Measurement of the Refractive Index of Liquids. 303 



the power of the system, acting as a thin divergent lens 



placed at the centre of the sphere and of power — 2K — . 



Putting Bfju for the error in the value of /j, introduced by an 

 error SF in measuring F, we find 



S >*=~-2ti 2 ( 3 ) 



But the numerical value of SF due to the thickness of the 

 glass is given by 



8F=2K- £-=■?. 



Hence the error introduced by the glass envelope is 



Let t = the thickness of the glass shell, and r i the external 

 radius, then Kn = *B„ 



whence S/z=^. / ^^ (4) 



To calculate the magnitude of the error, assume the 

 following values : 



4 / 3 s nr ., s -03. 



a= — a = - £ = 'U0 cm., then 0/4 = — ; 



and if t be taken = *04 cm., 



/*— u 



So that in the case of a flask 20 cms. in diameter, and of 

 thickness *05 cm., the error would be *003, and this is of the 

 order observed when using a flask of the size mentioned. 

 Even were this factor of no account, it appears from 

 equation (2) that an additional small error is introduced 

 owing to the difficulty of measuring accurately the internal 

 radius of the flask. It would be a great advantage if it were 

 possible to express the value of F in terms of the external 

 radius. By slight re-arrangement of the terms in the right- 

 hand side of equation (1) we get 



F=:2R 1 ^=- 1 ~2K(---A .... (5) 



