of Chromatic Dispersion. 169 
trusions being each denoted by X, these two quantities are always 
equal, and 2X may be regarded as the measure of the extrusive 
power of the medium. This, which may be called “the law of 
equal transference,” is the first to be recognized ; and it is found 
to prevail in all media whatever, whether regular or peculiar. 
From the above it follows that every regular medium presents 
two nodal points, at which the extrusion passes from positive to 
negative, or vice versd—the upper node lying between C and D, 
the lower between F andG. At these nodes the extrusion is nil. 
The second law may in all regular media be expressed as fol- 
lows: 3b,+2c,—d,=3h,+29,—f. It is proposed to call this 
the “ semel-bis-ter law.” 
From these two laws may be deduced the following general 
formula for expressing the extrusive power of a medium : 
B—(Q+a42X)=0. 
The two quantities K and Q have different values according as 
the medium is regular or peculiar. In the former, 
K=(B+C+G+H)—(D+E+F), 
and is constant for all regular media. Jn these, also, 
Q=(b+e+g+h)—(dtetf); 
so that the value of Q varies with the medium and temperature. 
The alterations in the constitution of these two quantities pre- 
sented by peculiar media will be afterwards explained. 
The third law governing the extrusions is as follows :—If these 
be taken in pairs equidistant from the centre e,, and if the differ- 
ence between 0, and h, be denoted by 6,, that between c, and g, 
by 6,, and that between d, and f, by 63, then the differences be- 
tween each pair of these three quantities 6,, 6,, and 6, will con- 
stitute a progression of the form %, 2¢, 3¢, the quantity ¢ vary- 
ing with the medium and temperature. This it is proposed to 
call “the law of the equicentral common difference.” The 
varieties which this law presents are interesting; and it is im- 
portant, as furnishing the means of detecting and correcting 
slight errors of observation. 
There is yet a fourth law, which may be termed “ the law of 
coincident nodes ;” but for the understanding of its nature, a 
little explanation is required. 
The series of internal wave-lengths 6,, cs, dg, based on the 
supposition of the medium being destitute of extrusive power, 
having been calculated from the formula 
B C 
——a=b ——aA=Co, &e. 
€ 2) € Q) ! 
