of Chromatic Dispersion. 173 
gz, d, and f, have like signs, as in regular media, their differences 
are to be taken to form the three quantities 6,, 6), 53, whose 
three differences form the required progression. But if the 
members of any of the above pairs have unlike signs, then their 
sum is to be taken instead of their difference. Thus if 6, and 
h, stand on opposite sides of the account, we must take the sum 
instead of the difference of this pair to constitute the quantity 6, ; 
and so with the others. 
Ath. The law of coincident nodes is not affected by these pe- 
culiarities, the indices of the nodes, and the nodes of the indices 
always coinciding very nearly, whatever may be the position or 
number of the nodes. 
With respect to the general formula for expressing the extru- 
sive power of a medium, namely a +Q+2X=0, the con- 
stitution of the quantities K and Q is materially modified by 
these peculiarities. As a general rule, all the fixed lines which 
undergo positive extrusion are to be added together in one sum, 
and all those negatively extruded into another, and the difference 
between those two sums will be K. Thus in /igh nodal media 
we have 
(C+D+E+F)—(B+G6+H)=K,; 
and in Jow nodal, 
(D+E+F+G6)—(B+C+H)=K;; 
and so with the others. 
In like manner, those of the quantities 6, c, d, &c., which are 
positively extruded, are to be collected into one sum, and those 
negatively extruded into another, and the difference between 
those two sums will be Q. 
Thus in high nodal media we shall have 
(c+d+e+f)—(b+y+h)=Q,; 
in low nodal, 
(dt+e+f+g)—(b+e+h)=Q;. 
The alterations introduced by an increase in the number of the 
nodes will be easily understood from the above. 
The calculations from which the foregoing laws have been de- 
duced have been based on the relative normal wave-lengths for 
the fixed lines, assuming that of B as unity, according to the 
values given in the separate paper on that subject*. These values, 
with their logarithms, stand as under :— 
B. C. D. E. F. G. H. 
1-000000, 0°953893, 0°856059, 0764567, 0:704210, 0:623398, 0570655, 
00000000, 19794999, 1°9325036, 1-8834154, 1:8477024, 1-7947653, 1:7563732. 
* This paper will be given in a subsequent Number.—Ep. 
