44 GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 



in the majority of cases this may not be very important, yet a 

 preference is clearly due to a method which is free from this ob- 

 jection, and combines convenience, uniformity, and all desirable 

 accuracy ; it is accordingly the method adopted by those who 

 take part in the term observations. 



This method is founded on the principle, that the mean be- 

 tween two positions of the needle, which correspond exactly to 

 two instants separated from each other by the time of one 

 vibration, coincides with that position of the magnetic meri- 

 dian which existed at the mean of these instants, in what- 

 ever parts of the vibrating period the instants might have 

 fallen. This principle would be mathematically true, if, on 

 the one hand, no external causes (such as the resistance of the 

 air, etc.) occasioned the successive diminution of the arc of vi- 

 bration ; and if, on the other, any possible change in the situ- 

 ation of the magnetic meridian might be regarded as uniform 

 for that short interval. The first circumstance has, however, no 

 perceptible influence, if the method is applied when the vibra- 

 tions are very small ; and, in regard to the second, the changes 

 of declination during so short an interval are generally of them- 

 selves hardly perceptible, and therefore we are the more justified 

 in regarding such changes as at least uniform for the short in- 

 tenals in question*. 



Thus, therefore, the question is solved. In order to learn the 

 position of the needle corresponding to the declination for the 

 time T, it is only necessarj', after the vibrations have been re- 

 duced by suitable means, to observe the actual positions for the 

 times T — }y t, and T + ^ t, and to take the mean ; t signifS'ing 

 the time of a vibration. For greater accuracy and certainty, how- 

 ever, similar determinations, and of equal number, shoidd be 

 made, at equal intervals, a few moments before, and a few mo- 

 ments after T: this being done, in as far as the alteration of the 

 declination may be considered uniform for the time in question, 

 the mean of all these results will be the final result correspond- 

 ing to the time T, and will deserve more confidence than the 

 single determination for T itself. 



The mode of performing this is very simple : if, for instance, 



• At times (although very seldom) cases have actually occun-eJ, where traces 

 of acceleration, or retardation of the change, in so short a period, could be plainly 

 demonstrated. This subject shall, at some future time, be more fully treated. 



