198 
MESSRS. A. E. H. LOVE AND F. BA PIDDUCK 
The equation for A 9 is 
105 { - 9B 4 + 9 . 10 (B, +1) B 3 + B 3 2 - 3 9 ' \ ( ;V- - (B 1 + 1 ) 2 B, 
l 2! 3! 
+ 9,10.11. 1 2 ( Bi + i ) , 
4 ■ 
+ 2<jB 4 -9(2B i + l)B3-9B 3 a +^(3B 1 +l)(B i +l)B 3 - ’ K ^V ll B i (B 1 + l f 
3! 
A A 
V 9 
J 
2! A., 
-^1 
+ |^{2B 1 B 3 +B/-9B 1 (3B 1 + 2)B 2+ ^Ab i 2 (B 1 + 1) ; 
9 3 a I A 9 4 R t A 
+ fj {ZBfB 2 -9B* (B 1 + 1)} —F + fi ^r-jf 
— 105 [...] + 45 [...] —10[...] 
3! A, 
V 7 
^1 
+ 
A 
-5B 4 +5.6(B 1 + l)B 8 +^B/-3^| [ ^(B 1 + lpB a + 5 - 6 4! 7 - 8 (B,+ l) 
+ 2^B 1 -5(2B, + l)B»-5B i , 1 +%f (3B 1 + l)(B 1 + l)B a -^|AB 1 (B 1 + l)“ 
5! A, 
V 5 
6! A, 
V 4 
-<l 
9, 2 
5 . 6 
+ |2B,B, + B/-SB, (3B, + 2) B 3 + ^Bf (B, + l) : 
+ | {3B,*Ba—5B, a (B, +1)} AA 4 J7Bi* -A" 
o I hi 4 1 —n 
7! A 7 
V 3 
^1 
= -ioAA“ 
a \S t 
B - AA (2B, +1) B„-ii B/+ AA B 9 B i + 1 ) B a 
11.12. 13 (B t + 1) 
3! 4 
(Bi—1) 
where the law of formation of the terms that are not written down is sufficiently obvious. 
The formulae of this article may, of course, be transformed into those of the previous 
article by means of the relations by which the coefficients B were expressed in terms 
of the differential coefficients of Q 1} and the relations by which the coefficients A 15 ..., A-, 
were expressed in terms of the same differential coefficients. They are useful in 
numerical work as affording a verification of the values obtained for the coefficients 
A g , A 7 , ..., from the previous formulae. 
Formulae similar to those of the present and preceding articles may be obtained for 
the coefficients in the expression for Z belonging to the first reflected wave from the 
right, but it seems hardly worth while to write them down. 
The Second Middle Wave. 
26. Method of determining the Second Middle Wave .—The first reflected wave from 
the left meets that from the right at the place and time determined by substituting 
