864 Mr. M. Ponton on certain Laws 
ascertained depth of the sea. By so doing, the tension will be 
kept within reasonable limits, the curve will always be slightly 
concave upwards, and there will be no waste. We also conclude 
that the mechanical structure and dimensions of the cable ought 
to be such as to enable it to bear a tensile strain of not less than 
three times the maximum depth. 
In calculations of distance, it will naturally occur that an 
additional length of cable will be needed to accommodate the 
irregularities of the bed of the ocean; and it may not be un- 
reasonable to entertain a conjecture as to whether or not any 
extensive fissures or chasms may exist at great depths, which can 
only be ascertained by repeated soundings. 
Note.—The mechanical or dynamical conditions which deter- 
mine the subsistence of both branches of the curve of steady 
movement, may be comprehended by conceiving two vessels, B’ B, 
to be sailing with equal velocities in the direction B’ B, and that 
the suspended cable curve B! A B is payed out from B and at the 
same time wound up to B! with the same velocity, so as to keep 
the lowest point A just on the verge of contact with the ground. 
The curve will be nearly the same in form whichever of the two 
be the paying out vessel; and when B and B! are supposed to 
coincide, the two branches of the curve will become duplicates of 
the limiting line mn. 
Alwyne Lodge, Canonbury, 
April 5, 1860. 
L. On certain Laws of Chromatic Dispersion. 
By Munco Ponvton, F.R.S.E. 
[Concluded from p. 272.] 
HE difference between the view of M. Cauchy, then, and 
that arising out of the foregoing investigation, may be 
shortly stated thus:—According to the former, the refractive 
index of the wave corresponding to each of the fixed lines is a com- 
pound quantity consisting of éwo terms, one constant for the me- 
dium and temperature, the other variable and inversely propor- 
tional to the squares of the normal wave-length. According to 
the latter view, the refractive index is still a compound quantity, 
but consisting of ¢hree instead of only ¢wo terms. One is constant 
for the medium and temperature. The second is variable—not, 
however, in inverse proportion to the squares of the normal 
wave-lengths. It corresponds to a further shortening of the 
wave-length beyond that corresponding to the constant portion 
of the index; and these further shortenings are in strict inverse 
proportion to the primary normal wave-lengths, or to the initial 
forces by which these are generated. The third portion of the 
index is also variable, and is that corresponding to those varia- 
