the Laws of Chromatic Dispersion. 257 



observations are in progress, may produce a considerable effect 

 in augmenting or diminishing the apparent extrusions of the 

 fixed lines, and in altering the relations of the indices to each 

 other. In this manner we may account for the differences in 

 the proportion of extrusion, and the consequent variations in 

 the exponent, in the three observations by Powell, and for the 

 better agreement of one set than another with the exponential 

 law. 



The extrusions for these three with the corrected indices, in 

 the order temp. 22 0, 5, temp. 14°, temp. 10°, are 



ftr— c x — d x + e x -\- fx-\- gx— h x — 



0-001703 0000625 0001123 0-001861 0001652 0000034 0002274 



1920 722 1248 2115 1901 7 2615 



1622 591 1074 1768 1563 40 2152 



These all conform to the regular type, so that the anomaly 

 formerly presented by this medium may be now fairly regarded 

 as quite removed. 



From the four sets of observations on oil of cassia, may be 

 determined the constant most suitable for ascertaining the ex- 

 ponent n with the improved normals. The most probable value 

 of this constant appears to be 10-953160, which is exactly twice 

 the sum of the normal wave-lengths. Hence the formula for 

 finding the exponent assumes the very simple form of 

 oy 4SX 



n=l +2S x — , or ft=l H . Thus all the elements of cal- 



a a 



culation are linked together by determinate relations. 



In a joint paper by Messrs. Dale and Gladstone in the Philo- 

 sophical Transactions, 1858, there are given the following indices 

 at temp. 15° C. for the bisulphide of carbon, the medium next 

 in importance to the oil of cassia : — 



These numbers give n= 2* 6,loge„= 0*202221 6, ff n =0"009561. 

 The differences between the indices calculated from these 

 elements and the observed indices are 



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



0000010 0-000081 0000036 0000037 0000080 0000360 0000240 



These differences all lie within the recognized limits of experi- 

 mental error. 



The extrusions arising from the rectified indices are 



Before the rectification of the indices the extrusions are 

 slightly irregular ; but the above conform to the regular type. 

 It is a delicate operation so to adjust the normals as to pro- 



