xxii Introduction to the Makerstoun Observations, 1845 and 1846. 



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

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

 (obtained by the above formula for T), Ti 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 



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

 for T, it being remembered that * 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 Tq was the time of vibration without the ring ; k^ 

 therefore, is the bifilar coefficient, given previously, h^ and \ are the mean bifilar 

 readings when the times of vibration Tq and Ti were observed, q is the temperature 

 coefficient for the deflecting bar, given above, t^ and ti are the mean temperatures of 

 the bar corresponding to the observations To and Tj. 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 angles 

 to the magnetic meridian, and is therefore unaff'ected by induction : the first equa- 

 tion. No. 22, therefore becomes 



m jL = 



T2 ( 



m J 



— is the induction coefficient, and is obtained from the formula 



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 

 north and south respectively, its centre being in the prolongation of the bifilar 

 magnet, b is the bifilar reading with the deflecting bar away. 



The deflecting bar was vibrated in the declinometer box after the observations 

 of deflection ; it was suspended in a stirrup of silk fibres of the same thickness as 

 the suspension thread, and a small thread of paper being gummed to the extremity 

 nejtt the reading telescope, the times of transits of the paper at the wire of the read- 

 ing telescope towards right and left were observed for every 5 vibrations each way 



