GAUSS AND WEBEK ON TEKRESTRIAL, MAGNETISM. 43 



susceptible of, and require much greater exactness ; and no such 

 immediate determination is possible. It is not in our power so 

 completely to quiet the needle of the magnetometer that it 

 shall have no visible vibration ; at least, it cannot be done with 

 certainty, without some expense of time, and not for long ; there- 

 fore, instead of an immediate observation, we must substitute 

 such indirect modes of determination as do not require the en- 

 tire absence of vibratory motion. 



The most obvious method consists in observing the needle 

 whilst in vibration ; noting two successive extreme positions (a 

 maximum and a minimum) on the scale, and taking a mean 

 between them. This, in itself unexceptionable course, requires 

 however some modification, if the vibrations are of consider- 

 able magnitude ; and if the vibrations are small, is admis- 

 sible only under limited conditions. In the first case, the 

 progressive decrease of the arc of vibration in successive oscilla- 

 tions will not be insensible ; consequently the deviation from the 

 true meridian on the maximum side will be less than it was on 

 the opposite side at the preceding minimum ; and the mean of this 

 minimum and its following maximum will be too small. From 

 the same cause the mean of that maximum and the minimum, 

 that follows it w ill give too great a result. As the decrease of 

 arc is nearly uniform for a few vibrations, the mean of two such 

 means may be considered sufficiently exact, and may be taken 

 to correspond to the instant of the second elongation. To 

 express this by a formula, if a, b, c are the readings for three 

 successive elongations (it is indifferent whether the first and 

 third are miiiima, and the second a maximum, or the reverse) 

 \ {a + 2b + c) represents the position of the magnetic meridian 

 at the instant of the elongation b. With small Adbrations this 

 course is only admissible when the declination does not undergo 

 sensible changes in a short time ; and, in such case, the mean 

 between two successive elongations may be taken as the true po- 

 sition of the needle corresponding to the middle time : but this 

 proceeding may be wholly unavailable when the declination is 

 subject to sudden and considerable changes. 



These methods of determining the position of the magnetic me- 

 ridian from observed elongations, have always this inconvenience, 

 that the instant to which the result obtained corresponds may 

 not be that for vvhich the position is required ; and, although 



