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XXII. — On Errors caused by Imperfect Inversion of the Magnet, in Observations of 

 Magnetic Declination. By William Swan. 



(Read 30th April 1855.) 



1. A compass needle, although freely suspended, will not always point with 

 accuracy in the direction of the magnetic meridian, for its magnetic axis may not 

 be strictly parallel to its axis of figure ; and hence, when a rigidly exact value of 

 the magnetic declination is required, it is necessary to take the mean of at least 

 two observations of the needle, first, in its usual position, and next, inverted. Some 

 time ago it occurred to me that the declination obtained in the manner now 

 described, will only be approximately correct, unless the inversion is accom- 

 plished with perfect accuracy ; and I wished to ascertain the greatest residual 

 error which, in given circumstances, is likely to affect the mean of two obser- 

 vations of a magnet, first in an erect, and then in an inverted position. I failed, 

 however, to find any allusion to such errors in those works on magnetism to which 

 I had access ; and I was therefore obliged to investigate the subject for myself. 



2. There are three forms in which a suspended magnet has been used to ascer- 

 tain the magnetic declination. First, The ordinary compass needle, traversing a 

 divided arc, or having a divided card attached to it ; secondly, The magnet, having 

 a small mirror attached to it, in which the divisions of a fixed scale are seen by 

 reflexion, and observed by means of a fixed telescope ; and, thirdly, The magnet 

 converted into a collimator, by attaching to it a lens with a divided glass-scale, 

 or cross fibres placed in its principal focus. I will consider the declinometer 

 magnet only in the last of these cases, where the collimator is observed through 

 the telescope of a theodolite ; but the formulae for computing the errors due to 

 imperfect inversion will apply to any kind of magnet. I will also at first assume, 

 that the magnet turns on its point of suspension without friction, or that it is 

 suspended by a fibre without torsion, and that no change occurs in declination 

 during the observations. These assumptions, it is evident, will in no way affect 

 the accuracy of the reasoning ; for, as torsion of the suspension-fibre, changes of 

 declination, and imperfect inversion of the magnet, are all totally independent 

 sources of error, which must be either by some means avoided, or have their 

 effects separately computed and applied to the observations, so also the theories 

 of these errors may be separately discussed. 



Definition of Accurate Inversion of a Magnet. 



3. Let ZO, Fig. 1, (Plate VII.) be a vertical line passing through the point of 

 suspension of the magnet ; being either the point on which the agate cap sup- 



VOL. XXI. PART II. 5 B 



