GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 4/ 



This process, by which the influence of the neglected frac- 

 tion of the time of vibration is still moi'e completely eliminated 

 in the final result, is particularly to be recommended to those 

 observers who employ smaller apparatus, or needles of compara- 

 tively 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 obsen^ers 

 ■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 

 di^ision 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 suffi- 

 ciently 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 Gottingen 

 the intervening time is, with the first method, 3"^ 20* ; with 

 the second, 2"^ 54* ; 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 i-esult. Where, how- 

 ever, the needle has a much longer time of vibration, and, con- 

 sequently, 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 vi- 

 bration, but by an aliquot part of one ; i. e. a half, or a third. 

 Besides the advantage of shortening the time required for the 

 obsen'ations 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 obser\^ers, therefore, frequently 

 prefer this modification even when the time of vibration is not 

 very long. In our observatory several observers make their no- 



