This process, by which the influence of the neglected fraction of the time of vibration is still more completely eliminated in the final result, is particularly to be recommended to those observers who employ smaller apparatus, or needles of comparatively shorter time of vibration.
It may also be observed, that as the addition of a small weight increases the time of vibration of the needle, it is possible so to arrange the weight, and the spot on which it is to be placed, that the time may be brought extremely near to an entire number of seconds. This resource has been adopted by some observers who had it not in their power to preserve their needles from vibrating in rather large arcs. It is, however, an insufficient expedient; for, even admitting that the conditions of the theorem are thus fulfilled, it is not possible to determine the fraction of a division of the scale corresponding to a given second with nearly the same exactness when the needle moves rapidly, as when its motion has been rendered so slow that the change in a whole second is scarcely perceptible. The importance of sufficiently quieting the movements of the needle cannot be too strongly insisted on. It is necessary for this reason that the intervals between the observations should be sufficiently long to admit of this operation whenever it is required.
With the needle of the magnetical observatory at Göttingen the intervening time is, with the first method, 3ᵐ 20ˢ; with the second, 2ᵐ 54ˢ; in both cases sufficient for the above purpose to practised persons. Observers commonly employ this interval (as the necessity of rendering the needle quiescent but rarely occurs) in calculating the final result. Where, however, the needle has a much longer time of vibration, and, consequently, the interval between two series of observations is much shorter, a modification of the above method is preferable.
The modification consists in this; that the partial observations are not separated from one another by the time of an entire vibration, but by an aliquot part of one; i. e. a half, or a third. Besides the advantage of shortening the time required for the observations of each series, and of thus gaining a longer interval between two series, we avoid the tedium of being unemployed during the greater part of the time intervening between the partial observations. Practised observers, therefore, frequently prefer this modification even when the time of vibration is not very long. In our observatory several observers make their no-
