Balance or Vertical Force Magnetomter. 
xxxvii 
1st, That it is found increased after the needle has been vibrated by any means 
through a large arc (2° or 3°). 
2d, That it depends to a considerable extent, much more than theory will ac- 
count for, on the arc of vibration. 
3d, That it is greater for the same arc, if it be deduced from a series com- 
mencing with a large arc, than if it be deduced from a series commencing with a 
small arc. 
4th, That it depends on the temperature of the needle. 
5th, That it does not vary appreciably with the changes of position of the needle, 
unless as co-existent (4th) with the changes in the position produced by temperature.* 
It does not seem likely that the source of error indicated in the 4th conclusion 
can be eliminated ; any zero of temperature to which the times of vibration might 
be reduced would be altogether arbitrary. I have also found, since the above results 
were obtained, 
6th, That the effect of one degree Fahrenheit on the time of vibration of the 
needle is variable, being sometimes as little as 0 S, 05, at other times as much as 0 S, 10. 
51. The following method of determining the value of tan e has been adopted 
for the reductions in the abstracts : — if q be the temperature co-efficient, or the 
value of for 1° Fahr., k = a tan e, where a = the arc value of one division of 
m 
the micrometer head in parts of radius (52.), if it be assumed that the value of f 
found, § 7, is dependent solely on the varying magnetism of the needle, or that the 
cause by which the time of vibration is affected has no effect on the position of the 
needle, assuming also that the value of q, determined by the usual method of de- 
flections, is accurate, then by the latter (Introduction, 1841-2, p. xliv), 
q = 0-000073, 
by the former (66.) | = 7-90, 
whence k = ° ^.qq 73 = 0-0000092 ; 0-000009 has been adopted. 
The mean value of the angle <5 should be determined by placing the deflecting bar at the distance r 
on opposite sides of the balance needle, and if the needle be nearly horizontal, the deflecting bar should 
be inverted in each position. 
This method has been tried since the previous portion of this note was written, and the mean of two 
results from deflections within the usual range of the instrument, which differ 0-0000003, gives 
k = 0-0000087, 
very nearly the value obtained No. 51, and adopted in the results ; larger deflections seem to give about 
0-000008, but they have not yet been completely reduced. The accuracy of this method seems to 
depend almost wholly on the determination of d, and it seems possible to obtain this certainly within 2'„ 
or that the error of k may not be above 0-0000002. 
* Transactions of the Royal Society of Edinburgh, vol. xvi, , p. 67. 
MAG. AND MET. OBS. 1843. k 
