UNIFILAR MAGNETOMETER. Xx 
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 are 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 ares 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 
K x? 
mX = Te 
where 7 is the ratio of the circumference to the diameter, T is the érue time of one 
vibration of the deflecting bar deduced from the observed time T’ by the formula 
: aw 3 
T=1(1-4 z)a+s) (tecan) 
where a and a’ are the semiarcs of vibration in parts of radius at commencement 
and termination. is the ratio of the torsion force to the horizontal component of 
magnetic force for the declinometer thread with the deflecting bar suspended, s is 
the daily rate of the clock in seconds, K is the moment of inertia of the deflecting 
bar obtained from the formula 
ee 2 
K=3(77+7/)M. T2_-T? 
MAG. AND MET. oBs. 1845 anp 1846. if 
