of Chromatic Dispersion. 175 
the particular medium. The constant a may be termed “the 
optical abstract,” because it must be taken from the normal 
wave-length corresponding to each of the fixed lines after it has 
been divided by the constant e, in order to obtain the internal 
wave-lengths b,, c,, &e. 
The quantity a is thus indicated as being a portion of the 
refracted wave-lengths, distinguishable from the main body, and 
of the same magnitude for all waves. But while it is thus con- 
stant for the same medium and temperature, yet in comparing 
one medium with anothez, the value of a will depend on the con- 
stant e, and on s the sum of the internal wave-lengths jointly ; 
for S being the sum of the normal wave-lengths, the value of a 
—-—s 
is =< 7 The constants ¢ and a are thus mutually indepen- 
dent, inasmuch as a may be indefinitely altered without affecting 
e, and vice versd. 
The product of these two constants, or ea, deducted from each 
of the normal wave-lengths, will show the extent to which each 
normal is shortened during its passage through the medium, in 
virtue of the dispersive power alone. The actual loss of length 
being represented by ae, is of the same magnitude for all waves ; 
but it of course tells more on those waves which are primarily 
shorter. Hence the numbers representing the loss of length 
sustained by each wave in proportion to its primary length, from 
the operation of the dispersive power of the medium alone, irre- 
spective of either its refractive or extrusive powers, are in exact 
inyerse proportion to the primary wave-lengths. 
Thus, taking as an example the bisulphuret of carbon (a 
medium of high dispersive power), its constant a is 0:038772, 
and ea = 0:058953, which, being deducted from each normal 
wave-length, gives as under: 
B1-000000 C0-953893 D0°856059 E0°764567 F0:704210 G0-623398 H0-570655 
0°058953 0°058953 0:058953 0:058953 0°058953 0-058953 0-058953 
0:941047 0°894940 0:797106 0°705614 0°645257 0:564445 0511702 
Dividing these remainders by the normal wave-lengths, we obtain 
B0-941047, C0-938197, D0-931135, E0:922894, F0-916285, G0-905433, 
H 0°896693, 
which numbers represent the reduced wave-lengths, reckoning 
each wave as unity; consequently the complements of these 
numbers, being 
B0-058953, C0-061803, D 0068865, E0:077106, F0-088715, G0-094567, 
11 0-103307, 
represent the loss of length sustained by each waye, in propor- 
