180 Mr. M. Ponton on Chromatic Dispersion. 
nent of least extrusion to be determined? On a careful analysis 
of all the media, it will be discovered that the value of this ex- 
ponent depends entirely on the proportion which the extrusive 
property of the medium bears to its dispersive power at a given 
temperature; in other words, it depends on the proportion 
which the irrationality bears to the length of the spectrum, with 
a given prism and at a given distance from the prism. Repre- 
senting the dispersive power by the optical abstract a, and the 
irrationality by the amount of the positive and negative extru- 
sions 2X, and calling > =P the ratio which the extrusion bears 
to the dispersion—representing also the exponent of least extru- 
sion by , we have the following equation universally applicable, 
p 
n—1 
The value of this constant, as determined from the best of the 
observations, appears to be as nearly as possible 0-0092598* ; 
at least this value is sufficiently near the truth for all practical 
purposes. The reciprocal of this number is 10:8, which, added 
to unity, gives 11°8 as the highest limit of these exponents, or 
that which the medium would have if p were = 1, or 2X=a. 
The lower limit of these exponents, being 1, obtains when a is 
equal to the above constant, or a=0-009259 and 2X =0. 
As pis obtainable with tolerable correctness from any set of ob- 
servations which are approximately accurate, the exponent of least 
extrusion may always be found from the equation 10°89 +1=n, 
for any medium and temperature. It is unnecessary, in estima- 
ting these exponents, to go beyond the first place of decimals, 
which gives their value sufficiently near for the purposes of cal- 
culation. 
The exponents calculated from this equation for the various 
media will be found specified in Table I. From this specifica- 
tion the muriate of zinc is excluded, because it forms an excep- 
tion. This circumstance, however, need not Jessen confidence 
in the correctness of the law; for it only tends to confirm the 
opinion expressed by the observer himself, that the indices which 
he has given for this medium are so inaccurate, that no conclu- 
sion can be formed with respect to it till further observations be 
made. 
The exponents of least extrusion having been thus ascertained 
from the observed indices of refraction, the next step is, by means 
of the exponent, so to correct the indices as to reduce the extru- 
sions to zero—a matter of easy accomplishment ; for the extru- 
sions being thus eliminated from the calculation, the formula 
= constant. 
* This value is of course open to future correction. 
