OBSERVATIONS. 73 



When this is screwed up enough to raise the washer off the hase of the instrument, the hand 

 may be regulated backwards or forwards by turning the screw, but at the same time tlie con- 

 stant action of the spiral is against the washer, and will in time force it down, particularly 

 when there is any jarring^ as there is in travelling. I found that the comparisons remained 

 constant when the washer was resting on the base of the instrument. It is to be remarked, 

 however^ that I made but a short series of observations. 



MAGNETIC DETERMINATIONS. 



The declination and inclination were determined in the usual mode, with a portable decli- 

 nometer and Barrow's dip-circle. It is therefore unnecessary to say anything respecting them 

 in this place, except that the observations for inclination are the least reliable of all. The 

 axis of the needle has a shoulder on each side, of such short ^proportions that, in raising the 

 needle between readings, if great care has not been taken to re-place it, the Y's only take hold 

 on one side, and therefore, in returning it to its place on the agate supports, it is apt to lodge 

 diagonally. I did not discover that this was the cause of the discrepancies until I had finished 

 the work. 



The horizontal force was determined from the usual data, by the formulae of Kiddell. 



The moment of inertia of the magnet found, by vibrating it with two different rings, and 

 also without weight between the two sets of ring vibrations, to be equal to 2.66092, by the fol- 

 lowing formula : 



(rp2 V 



"Where K^ is equal to the. moment of inertia of the ring, and T and T^ = the times of vibra- 

 tion with and without weight, T and Tj were corrected by the formula — 



in which T = the recorded time of one vibration in seconds. 



=: the rate of the chronometer per second ; -|- when gaining ; — when losing. 



86400 



^=io?dd} X 0.000072722^ 

 16 



d and d^ denoting the semi-arcs of vibration in divisions of scale, and a the angular 



value of one division. 



TT 



— = the ratio of the torsion and magnetic forces. 

 F ° 



K^ = ^ (r^ — r^) w, where w is the weight (in grains) of the ring used, and r and r^ 



the exterior and interior radii, in decimals of a foot. 



The value so found is corrected for the difference of temperature between what it was when 



K was determined and the actual temperature at the time of observation, by multiplying it by 



1 -f- 2 e (<' — t), where t^ denotes the actual temperature of the magnet^ t the temperature at 



the time of the original observations, and e the coefficient of dilatation of steel for 1° Fahrenheit : 



the numerical value of e being 0.0000068. 



The change of magnetic moment for a difference of 1° of temperature was found to be 



0.000394, by the formula— 



„ — X a TO, CO tan u: 



'1-t — t, 



q denoting the temperature coefficient. 



a denoting the arc value of one division of the scale in terms of radius. 



n denoting the difference of scale readings, corrected for change of declination. 



t and Iq denoting the corresponding differences of temperature. 



u denoting the angle of defiection at the lowest mean temperature. 



10* 



