On certain Laws of Chromatic Dispersion. 263 
curacies necessarily involved in the drawing of lines through 
points formed by the intersection of straight lies or circular 
arcs. 
Let it be required to divide the given are ABD, whose 
centre is C, into any number of equal parts. (In the example 
here given, the are is divided into seven equal parts.) 
First approximation.—Bisect the given arc in G, and draw 
the chord AG. Through A draw the diameter ACB, and divide 
it into m equal parts in the points 1, 2,3, &c. Bisect the chord 
A G by the perpendicular F CO; from A and B as centres, with 
the diameter A B as radius, describe ares cutting each other in 
K; and from the centre C, with C K asa radius, describe the 
arc KO, cuttmg FCO in OQ. Through the point 2 draw 2E 
parallel to O F, meeting AG in E; and through E and O draw 
the straight line O Ea, meeting the are in a; then Aa will be 
approximately the nth part of the are AGBD, but which may 
be determined with greater precision as follows. 
_ Second approximation.—Take off the chord Aa in the com- 
passes, and apply it on the are A G D proceeding from a towards 
D; let & be the last point in the division ; apply this chord from 
D to p, and jompC. Bisect Al in m; from the centre C, with 
Um as a radius, describe an are cutting Cp in e; through e 
draw en parallel to C k, cutting the are im the pointn; then Dx 
will be practically the nth part of the given are AGB D, as 
required. 
When the number of parts into which the given arc is to be 
divided is considerable, especially when the are is equal to or 
nearly equal to the whole circumference of the circle, the second 
operation in the foregoing process becomes necessary in order to 
attain a sufficient degree of accuracy. 
The proposition contained in the first approximation is a 
generalization of a well-known method, sometimes employed by 
practical men, for the division of the whole circumference of the 
circle into a given number of equal parts. 
Hastings, March 6, 1860. 
XXXIV. On certain Laws of Chromatic Dispersion. 
By Munco Ponton, F.R.S.E. 
[Continued from p. 181.] 
ITH a view to an examination of the results arrived at in 
the previous part of this paper, it will be found con- 
venient to classify the observations. Fraunhofer has fortu- 
nately given two sets of observations for water, and also for 
flint-glass No. 23; and from these a judgment may be formed 
of the degree of accuracy attainable. It will be found that, while 
T2 
