

Measurement of the Refractive Index of Liquids. 305 



assume that the greater part o£ the aberration is produced by 

 the water sphere. Assigning the value 4/3 to //, in the 

 aberration term, we see that the error introduced in the value 



11a 2 

 of / is numerically ,^ . 



Now, reverting to equation (5) we see that the value of/, 

 when the thickness of the glass is taken into account and the 

 aberration is negligible, is given by 



J 2(/*-l) + 2(^-1) V 



or, since K = 



7 2(^-1) " + 2r 2 {fjL-l) V l ' j 



Substituting yit = 4/3and /a' = 3/2 in the second term on the 

 right-hand side of equation (7), we find that the numerical 

 value of that term is 



2 t 'j 



Hence the thickness of the glass tends to increase the focal 

 length by an amount 



9 * ' 



o r 2 

 and the spherical aberration tends to decrease it by 



11a 2 



64 r 2 * 



Hence it is possible by adjustment of the diameter of the 

 aperture of the entrant beam to arrange that these errors 

 should just compensate. This will be the case when 



2t r, _ 11 a 2 



3 ' r 2 ~ 64 r 2 ' 



a ' 2 128 . 



or - = ——t = 4:t ) approximately. . . ($) 



