366 Mr. M. Ponton on certain Laws 
between the particles being halved, each of those waves would 
now be reduced to one-half of its original length. When the 
zther is compressed in the pores of a refracting medium, how- 
ever, this rule does not hold. The B wave now appears to em- 
brace in its length less than 1,000,000, and the H wave less 
than 570,655 particles. If the B wave thus seem to lose, say 
50,000 of its particles in the direction of its length, the H wave 
will seem to lose exactly the same number; so that this loss 
tells very differently on the lengths of these two waves. The 
H wave becomes proportionally more shortened by this loss than 
the B wave; so that the motive force progresses more slowly in 
the H wave, in proportion to its rate of progress in the B wave, 
than it did before entering the medium. Hence to keep up with 
its more rapid neighbour, and present a straight front to the 
observer, the H wave takes a shorter cut in passing through the 
medium. It pursues a different path; the two waves become 
more or less separated, and this constitutes dispersion. 
Now this want of power in the motive force to extend to its full 
number of particles during the period of the individual excursionof 
each particle, must be due to an increase in the persistence of the 
particles in their normal positions. This persistence will of course 
be increased by the greater proximity of the particles; but the 
increase of persistence thence arising exhibits itself in the general 
shortening of the wave-length, in proportion to the compression 
of the ether. Were the additional loss of length which mani- 
fests itself in the dispersion of the waves due to this cause alone, 
then would the dispersive power of every medium be proportional 
to the density of the cether in its pores, or to its general refract- 
ive power. But this is far from being the case. The oil of 
cassia, for example, which exerts a smaller compressing force on 
the ether than does crown-glass, has nevertheless a much higher 
dispersive power; so that the latter must be due to some other 
force than that which causes the refraction. 
Suppose now a medium in which the value of ae is 0:05, and 
that of e 1:5, so making the density of the ether one-half more 
than it is in the planetary spaces, the intervals between the 
ethereal particles being thus reduced in the proportion of 0°66 
to 1. Were there no other cause operating than this greater 
proximity of the particles, and if the wave-length continued to 
embrace its primary number of particles, each wave-length ought 
to be diminished in this same proportion, at least very nearly so ; 
for some little allowance must be made for the size of the par- 
ticles as compared with that of the intervals. But it is found 
that, leaving out of view that peculiar property of the medium 
which exhibits itself in the irrationality, and confining attention 
to its dispersive power alone, the number of particles embraced 
