162 Prof. Weber on the Application of Magnetic Induction 



In each of these series it will be seen that the distance of 

 elongation increases, not uniformly, but according to a known 

 law; it approaches a certain limit, from which the damping 

 power, or the decrementum logarithmicum, may be easily calcu- 

 lated. Let a represent this limit, and log ^ the decrementum loga- 



rithmicum, then the distance of elongation No. ra=a;,j=fl(l — ^"), 

 hence 



and 



2-r — r ' 



11 r 



decrem. log. = log ^ = - log ^^'^ '^^^ . 



According to this formula, the decrementum logarithmicum 

 calculated from the above observations is 



log^ =0-075, nearly; 



and the approximate limit for the' series of observations A, F 

 = 261-7; for the series of observations B, C, D, E = 627. 



The following corrections must be applied to the above values 

 of the distances of elongation : — 



1, The correction due to the influence of the oscillation of the 

 needle at the commencement of the observations. 



If +e be the elongation of the needle immediately preceding 

 the first induction stroke, then to the next following + ed must 

 be added, to the second +e^^ to the third '^eO^. For the 

 above observations, where e = 0, this correction is unnecessary. 



2. According to the laws of catoptrics, the observed distances 

 of elongation are proportional to the tangents of double the 

 angles of deflection; they must be reduced to values propor- 

 tional to the sines of half the angles of elongation, i. e. to the 

 deflecting forces. For this purpose the horizontal distance from 

 the mirror to the scale must be known ; in the present case this 

 distance r = 3685 divisions of the scale. If x be the observed 

 distance of an elongation, then its reduced value is 



11 aP_ 



~^ 32 '^-r' 



After this reduction, a determination of the tangent of the incli- 

 nation may be obtained from each observation in the columns 

 B, C, D, E by dividing it by the mean of the observations in 

 the columns A, F. The following table shows the results : — 



