258 Mr. M. Ponton's further Researches regarding 



duce the least amount of error in these two media — the oil of 

 cassia and the bisulphide of carbon — and to render both regular 

 lb their extrusions while at the same time preserving definite 

 relations among the normals themselves. Those adopted in the 

 foregoing calculations fulfil all these conditions, of which one or 

 other would be violated by even a comparatively small departure 

 from the values above assigned. Thus the exponential law, 

 combined with the laws of extrusion, while first detected by 

 means of an assumed set of normals, have in their turn become 

 the means of discovering the best values of the normals them- 

 selves. With media of lower refractive and dispersive powers, 

 any inaccuracy in the normals is of less moment, and might 

 easily escape detection. 



For hydrate of phenyle, temp. 13° C, Messrs. Dale and Glad- 

 stone's indices are 



whence n=2'34, log e n = 0-1831359, and tf n =0«007193; but 



a n = 0*00721 5 gives a better equalization of errors. 



The differences between the calculated and observed indices 



are 



B- C-f D-f E+ F- G+ H-f 



0000115 0-000219 000270 0000244 0-000552 0000537 0000182. 



The observed indices being the results of a single observation, 

 these differences all lie within the limits of probable error. 

 Before correction of the indices, the extrusions are slightly irre- 

 gular ; but with the corrected indices they become regular, and 

 are as follow: — 



K- c x~ d *+ e *+ /*+ 9*- K- 



0-000579 0000190 0000395 0000621 0-000531 0000036 0000733. 



For anhydrous ether at temp. 15° C, Messrs. Dale and 

 Gladstone give these indices, 



B C D E F G H 



1-3545 1-3554 1-3566 1-3590 1-3606 1-3646 1-3683, 



whence rc=2-73, log £ n =0'1306117, and « n =0-002072. The 

 differences between the calculated and observed indices are 



B+ C- D-f E- F-f G+ H+ 



0-000156 0000214 0-000076 0000214 0000111 0000113 0000058. 



With the corrected indices the extrusions are 



b x — Cx— dx-\- e x + fx+ g x — Ax— 



0-000278 0-000099 0000187 0000230 0000263 0-000012 0000361. 



For absolute alcohol, temp. 15° C, their indices are 



B C D E F G H 



1-3612 1-3621 1-3638 1-3661 1-3683 1-3720 1-3751, 



