48 The Spectroscope : [January, 
lengths of these lines are all interdependent, resembling the 
strings of a perfectly-tuned instrument, the key-note corre- 
sponding to the more refrangible E. 
The extreme closeness of the agreement between the 
wave-lengths as given by M. Angstrom’s observations, and 
those calculated by the formule, combines with this last- 
mentioned relation to show both the accuracy of the obser- 
vations and the truth of the relations which the formule 
express. Great confidence may therefore be placed in the 
correctness of the wave-lengths as calculated from those 
formule. 
It became interesting to inquire to what extent the laws 
of chromatic dispersion, as deduced from Fraunhofer’s 
normals, might be affected by this alteration in the wave- 
lengths corresponding to the principal fixed lines. Investi- 
gation shows that those laws remain unshaken in their 
principles by this change in the elements of calculation. 
The important practical use to which those laws may be 
applied is to check the accuracy of observations on the 
indices of refraction corresponding to the principal fixed lines 
in different media, for the observed indices rarely give 
results which tally quite exactly with the laws; but the 
alterations which they must undergo, to render the agree- 
ment perfect, are in general so small as to establish the 
laws, which may accordingly in their turn be employed to 
correct the indices. 
The media, whose indices of refraction for the different 
fixed lines have been experimentally determined, fall under 
two categories,—Ist, regular; 2nd, irregular. ‘The former 
embraces by much the larger number of media; and as it is 
only with such that the spectroscope has any connection, it 
is to them that attention shall here be confined. 
In all media whatever, the relation between the wave- 
length in the free ether and that within the refracted medium 
may be expressed by one and the same formula. If U re- 
present the normal undulation, and w its reduced length 
within the medium, then is 
ae 
é 
where « and a are two quantities constant for the medium 
and temperature, while x is a small quantity peculiar to 
each wave, and represents what is termed the irrationality 
of the medium, or, in other words, the extent to which the 
fixed lines are extruded or thrust out of their proper places. 
It is this quantity x, however, that is all-important in the 
