Friction affects the Motions of Time-Keepers, 139 



TABLE I. 



i \ 2 



Logarithms of Coefficients 

 Sec. 



Coefficient. 



(i) 2 



(¥J 



\2.W 



\ 2..12/ 

 \2..14/ 

 V2..16/ 



(blly 



\2..18/ 

 /1...19\2 

 \ 2..20/ 

 /1...21\2 

 \ 2..22,J 



/1~23\ 2 

 \2-24/ 

 /1..25\2 

 Vl-26/ 

 /1»27\2 

 X2..28/ 

 /l-29\2 

 \2-30/ 

 /1..31\2 

 V 2.-32/ 

 / l-33 \2 

 V2-34/ 



\2..36/ 



/l-37\2 

 \2..38^ 

 /L.39\2 

 X2..40/ 



Logarithm. 



9.39794 

 9.14806 

 8.98970 

 8,87371 

 8.78220 

 8.70662 

 8.64225 

 8.58619 

 8.53655 

 8,49199 

 8.45159 

 8.41462 

 8.38055 

 8.34896 

 8.31952 

 S.29194 

 8.26601 

 8.24154 

 8,21838 

 8.19639 



60087 

 25355 

 00434 

 61494 

 11683 

 40465 

 46798 

 72326 

 00651 

 72757 

 05035 

 36921 

 70135 

 84792 

 19655 

 53965 

 54422 

 65294 

 27843 

 20157 



TABLE II. 



Logarithms of Coefficients 



Coefficient. 



Logarithm. 



2.4 



3.5 



2.4.6 



3.5.7 



2...8 



3...9 



2..10 



3.. 11 



2.. 12 



3..13 



2.. 14 



3..15 



2..16 



3..17 



2..18 



3..19 



2..20 



3..21 



2.,22 



3..23 



2..24 



S..25 



2..26 



S..27 



2..2S 



3..29 



2-.30 



3..31 



2..32 



3..33 



2..34 



3..S5 



2.-36 



3..37 



2-38 



3 39 



2..40 



3..41 



9.82390 

 9.72699 

 9.66005 

 9.60889 

 9.56750 

 9.53274 

 9.50278 

 9.47645 

 9.45297 

 9.43178 

 9.41247 

 9.39474 

 9.37835 

 9.36311 

 9.34887 

 9.33551 

 9.32292 

 9.31102 

 9.29974 

 9.28902 



87409 

 87279 

 19383 

 94159 

 67307 

 46244 

 14011 

 24623 

 13665 

 20674 

 69122 

 81453 

 77291 

 77625 

 73234 

 33618 

 42345 

 50112 

 40008 

 01354 



The value e = corresponds to a — — A — £> 9 while 

 € — — -J corresponds to a — q> — — A + <p ; whence the entire 

 time of the first oscillation is 



