to tJie Antarctic Regions. 233 



in which equation all the quantities of the second member may be ob- 

 tained by direct measurement. The chief difficulty in this method 

 consists in the determination of the quantity a, which should be known 

 to a very small fractional part of its actual value. This difficulty 

 has been overcome by the measuring apparatus connected with the 

 suspension, which (as has been already stated) serves to determine 

 the interval of the wires, at their upper extremity, to the 2Tun)^^^ °^ 

 an inch. The numbers given in Table III. for the lower interval, 

 may be relied on to the same degree of accuracy. It is scarcely 

 necessary to mention that the length of the wires, I, is to be mea- 

 sured between the points of contact above and below. 



The product of the earth's magnetic force into the magnetic mo- 

 ment of the bar being thus known, the ratio of the same quantities 

 is to be determined by removing the bar from its stirrup, and using 

 it to deflect the suspended bar of the declination instrument, accord- 

 ing to the known method devised by Gauss. The experiments of 

 deflection may, however, be performed without the aid of the second 

 magnetometer, by operating upon another bar placed in the reverse 

 position. This method has even the advantage in point of delicacy; 

 but it labours under the disadvantage of requiring that the value of 



V 



— - should be determined for the second bar. 

 G 



The chief use of this apparatus is in observing the variations of 



the intensity. In these observations it is only necessary to note, at 



any moment, the point of the scale coinciding with the vertical wire 



of the fixed telescope, the mode of observing being precisely the 



same as in the other instrument. Let n be the number of divisions, 



and parts of a division, by which the reading at any moment diffisrs 



from its mean value ; then the corresponding variation of the angle 



(in parts of radius) is 



du = na; 



a denoting the arc value (in parts of radius) corresponding to a single 



division. Substituting this in the formula of page 230, we have 



dF , ; 



-— - = « a cotan u = « n ; 

 F 



k being the value of the constant coefficient a cotan v. The values 

 of a have been determined for each of the instruments, and are give?i 

 in Table II. 



The quantity F, in the preceding formula, is the product of the 

 earth's magnetic force into the moment of free magnetism of the bar; 

 and, as the latter quantity varies with the temperature, it is neces- 

 sary to apply a correction, before we can infer the true changes of 

 the earth's force. This correction is easily deduced. Since F = X m, 

 there is 



dF _ _rfX djn ^ 

 F X ^ ' 



so that the correction to be applied, in order to deduce the value of 



-r^r-, is Let t denote the temperature, in degrees of Fahren- 



X m 



