UnIFILAE MaGNETOMETEE. XXV 



intensity in terms of the units used, and f' and (^ quantities depending on the mode 

 of distribution of magnetism in the magnets. The term tan u is obtained from the 

 formula 



t.a.n ^. =ia.n / j" K +i^-»^o + o^)-/K + i^-^7^iV) | { 1 +^} [l + ^r (^, - ^ + A (6.. - 500j] 



v^here u^ and ^u are the observed mean readings of the unifilar magnetometer, the 

 deflecting bar, with its north pole towards the east, being at the distance r to the 

 east and west respectively of the suspended magnet ; similarly, u^ and ^u are the 

 readings when the deflecting bar, at the distance r, has its north pole towards the 

 west; c?^, j<?, &c. are the simultaneous readings of the declinometer corresponding 

 to w^, ^w, &c. ; /=:1*115 is the co-efficient for reducing the scale values of the decli- 

 nometer to those of the unifilar ; a is the angular value of one scale division bf the 



unifilar ;(■'• + jr ) = 1*00212 is the torsion factor ; 5' = 0'000288 the temperature co- 

 efficient for the deflecting bar (60.) ; ^d and t^ its temperature at deflection for the 

 distance r and for vibration, respectively ; h the co-efficient for reducing the scale 

 divisions of the bifilar magnetometer to parts of horizontal force ; 6^ the bifilar mag- 

 netometer mean scale reading during deflection at the distance r. 



27. The comparative observations for %i and d were rendered simultaneous, thus : 

 The times of vibration of the unifilar and declination magnet 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 

 to 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 



* The formula actually used was tan {a (Mj + &c.)}, as it was considered more convenient and 

 sufficiently exact for such small deflections, especially when the method of determining a was taken into 

 consideration. (See note to No. 8.) 



MAG. AND MET. OBS. 1843. g 



