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XXII.—On Errors caused by Imperfect Inversion of the Magnet, in Observations of 
Magnetic Declination. By Wiu1am 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. irst, The ordinary compass needle, traversing a 
_ divided are, 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 formule 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 VIL.) 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. 5B 
