xxviii Introduction to the Makekstoun Observations, 1844. 



of till" thermometer, with the graduations, being above the lid of the outer box ; the 

 bulb of the thermometer rests in a cuji, formed in a brass bar of the same dimensions 

 as the bifilar magnet ; the brass bar is supported on a wooden stand, and lies parallel 

 to the magnet ; the bulb of the thermometer is also covered loosely by a small brass 

 cap. It was found from comparative observations (p. xxx., Introduction, 1843) that 

 a thermometer, with its bulb free, would differ 1° from the thermometer resting in 

 the brass bar in the course of a daily change of 10° of temperature. The whole in- 

 strument was covered with a double thick cotton cover Jan. 31* &" 1844. The read- 

 ing telescope is fixed to a stone pier, 8 feet south of the magnet. 



31. In the adjustment of the instrument, the magnet is forced to a position at 

 right angles to the magnetic meridian, by turning the arms of the torsion circle. 

 As, in forcing the magnet from the meridian, the upper extremities of the wire will 

 move through a greater angle than the lower extremities, the wires will be no longer 

 vertical, and the magnet and appendages will be raised ; the forces producing equi- 

 librium will, therefore, be the weight suspended endeavouring to attain the lowest 

 point, and the horizontal component of the earth's magnetic intensity acting on the 

 free magnetism of the bar. 



32. If V be the excess of the angular motion of the arms of the torsion circle, 

 or upper extremities of the wire, over u, that of the lower extremity or magnetic bar 

 in moving the latter from the meridian, the equation of equilibrium will be 



a' 

 m X sin u =; W — - sin v 



m, X, W, a, and I being respectively the magnetic moment of the bar, the hori- 

 zontal component of the earth's magnetic force, the weight suspended, the interval, 

 and the length of the wires. The differential of this equation (m = 90°) divided by 

 it, gives 



A \ 



=: n a eoi v + 1 {Q + 2 e — e') 



n being the number of scale divisions from the zero, or scale reading when m=90'', 

 a the arc value in parts of radius of one scale division, t the number of degrees 

 Fahrenheit which the temperature of the magnet is above the adopted zero, Q the 

 coefficient of the temperature correction for the varying magnetic moment of the 



bar or the value of — for 1" Fahr., e and e the coefficients of expansion for the 

 m 



brass of the grooved wheel and silver of the wires. 



33. It is assumed, in the previous investigation, that the suspending wire does 



not act by any inherent elastic force ; that the torsion force depends wholly on the 



length and intei-val of the two portions of the wire and the angle of twist : it seems 



extremely probable that this condition will not be rigorously sustained, and it is 



very possible that there may be considerable twist in the suspending wire or thread ; 



