46 GAUSS AND WEBER OX TERRESTRIAL MAGNETISM. 



the same at different periods. Instructions for the accurate 

 determination of the time of ^dbration will be given subse- 

 quently; but a very accurate knowledge is not requisite for 

 the present purpose ; and not only may the small variations 

 to which it is subject be neglected, but it is even allowable to 

 substitute the next full second for the accurate value, in order 

 that the instant at which the obser^^er has to determine the point 

 of the scale under the vei-tical line of the telescope, may corre- 

 spond always to full seconds. This happens of itself when the 

 approximate time of vibration is an ei^en number of seconds ; 

 when it is an odd number, one of the three follo'oing means 

 may be chosen. 



I. We may still keep to the nearest even number ; and wc 

 may adopt this course the more readily if the difference between 

 this number and the true value does not exceed half a second. 

 The greater the time of vibration, the more easily will the needle 

 be kept in a nearly quiescent state. The needle in the magnetical 

 observatory at Gottingen has, for instance, at present, a time of 

 vibration of 20^*64 ; now, although the number 21 is here the 

 nearest, yet we may generally employ the more convenient num- 

 ber 20^, as the arc of vibration seldom exceeds a icw divisions 

 of the scale : it can easily be demonstrated, that the eiTor origin- 

 ating thence cannot sui-jiass the twentieth part of the arc in a 

 partial result, or the hundredth in a final result. On the other 

 hand, to an obsei'vcr whose needle has a time of vibration of 

 10^'64, and especially if he has not a hkc perfect quiescence at 

 his command, it is recommended that the number 1 1 should be 

 chosen, and one of the following modifications adopted. 



II. Choose the odd number ; but the instants of observation, 

 which, according to the above formula, would fall on half seconds, 

 must be taken either all half a second later, or half a second 

 sooner ; which obviously makes only this difference — that the 

 final results do not con-espond to the full minutes of clock-time, 

 but to a half second more or less. 



III. If the final result is not, as above, based on an odd, but 

 on an even number of partial results, the times of observation 

 fall of themselves on full seconds, whether the next entire num- 

 ber taken for the true value be odd or even. If, for instance, 

 the final residt depend on six partial residts, then the times of 

 observation are 



T - ^ t, T - 2 t, T - t, T, T + t, T + 2f,T-]-3t. 



