xxii INTRODUCTION TO THE MAKERSTOUN OBSERVATIONS, 1845 anv 1846. 
where 7; and 7, 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 ¢rue 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/(1-4%)a +0) (1-555) {14% -4)-96'-4)} 
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 T, was the time of vibration without the ring; &, 
therefore, is the bifilar coefficient, given previously, 6, and b, are the mean bifilar 
readings when the times of vibration T, and T, were observed, qg is the temperature 
coefficient for the deflecting bar, given above, f and ¢ are the mean temperatures of 
the bar corresponding to the observations T, and T,. 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 unaffected by induction: the first equa- 
tion, No. 22, therefore becomes 
K x? 
a om 
T? Ca) 
m 
om. 5 5 5 5 ° 
— is the induction coefficient, and is obtained from the formula 
me n—s 
where 7 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, 6 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 
next 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 
