azb = AZB = <£; 

 and if cT> = 8 Z , 



8 3 = 8 - cj), 



where 8 3 is the apparent reading for the magnetic meridian in the new position 

 of the magnet. 



Finally, adding, </> is eliminated, and we have 



* = *(4 + *.); 



which shows, that if the magnet be inverted, in the manner described, the mean 

 of the readings in the erect and inverted positions will give a rigidly accurate 

 result. 



