456 



Prof. D. MendeleefL Experimental 



From every set of four to five readings the position of equilibrium 

 L tt was deduced, and the amplitudes r n , by taking the differences 

 between l n and L w . The difference between r n and r a +i is called in 

 what follows the decrement D M . 



2. The time of the passage through the position of equilibrium, 

 T n , was determined partly by the use of a chronographic watch, 

 partly by Marey's cylindrical chronograph, reductions having been 

 made to true astronomical mean time by comparisons with our 

 standard clock (Hohwii 31) controlled by signals from the Pulkova 

 Astronomical Observatory. 



From the observed T was deduced the mean duration (in seconds 

 of mean time) of one oscillation, i.e., from l tl to /+,. 



3. k, the number of milligrams corresponding to one division of 

 the scale. 



4. e, the weight in milligrams of a litre of air inside the balance 

 case, according to readings of the thermometer (0'003), barometer 

 and Assman's psychrometer. 



5. p, the weight of the load on each pan expressed in grams. 



6. P, the weight of the whole moving mass of the balance and the 

 load in grams. 



7. r, the volume of the load in millilitres. The same has an 

 influence on t n and D M , and we have examined the change of D M 

 and t n . 



I. The Variation o/D and t depending on the value of one oscillation, 

 B = lfilu+i, or amplitude, r n = (L Z)( l)*.* 



The duration of one oscillation, all other conditions being constant 

 in all six examined balances without exception decreases with decreasing 

 oscillations or amplitudes. These variations are not only many times 

 greater than the errors of the readings, but many hundred times 

 surpass the corrections of the time of one oscillation, as deduced 

 from the usual formula for the reduction of the oscillations of a 

 pendulum to infinitely small amplitudes. The decrease of the time 

 of one oscillation in the most simple manner can be expressed in first 

 approximation by the formula 



t n = 



Therefore 



where 

 and 



log. nat. 



Q = TO-TJ. 



* r, t is very nearly equal to iR, but I prefer to give D and t in relation to r,, 

 because by this method the small errors in L n disappear. 



