774 
Finally, from (1) § 6, (3) § 7 and (14) § 4, we derive 
Jc== \n 0 2 — n 2 \ lo g 10 tg (45° — (p) 
4=n\ip\ ‘ log 10 e 
where, in order to avoid double signs, the absolute values of 
n 0 2 — n 2 and of ip are to be taken. 
§ 9. Equation (2) of the preceding Article shows that the curve 
(i) = 
intersects the axis of A at the point A — A 0 and that it exhibits 
two maxima values of \ip\ which occur when 
m a 2 = a 0 2 + fa 0 . 
Hence if A ml and A m2 are the corresponding wave-lengths, 
( 3 ) . i — A 0 2 ' 
(4) -j- (A„2 — — ta 0 . 
Thus, assuming merely that the march of the curve ip = îp (A) is 
known, we can ascertain the value of T and of &, without any 
reference to the magnitude of <p. This, it will be seen, is an im¬ 
portant proposition. To arrive at the nearest estimate that can yet 
he made of the constant k. it will be most convenient to make 
direct use of the result just proved. 
The maxima values of | ^ | are . ;/ 
( 5 ) } 
Thus 
_ D 
^ ml — J’(2i 0 — T) 5 
_ D 
— J , (22 0 + P) ' 
T 
(6) tyml *• ' l Pm2 - Ä i^ 1 ) : {A 0 - i^ 7 )' 
The diagram on page 777 (Fig. 2) shows under aaa the general 
form of the curve ip = ip (A) for a positive value of the constant î)± 
§ 10. The curve (p — (p{A ) is quite [different. The angle cp 
reaches a maximum for 
(i) - 2ß +2 v(i - ß +>)] 
[see equation (4), § 8.] where ß= F 2 /4:A 0 2 . If we suppose ß small 
(as will generally be the case) we can write, to a first approximation/ 
( 2 ) A* = A 0 V(l-ß). 
On both sides of wave-leügth ,.A — A * the angle (p rapidly dimin- 
