TRANSACTIONS OF THE SECTIONS. 4l5 



est when the polarity is preserved in the usual way, and of 

 consequence loses in intensity of directive force whenever the 

 polarity is changed. This effect, then, if the needle be not 

 perfectly balanced and suspended, — which, strictly speaking, it 

 scarcely can be expected to be, — must necessarily follow, that 

 the calculated position, by the usual formulae, derived from 

 observations made with the needle in opposite conditions of 

 polarity, will not give the true direction of the magnetic force. 

 For wherever there is any defect in accuracy of suspension, 

 balancing, or adjustment, then the needle being acted upon 

 by two forces, — that of magnetic direction, depending on its 

 magnetic intensity, and gravitation, depending on the horizontal 

 leverage of the centre of gravity of the needle in respect to the 

 axis, — its position will, of course, be the resultant of the two 

 operating influences. But if with one direction of the poles 

 the magnetic intensity be less than in the other, then the re- 

 sultant of the combined forces must change its direction from 

 the preponderating of gravitation there ; and, consequently, 

 the effect of gravitation will not be neutralized by the ordinary 

 mode of mutual correction, because of the relations of that 

 force to the directive being changed. Of this, an example 

 taken from arithmetical means will be sufficient for illustration. 

 Suppose the dip, as determined by the mean of various ob- 

 servations in the usual position of the needle, to be, say 70°, 

 and the result on inversion of poles be 72°, then the actual 

 dip will evidently not be the arithmetical mean of 71°, neither 

 the mean of the tangents of 70° and 72°, that is, 71° 3', unless 

 the magnetic intensity be in both cases precisely the same. But 

 as the intensity in the original direction of the polarity would, 

 probably, be very considerably greater than the other*, the 

 real dip might be 70° 50', or even 70° 40', rather than 71° ! 

 Hence, for accuracy of result in such cases, a new element 

 seems to be requisite — that of the relative magnetic intensities 

 or powers of the poles of the needle under each condition of 

 polarity — and by observing the number of vibrations of the 

 needle in a given time, in each state of polarity, these reduced 

 to actual intensities would afford an element as a corrective for 

 the source of error herein under consideration. 



* The difference of intensity on changing the poles will he the most consider- 

 ahle in the hardest-tempered needles, or in cases where the fixedness of the axis 

 renders the hest modes of magnetizing impracticahle. In soft bars, or where 

 very powerful magnets are used, the differences from this cause become com- 

 paratively trifling, and sometimes altogether disappear ; hut still there is no 

 security without verification, that in any case the intensities of the changed 

 poles will be the same. 



