166 Mr. M. Ponton on certain Laws 
the length of undulation corresponding to a luminous wave that 
should occupy the place of any one of the fixed lines of the 
spectrum in the free ether, as determined by Fraunhofer’s 
method of transmitting a divergent beam through a system of 
fine equidistant lines so as to obtain chromatic dispersion with- 
out refraction. Let yu be the refractive index of this undulation 
in any medium. Call 4 =w the length of the undulation within 
the medium after refraction. Then the relation between U 
and u may be expressed by the general formula J ate=u A 
or conversely, e(u-++a+a2)=U. Here the quantities « and a are 
constant for the same medium and temperature, being the same 
for all undulations. The quantity z, again, which is compara- 
tively minute, is peculiar to each wave, the medium and tempe- 
rature remaining the same. It is not, however, a mere wregular 
fragment applied either to remove an excess or supply a defi- 
ciency, but it is subject to symmetrical laws to be hereafter ex- 
plained. Suffice it meanwhile to state that these variable quan- 
tities, represented by 2, added to, or subtracted from each wave- 
length, constitute the wrationality of the spectrum. 
Save for these small quantities, every spectrum formed by a 
refracting medium would present the same appearance as the 
spectrum formed by transmitting a divergent beam through a 
system of equidistant fine lines. The fixed lines of the spectrum, 
whatever might be their actual distances, would preserve the 
same relative mutual distances. The above formula would thus 
assume the yet simpler form of = —a=u, or e(u+a)=U. There 
would then be no irrationality in the various spectra; and the 
constant relations of the fixed lines B, C, D, &c. to the same 
lines when refracted, or to 4, c, d, &c., would always be 
Bru =b—c, ia ene Ra =b—d, 
€ € e 
and so on. 
In every refracting medium, however, the fixed lines are more 
or less extruded or thrust out of the places which they occupy m 
the unrefracted spectrum, and their mutual distances are altered ; 
so that the above relation no longer subsists. This extrusion 
constitutes the irrationality, and every medium accordingly pos- 
sesses an extrusive power besides its refractive and dispersive 
powers. 
To study the laws by which these several powers are governed, 
it is needful to separate the effects due to each, and especially, in 
the first place, to eliminate the quantity 2 from the formula with 
