4 Prof. R. Bunsen on a Method of determining the 



other vessels, and the differences of weight of each ascertained. 

 If the unknown weight of V. be represented by T v , the succes- 

 sive differences by A„, A m , A IV , and the weight of the corre- 

 sponding vessels by G n , G m , G IV , we have 



G H =T V +A„ 

 Gr III =T v + A m , 

 G IV =T v -t-Ai V , 

 G v = T V . 



In order to determine A, which is seldom more than a frac- 

 tion of a milligramme, it is best not to wait until the beam has 

 arrived at a position of equilibrium, but to calculate the corre- 

 sponding deviation of the pointer from the observation of a 

 number of oscillations. Each of the vessels is filled, before the 

 weighing, with the air of the balance-case by sucking the air out 

 with a long hollow thread of glass, then wiped with a linen cloth, 

 and quickly drawn through the flame of a non-luminous gas-lamp 

 to get rid of any adhering electricity, and then weighed after 

 waiting three-quarters of an hour, the vessel I. being always 

 placed as tare on the right-hand pan. 



The deviations from the vertical of the downwards directed 

 pointer of the balance are taken to be positive when they occur to 

 the left of the observer, and negative when they occur to his 

 right. If flj, tf 2 > a 3 • • • represent the consecutive maxima and 

 minima of deviation, obtained in this way, in the vibrations 

 of the beam, we have, for the position of equilibrium of the 

 pointer, 



_ 1 / «! + % a 2 + a 3 a n + a n+l \ 



n\ 2 + 2 " i ~ ,,, 2 / 



In all the weighings seven vibrations were observed with the 

 telescope, and the readings were commenced when the maximum 

 deviation of the pointer was between -f 5 and + 6. This is seen 

 in the following example : — 



+ 5 ' 9 -f075 



- 4 ' 4 + 0-45 

 + 5-3 + . 70 



~ 3 ' 9 + 0-45 

 + 4 ' 8 + O70 



- 3 ' 4 + O50 



+ 4-4 



r= ^| 5 = -f 0-592. 



