Investigations on the Oscillations of Balances. 455 



making arrangements for accurate weighings, whereby some improve- 

 ments have been introduced in the usual methods ; a detailed 

 description will be found in the official report on the renewal of 

 Russian standards of measure and weight. 



The results of the work show that with the balances of oar 

 Institution we are able to find the difference between two platinum- 

 iridium kilogram weights by one single weighing with an accuracy 

 of 0'02 milligram, and by a system of weighings to 0'002 

 milligram with a probable error of a few ten-thousandths of a 

 milligram. 



We have a number of such balances, but those mostly used were 

 constructed by the well-known balance makers of Vienna, Rnprecht 

 and Nemetz; some important improvements have been made upon 

 these balances, especially in the direction of minimising the in- 

 fluence of the observer. 



Having obtained such results in accurate weighings, I have used 

 them, not only in the comparison of standards of weight, but also in 

 an experimental research on the oscillations of a balance, hoping ta 

 collect some material, not only for an investigation of balances of 

 different systems and constructions in general, and of the friction of 

 the knife-edges, but especially to find the action of gravity and 

 moment of inertia on such a pendulum as is represented by an 

 accurate balance. 



If we consider the time of one oscillation (from 30 to 60 seconds), 

 we find that our balances correspond to synchronous mathematical 

 pendulums of a length equal to 1000 3000 metres. The investiga- 

 tions in this direction are not yet completed, but one part of the 

 results obtained is now in print, and I would like to communicate an 

 abstract to the Fellows of the Royal Society. 



Before going into the matter, I must explain that the many 

 hundreds of observations of the times of oscillation and the changes 

 in the scale-reading have been made by my friends and assistants,, 

 especially F. P. Zavadsky, Y. D. Sapogenikoff, and also by Messrs. 

 Dobrokhotoff, K. Egoroff, Miller, and Misses Ozarovskaya and 

 Endymionova. Their active co-operation has greatly contributed 

 to the success of the experiments, and I am much indebted to them 

 for verifying the numerous calculations which this research involves. 



In the investigations mentioned, the following data were ob- 

 served : 



1. The readings of the scale, Z M , were observed through a tele- 

 scope after reflection from a mirror attached to the beam of the 

 balance, li is the first reading. One division of the scale corresponds 

 in the different balances to an angle of from 0'5 to 4 minutes. The 

 readings were taken by estimation to 0'05 division, which agrees 

 nearly with the probable error in Z. 



