XXXVIil INTRODUCTION. 
The moveable wires of the two micrometers are made to bisect the crosses of 
the magnet, the interval between the bisections being the time of the needle’s vibra- 
tion in the vertical plane, 10s was used ; the first comecidence was therefore 5° before, 
and the second 58 after, the minute of observation. 
The mean of the two readings is taken for the position of the needle. 
The reading is nearly zero when the needle is horizontal. The readings increase 
negatively or positively as the north pole of the needle moves above or below the 
horizontal ; it is generally above it, and in this case the readings have been sub- 
tracted from a constant plus the temperature correction, in order that they may 
always be positive, and increase with increasing force. 
44. The variations of the vertical force depend chiefly for their accurate deter- 
mination on the accuracy of the value of T. There are sources of error, however, 
in the determination of the latter, which are not taken account of in theory. 
From several series of observations made in 1843 and 1844, I have found that 
the time of vibration in the vertical plane depends on the arc of vibration to a much 
greater extent than theory would allow; that it is considerably increased if the 
needle have been previously vibrated through a large arc, and the effect of this large 
vibration remains for a considerable period (at least some weeks), but above all it 
depends on temperature. The effect of a rise of 1° Fah., is equivalent to an increase 
in the time of vibration of about 0°07. 
The full discussion of these observations must be reserved for another place. 
It was necessary to mention them here, however, as they affect the reductions in 
this volume.* 
45. The observations are given in micrometer division, it was necessary, there- 
Am : ey 
fore, to reduce the value of —, +0 Micrometer divisions, for the purpose of correc- 
tion. The values of T have been placed in groups, and a mean value taken for the 
period to which the group belongs. 
If n be the number of micrometer divisions, « the arc value of one in parts of 
radius, the equation of equilibrium becomes 
AY peigatidee pe 
a T2 mm 
A a 
“Y acotéT2 4m acotéT”? 
at bie A A 
The values of K=a rr of g=-— -* t being the number of degrees from 
the assumed zero, and the corresponding value of Z or the values of g, in micrometer 
* See a paper, entitled “The Balance Magnetometer and its Temperature Correction,” in the 
Transactions of the Royal Society of Edinburgh, Volume xvi., Part i. 
