EXAMPLE OF GAUSS'S METHOD OF REDUCTION. 47 



The corresponding elongations in the two first series give for the 

 time of 147 oscillations : 



h. m. s. 



Between the elongations o and 147 i 43 22-70 



i> i and 148 i 43 22*75 



,, 2 and 149 i 43 22*70 



3 and 150 i 43 22*80 



4 and 151 i 43 22.75 



The mean i h 43 m 22*74 s gives 42*i95 s for the mean time of an 

 oscillation in the first interval: we obtain in the same way 42*1 76 s for 

 the second interval, and 42*1 79 s for the third. The general mean 

 is 42 "1 834 s . 



Between the successive series i and 2, 2 and 3, 3 and 4, we find 

 0*002689, 0*002813, 0.002996 for the logarithmic decrement. These 

 values are slightly increasing ; the amplitudes diminish then a little 

 more rapidly than is required by the law of geometrical progression. 



The distance of the scale was 4775*9 mm. The reduction to 

 infinitely small oscillations calculated by formula (34), gives for the 

 interval which separates the middle of two consecutive series 



Elongations. r 



1t ft* 



s. s. 



2 and 149 1*611 0-0109 42*184 



149 and 279 0*622 0-0051 42*171 



279 and 420 0*328 0-0023 42*176 



The mean 42 -17 7 s represents the value of / with a probable error 

 less than the five-thousandth of a second. 



