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 accomplished with perfect accuracy; and I wished to ascertain the greatest residual error which, in given circumstances, is likely to affect the mean of two observations 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.