Measurement of the Refractive Index of Liquids. 307 



the spherical aberration of a parallel beam may be written 



AF = R 8 a 2 0(/u), (9) 



A/=-RaVM, ' (10) 



where (/>(//,) and ^{fi) are certain functions depending on the 

 type of lens employed. The curves are drawn for (1) a 

 sphere, (2) a plano-convex lens with light incident on curved 

 face, (3) a plano-convex lens with light incident on plane face, 

 (4) double convex lens with faces of equal curvature. Fig. 2 

 represents the graph of equation (9) for values of //, between 



Pijr. 2. 



W 



-2 



















/ DOUBLE 

 J(eQO/IL Ci 



CONVEX 

 'ftVATCJfte) 









































SPHSffE. 



^ — --- 













5 



^ 



/* 











>> 



1 and 2, and R 3 a 2 being unity in all cases. Fig. 3 gives the 

 graph of equation (10) for values of /a between 1 and 2, the 

 value of Ra 2 being unity in all cases. It is noticeable that the 

 errors in the case of the sphere are considerably less than 

 they are for any of the other lenses. 



