Investigations on the Oscillations of Balances. 457 



More clearly visible is the decrease of D with decreasing amplitude 

 r n , and it is sufficient to observe four readings. The experimental 

 law of the decrease of D by first approximation can be represented 

 by the formula 



D re = 



where d is the limit of the decrement in the case of infinitely small 

 amplitudes, and a constant coefficient, which in all examined 

 balances varied between O0010 and O0002. Observations relating 

 to t n and D n have been made in a very great number, and all of them 

 confirm the above given result.* 



Therefore r n = - 12 - , 



or 



where N = = - , 



a 1 



and K = ]srH- . 



r 



Similar facts about t and D have been shortly mentioned before,f 

 but little notice of them has been taken. But in our very numerous 

 observations these facts stand out so clearly and beyond doubt, that 

 also in the ordinary simple pendulums we must suppose the existence 

 of similar deviations which only by their smallness have escaped the 

 attention of the observers. I have commenced the investigation of 

 a simple pendulum in this direction. 



As D and t are varying with the amplitude r, in what follows 

 D and t will be given for the case when r = 15 divisions, using the 

 signs D 15 and 15 . 



II. Variation of D i6 and f 15 icith varying load. 



The time t u in all balances decreases with decreasing load and k. 

 (a) For one kind of balances very quickly, as, for instance, 

 Ruprecht's balance : 



1. 2. 3. 4. 



p ...... grms. 105 grms. 430 grins. 563 grms. 



P ...... 1234 1440 2099 3358 



D 15 ..... 1-0136 1-0180 1-0217 1-0244 



t l5 ...... 27-3 sees. 28'5 sees. 38'3 sees. 48'2 sees. 



* For details see the above mentioned Official Eeport. 



t Cf. O. E. Meyer, 1871, Mercadier, 1876, T. Thiessec, 1886, and others. 



