xxxviii 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, 10^ was used ; the first coincidence was therefore 5^ before, 

 and the second 5^ 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 hQen 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- 



fore, to reduce the value of to 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, a the arc value of one in parts of 

 radius, the equation of equilibrium becomes 



A Y ^ , T'2 ^m 



Y i^ m 



aY T2 Am T2 



= n — 



Y « cot ^ T'2 ~ ma cot 6 T'^ 



The values of ^ = a — ^2 — , oi q = r, t being the number of degrees from 



the assumed zero, and the corresponding value of | or the values of q^ 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. 



