MAGNETIC OBSE II V ATIO N S . 45 



scale readings with the north end of the deflecting magnet to the east, and two scale 

 readings with it to the west. From the mean of the two scale readings obtained 

 with the north end of the deflecting magnet east, the mean of the two scale read- 

 ings obtained with its north end west were subtracted. The difference was twice 

 the value of the angle of deflection, as resulting from observations made with the 

 deflecting magnet east' of the suspended magnet. The mean between this result 

 and that obtained from the observations with the deflecting magnet west of the 

 suspended magnet, was adopted as the true value of twice the angle of deflection, 

 with the deflecting magnet at a distance of two feet from the suspended magnet, 

 9°. The thermometer inside the magnet-box was read. 10°. The time was noted. 

 11°. All the observations just described were repeated with the deflecting magnet 

 at a distance of two and a half feet from the suspended magnet. 12°. The torsion 

 of the suspension fibres was determined, precisely as described under the head of 

 "observations of vibrations." 



Horizontal Force was calculated from the observations of vibrations and deflections 

 by the following formulae : 



T = observed time of one vibration of the magnet. 



7" = time of vibration, corrected for rate of chronometer and arc of vibration. 



T = time of vibration, corrected for rate of chronometer, arc of vibration, torsion 



force of the suspending thread, temperature, and induction. 

 s = daily rate of chronometer, -\- when gaining, — when losing, 

 a, a'= semiarc of vibration, at the beginning and end of the observation, expressed 

 in parts of radius. 



TJ 



— - = ratio of the force of torsion of the suspending thread to the magnetic directive 

 force. 



q = coefficient of the decrease of the magnetic moment of the magnet produced 

 by an increase of temperature of 1° Fall. (This is not constant for all 

 temperatures, and the correction is more exactly expressed by a formula 

 of the form — correction to t'=q(t' — O + ^'C^' — 0% where V is the 

 observed temperature, and t an adopted standard temperature.) 

 K = moment of inertia of the magnet, including its suspending stirrup and other 

 appendages. (This is constant for the same magnet and suspension, but 

 varies slightly with the temperature, owing to the expansion of the 

 materials.) 



7t = jatio of the circumference of a circle to its diameter = 3.14159. 



jt/ = coefficient of increase in the magnetic moment of the magnet produced 

 by the inducing action of a magnetic force equal to unity of the English 

 system of absolute measurement. 



r = apparent distance between the centres of the deflecting and suspended mag- 

 nets in the observations of deflections. 



r = the same distance corrected for error of graduation and temperature, 

 (r = r [ 1 + 0.00001(r — 62°)] + correction for scale error.) 



(/ = value, in minutes of arc, of one division of the magnet scale. 



u = observed angle of deflection, in scale divisions. 



