xiv Introduction to the Makerstoun Observations, 1844. 



the observations, and it is altogether inappreciable, compared with the error due to 

 the second. 



If the plane of detorsion be that of the magnetic meridian, and the magnet be 

 deflected through an arc u by turning the arms of the torsion circle w, the torsion 

 is w — u, and the equation of equilibrium is 



m X u = (w — u) H 



where m is the magnetic moment of the bar, X is the horizontal component of 

 the earth's magnetic force, and H is the torsion force for an arc equal to radius, 

 whence, if m X = F, 



u _H 



w — u F 



is the quantity by which the deviations of the magnet from the plane of detorsion 

 should be multiplied to obtain the decrements due to torsion. If n be the observed 

 deviation, a> n = the true deviation. The following are observations for the value 

 of $ for the suspension thread placed in the instrument, June 22, 1843, and for the 

 long scale magnet : — 



Aug. 7 d 2 h , 1843. Arc" 1 w = [ + gjjo ; arc" 1 u = [ £|J ; mean value of * = 0-00147. 



Dec. 26 d 23 h , 1844. Arc" 1 w= I ^gjj c ; arc" 1 u= I J'.gg ; mean value of * = 000140. 



These values have not been used for this correction ; the last determination has 

 been employed in the observations of absolute horizontal intensity made in 1844. 



11. The second and most important error due to the torsion force is that pro- 

 duced by the variation of the plane of detorsion. Unless when the period and extent 

 of change is known, this can only be corrected by removing it ; this is done occa- 

 sionally in the following manner : — The magnet, with its stirrup, being removed, a 

 brass bar and stirrup of nearly the same weight and dimensions is suspended ; the 

 rectangular box being removed, the cylindrical box being completely closed, and the 

 shutters removed from the glazed lid, the extremities of the arc of vibration are 

 observed through the latter ; the marble slab beneath having radii drawn for every 

 5° on each side of the magnetic meridian, the positions of rest at the extremities 

 of the arcs are estimated to ^ c ; the deviation of the mean position from the magnetic 

 meridian is known, and the arms of the torsion circle are turned through an equal 

 angle in the opposite direction ; the position of rest is then in the magnetic meri- 

 dian. Much time and care were bestowed upon these observations, as the error 

 due to this cause is by far the most serious that occurs in connection with the de- 

 clinometer. 



