‘Dispersion of Colors in perfectly transparent Media. 267 
8 The value of Pot § may be easily found by integration, 
but perhaps more readily by Poisson’s well-known theorem 
that if ¢ is Pan function of position in space (as the density of 
a certain mas 
eons @ Potg ,@Potq _ 
dal dt Cdytte aap ee (5) 
where the direction of the codrdinate axes is immaterial, pro- 
vided that they are rectangular. In applying this to Pot é, 
we may place two of the axes in a wave-plane. This will give 
PPoté _ nee 
qt = AE: (8) 
In a nodal plane, Pot &=0, since € has equal positive and 
negative values in elements of volume symmetrically distributed 
with respect to any point in such a plane. In a wave-crest (or 
plane in which € has a maximum value), Pot £ will also have 
& maximum value, which we may call K. For intermediate 
ints we may determine its value from the consideration 
of waves, on ving a wave-crest, and other a nodal 
plane passin stabagt the point for which the potential 
1s sou e maximum amplitudes of these component 
System as cos one and sin Qn to unity. But the second of the 
component aan will contribute nothing to the value of the 
potential. We thus obtai 
Pot €=K cos ans, 
@ Pot § 
ae 
Comparing this with equation (6), we have 
> Pot E=—4z, 
47° u 4n’ : 
7 K cos 275 Te Pot &. 
Pot €=— Zee (7) 
Hence, and by equations (4), 
$2/E Poté dy == >/ do=*Z (a? +? +y’) f cos? ans dv. 
The kinetic energy of ras cate part of the flux is there- 
fore, for each unit of volum 
Am. Jour, me .—THIRD SERIEs, vo XXII, No. 136.—Apriz, 1882. 
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