28 



MEASUREMENT OF OSCILLATIONS. 



progression. In his experiments on the measurement of the in- 



2 



tensity of gravity,* the amplitude becomes - of its value in the 



3 



course of an hour that is, after 1800 oscillations, which gives 

 0*0001 for the logarithmic decrement. 



In these conditions the square of A x may be neglected and the 

 time of the oscillations is to within o'ooooooooi, the same as if there 

 were no damping. 



682. We observe that if, besides the term proportional to the 

 velocity, we introduce a constant / x into equation (n) like that 



Fig. 132. 



arising from the friction of a cap against a pivot, the equation 

 acquires the form 



In order to solve this fresh problem, it is sufficient to replace x 

 in the preceding solution by x + ^. The time of the oscillation 

 is not modified, and therefore the isochronism is not altered. In 



2p 



this case the amplitudes, increased by a constant , still vary in 

 geometrical progression. The damping is more rapid, and the 

 motion soon stops. 



* BORDA. Base du Systeme Metrique, Vol. ill., p. 345. 



