xxii Introduction to the Makerstoun Observations, 1844. 



and termination. o> is the ratio of the torsion force to the horizontal component of 

 magnetic force for the declinometer thread with the deflecting bar suspended, s is 

 the daily rate of the clock in seconds, K is the moment of inertia of the deflecting 

 bar obtained from the formula 



K = H^ + ^)M. m2 T ° 2 



where r* and r e are the internal and external radii of a regular metallic ring, M is 

 the mass of the ring in grains, T is the true time of one vibration without the ring 

 (obtained by the above formula for T), T\ is the true time of one vibration with the 

 ring placed horizontally on the magnet, and is obtained from the observed time T/ 

 by the formula 



T - = T -'( 1 -if)' 1 ^H 1 - 8<S00) ( 1 + *(*»-« -»«• " '■>} 



where the symbols in the first four factors have the same meaning as given above 

 for T, it being remembered that <J> is the ratio of the torsion force to the horizon- 

 tal force for the declinometer thread when carrying both the deflecting bar and ring. 

 The last factor contains the reduction of the time of vibration to the value of the 

 horizontal component for which T was the time of vibration without the ring ; k, 

 therefore, is the bifilar coefficient, given previously, 6 and b t are the mean bifilar 

 readings when the times of vibration T and T\ were observed, q is the temperature 

 coefficient for the deflecting bar, given above, t and < x are the mean temperatures of 

 the bar corresponding to the observations T and T x . As the observations for de- 

 flection are corrected for temperature to the temperature at the time of vibration, 

 the value of m at the time of vibration is taken as the standard value for the series, 

 as far as temperature is concerned, but it requires a correction for the inductive 

 action of the earth, due to the position of the magnet during vibration in the plane 

 of maximum magnetic force ; during deflections the magnet is placed at right angle," 

 to the magnetic meridian, and is therefore unaffected by induction : the first equa- 

 tion, No. 22, therefore becomes 



v K * 2 



m X = — 



5 m 



(l + H) 



is the induction coefficient, and is obtained from the formula 



m 



d m _ n + s — 2 b 

 m n — s 



where n and s are the mean scale readings of the bifilar magnetometer when the 

 deflecting bar is placed in the magnetic meridian with its north end towards the 



