Unifilar Magnetometer. xxi 



20. The following are the values of the constants used in the previous formula : — 



a = 40"-35 (No. 8.) / = 1115 (No. 8.) q = 0-000288.* 



Aug. 10— Nov. 9, 1843, k = 0-00013. Nov. 9, 1843— Dec. 31, 1845, k = 000014. 

 For the thread in the unifilar box and long scale magnet, $ = 0-0012. 



21. The comparative observations for u and d were rendered simultaneous thus : 

 The times of vibration of the unifilar and declination magnets being nearly the same, 

 the time at which the unifilar magnet attained one extremity of its arc of vibration 

 was instantly indicated by me to Mr Welsh, who could observe my motions through 

 one of the north windows of the Observatory. He immediately commenced counting 

 the beats of the mean time clock, and at the end of the 18th second (the time of 

 one vibration) both observers commenced making readings of the magnetometers ; 

 those by Mr Welsh being made at the end of the 18th, 36th, 54th, &c, seconds, 

 and those by myself at the extremities of the arcs of vibration. From 7 to 12 con- 

 secutive readings were made thus at every position of the deflecting bar, and from 

 these the mean readings are deduced. In order to render the arcs of vibration of 

 the unifilar as small as possible, the deflecting bar was at first moved gradually up 

 to its nearest distance (5 feet) ; in placing it at the next distance, it was moved 

 rapidly nearly half way, and 18 seconds counted, when it was immediately shifted 

 the other half. When the farthest distance was attained, it was placed vertically, 

 and after 18 seconds, laid down in the reverse position ; it was then moved as before, 

 by half-shifts, to its next position, and so up to the nearest. After comparative 

 readings for that position, the magnet was again placed vertically, and carried to 

 the beam on the opposite side of the suspended magnet ; at the end of 36 seconds 

 it was laid down at the same distance, and with the north pole in the same direc- 

 tion as before. In general, the vibrations were small, seldom above 10' ; when 

 larger, the magnet was checked by slightly approaching or removing the deflecting 

 bar at proper times, with reference to the directions in which the suspended magnet 

 was moving. Mr Welsh observed the bifilar magnetometer before and after each 

 comparison, and after each comparison I observed the temperature of the deflecting 

 bar by means of a thermometer lying beside it. 



22. The value of the product m X is obtained from the formula 



where tt is the ratio of the circumference to the diameter, T is the true time of one 

 vibration of the deflecting bar deduced from the observed time T' by the formula 



T-r(i-^)<i + .)*(i- g & 6 ) 



where a and a are the semiarcs of vibration in parts of radius at commencement 



* See Introduction, 1843, p. xliii. 

 MAG. AND MET. OBS. 1844. / 



