Undulatory Theory of Light,—continued. 503 
Professor Powell in the recent Numbers of your Journal. 
This I have shown more explicitly in your Number for Ja- 
nuary last, p. 7. 
Since, by the last equation, the velocity of the waves, and 
consequently the refraction of the light at the surface of the 
medium, depends chiefly upon s,, while the dispersion depends 
fo 
s/@ : : 
upon =a i? and the following terms of the series, we see that 
the dispersion may be different for different media, though 
the mean refraction be the same; contrary to the opinion 
which so long retarded the improvement of refracting tele- 
scopes. 
The equations (3.) may, perhaps, lead to a theory of ab- 
sorption as well as of dispersion; since it is obvious that they 
may become impossible for particular values of 4 It should 
be observed that the sums s”, 5,°, s,°, s!°, &c. are not necessarily 
positive, and I now think it would be better to denote them 
by s, s,5 Sj s';&c. I adopted the other notation in order 
to assimilate the formula to those employed in the theory of 
sound. 
In the case of undulation which we have been considering, 
the waves are plane waves, perpendicular to the axis of 2 ; we 
now pass on to the consideration of converging and diverging 
waves. 
Let us take the case of a system of waves going and re- 
turning to and from a certain point; calling this point the 
centre of agitation. ‘Then the diameter of the sphere of in- 
fluence of any molecule being an insensible quantity, it is evi- 
dent that the minute portion of one of the waves contained 
within the sphere cannot, at any sensible distance from the 
centre of agitation, differ sensibly from the same portion of 
a plane wave. ‘Therefore, as the motion of any molecule is 
affected only by the molecules within the sphere of its in- 
fluence, it follows that the equations (3.), which give the ve- 
2 " au of plane waves, will also give, at any 
| 7] 
point of the system, the velocities with which diverging or 
converging waves are transmitted in the direction perpendi- 
cular to the wave-surface at that point. 
When the molecules are so arranged that the sums s°, 5°, 
$75 &c. are the same for all directions of the rectangular co- 
ordinates, the velocities of the waves are the same for every 
radius drawn from the centre of agitation; and consequently 
the wave-surfaces are spherical. 
bia n 
locities 7 
