GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 45 



the final result is to rest on five partial results, we note the 

 actual position of the needle for the six times : 



T-jt,T-^t,T-^t,T+:^t,T+^t,T-\.^t. 

 If the divisions of the scale noted are called a, b, c, d, e, f, 

 then ^ {a + b) will be the result for the time T— 2t;'va the same 

 manner i (6 + c), ^ [c + d), h [d + e), \ [e + ,f) for the times 

 T—t, T,T+ t, T + 2t; and the mean of these partial results, 

 or the fifth part of their sum, is to be taken as the corrected 

 final result for the time T. 



The detail of the observations in Gottingen, on the I7th of 

 August, 1836, for 15'^ SO'" may serve as an example. The ob- 

 server was Dr. Wappaus. 20* was taken as the value of t. 

 15'' 29" 



30 



866-35") 

 866-85 I 

 867-10 )>867-lG 

 867-65 I 

 8C7-90J 



The first column contains the times of observation ; the se- 

 cond the divisions of the scale noted ; the thu'd the means be- 

 tween each two successive notations ; which are, consequently 

 the partial results con-esponding to 15»> 29' 20", \b^ 29' 40", 15^ 

 30' 0", 15^ 30' 20", 151^ 30' 40", and the final result to 15^ SC 

 0". In this example the continual variation of the declina- 

 tion in the com*se of the observations is evident, and is also con- 

 finned by the preceding and following results : which were 



IS"- 25' 0" 862-82 



15 35 872-32 



For the short time which this method of observation requires, 

 it more frequently happens that the declination is nearly sta- 

 tionary throughout : when it is so, the greater or less delation 

 of the partial results from the mean serves as a sort of measure 

 of the greater or less confidence due to the observations ; whether 

 depending on the degree of skill and attention on the part of 

 the observer, or the goodness of the apparatus, or on more or 

 less favourable external circumstances. 



The method described is that which is followed by most of 

 the participators in the term-observations. It presupposes the 

 knowledge of the time of vibration of the needle, Avhich, as is 

 well known, is dependent on the magnetism of the needle, and 

 on the intensity of the horizontal portion of the terrestrial 

 magnetic force ; so that, strictly considered, it is not quite 



