170 Mr. M. Ponton on certain Laws 
the series of refractive indices corresponding to it may be found 
from the formula 
B C 
—=B, =? 3 OF 
2 Cg 
and so on. This series of indices, “°B, “C, &c., is that which 
the medium would present had it only a refractive and disper- 
sive, but no extrusive power. The differences between the ob- 
served indices and this second series show what portion of the 
former is due to the extrusive power of the medium. The posi- 
tive and negative quantities do not here balance each other, as 
in the case of the wave-lengths; nor do they, like the extrusions, 
exhibit any symmetrical arrangement; but they present nodes 
corresponding to those of the extrusions. It might @ priori be 
expected that this correspondence would be quite exact. It will 
accordingly be found to be very nearly so in every case, taking 
the indices as given by observation, or after having been subjected 
to the corrections required by the third law; and where the co- 
incidence is not perfect, the difference is generally traceable to 
the defects of decimal calculation. There can therefore be no 
doubt of its being’ a general law that these two sets of nodes 
ought exactly to correspond; that is, the refractive indices of 
the nodes, deduced from the: extrusions, should precisely tally 
with the nodes of the two sets of refractive indices. 
To exhibit this fourth law, it is needful to determine the nodes 
of the wave-lengths and the nodes of the refractive indices. To 
find the nodes of the wave-lengths in a regular medium: Let 
c, be the extrusion of ¢, and d, the extrusion of d, then 
le a ee :e—d: c—n, 
whence n, is easily found. So from 
So+GYe ids : :f-g9 > f—No 
ng may also be easily found. Then 
Cptd,y:ty::C—-D:C—N, 
gives N,, and 
SetGer fei: F—G:F—-N, 
: sonst N 
gives N,; whence should arise —?—a=n, and 7 a= Mg} also 
€ 
PisHe.. n—MNo. The nodes having been calculated and checked 
€ 
by these formule, the refractive indices of the nodes result from 
N 
Ni en, and 32=*N, 
ny Ng 
The nodes of the refractive indices v,, vg will be found by a 
similar process. Here “C—C corresponds to ¢,, and “"D—"D 
