302 Mr. 0. W. Griffith on tl 



ie 



sphere, and R is the curvature of the sphere whose refractive 

 index is yu,, then (with the usual modern convention as to 

 signs) 



u+y=2R 



p 



We may call the right-hand side of this equation the con- 

 verging power of the sphere. If then F is the power, 



F = 2R.^— - 1 . 



Hence, since F and R can be easily measured, /x for the 

 sphere may be as easily calculated. 



In the case of a spherical flask filled with a liquid, there 

 are two disturbing factors which vitiate the values of fi 

 obtained from the above equation directly. They are (a) 

 the thickness of the glass, and (b) the spherical aberration. 

 It will be an advantage to consider these two sources of 

 error separately. 



(a) Effect of the tldckness of the glass. 



Consider the refraction of a narrow axial pencil through a 

 sphere of index fx enclosed in a concentric spherical shell of 

 index fi. Let the pencil diverge from a point in air the 

 reciprocal of whose distance from the centre of the sphere 

 is U. Let Vj, V 2 , V 3j V be the corresponding quantities for 

 the successive conjugate points after refraction at the several 

 surfaces ; and let R x and R 2 be the external and internal 

 curvature of the shell respectively. Then we have the 

 following equations for the refraction at the different surfaces, 



/a'U+V^R^'-l) 



^v 2+/ *v 3 = r 2 (>-V) 



V,+/*'V=B 1 (/* , .-l) 



whence U + Y = 2(u i ^^ + R 2 ^— 4) . . . (1) 



If F is the power of the system and K = R 2 — R l5 



then F = 2R 2 ^-2K^ L (2) 



In the case of a thin spherical flask containing a liquid, 

 equation (2) shows that the effect of the glass is to decrease 



