263 Researches regarding the Laws of Chromatic Dispersion. 



For we have (A M -H'0^(»«^J = 6 «> and 



fA* + D w -H n , -Viifji 

 *{- 6n -( a « + < + ^n)j=« n , 



whence all the other indices may be found from/x=X n -j- — — a n . 



These will be the same as those deduced from all the eight 

 observed indices. 



Take now the observed, instead of the coirected indices 

 M A, *D, *H. With exponent n = 3, we have - = 0004642 ,• 

 with 7i=2-5 we have 0-0=0-001587, sum = 0-006229, one- 

 fifth whereof, or 0*001246, is the rate for each O'l of exponent, 

 being nearly the same as before. This makes the true exponent 

 more nearly 2-62 ; but 2*6 is sufficiently near for calculation. 

 Hence we have log e n = 0-022553, instead of, as formerly, 

 0-2022496, and « n =0-009553 instead of 0009543. The 

 differences between the calculated and observed indices thence 

 arising are 



A- B+ C+ D+ E+ F- 



0000033 0000099 0-000185 0000063 0000050 0-000002 

 G+ H- 



0000427 0-000326. 



These results, though probably less accurate than those ob- 

 tained by using the whole eight observed indices for mutual 

 correction, yet differ so little from them as to show that, except 

 where great accuracy is required, the foregoing abbreviated pro- 

 cess may be found practically useful. Indeed it may generally 

 be trusted, at least to the extent of ascertaining the exponent. 



When all the eight indices are taken into account, the aspect 

 presented by the extrusions is wholly changed. The upper node 

 is shifted from between C and D to between B and C, so that 

 the transfer of motive energy appears to be from A, B, G, H to 

 C, D, E, F. The following are the extrusions arising with the 

 corrected indices, in the case of bisulphide of carbon : — 



The mutual relations of these are exhibited in this formula, 



(7a x + 5b x )-(Sc x +d x ) = (7h r + fy x )-(Sf x +c x ); 

 also calling h x -a x =8 l} g x -b x =B 2) f x -c x =8 3) and e x -d x =8 4 , 

 then 8 4 — 8j, £ 2 — 8 4 , and8 3 — $ 2 form an arithmetical progression. 

 In the above example the conformity to these two laws is not 

 quite exact ; but this arises merely from decimal imperfections. 

 The above extrusions probably represent the actual displace- 

 ments of the fhed lines, arising from that property of the 



