REDUCTION OF OBSERVATIONS OF HORIZONTAL INTENSITY. 39 



From this follows 



or again, to the same degree of approximation, 



(33) ^-lir-^T- 



If the amplitudes of the vibrations are given by the readings a 

 of a scale seen by reflection, and at a distance D from the axis 

 of rotation, we have 



a a 2 



a = , cr * 



4 D' 



we thus obtain 



(i6D) 2 2 A S i2D a A 



Damping does not in general much alter the time of vibration. 

 Suppose, for instance, that the angle of deflection has diminished 

 from 10 in the first to 2 in the hundredth vibration; the value of 

 the logarithmic decrement is 



A = / . = o *o 1 63. 

 99 2 



y 



The correction -, which should be introduced in the mean time 

 n 



of an oscillation calculated by equation (32) does not then exceed 

 0*0005. 



693. We shall take as an example the observation of a compass 

 of horizontal intensity made at Pondicherry, June 7th, 1837, by 

 Durandeau and Chevalier.* The observers had marked 1400 

 oscillations in series of 50 ; but, for the sake of brevity, we shall 

 only give the readings relating to the hundredths. 



* DURANDEAU and CHEVALIER. Voyage de la Bonite. Observations Mag- 

 netiqueS) Vol. II., p. 131. 



