1905 - 6 .] Lord Kelvin on Groups of Deep-Sea Waves. 
409 
side of fig. 34, we see in diagram 1 a single zero numbered 1. 
The future zeros are to be numbered in the order of their coming 
into existence, 2 ; 3 , 3 ; 4 , 4 ; . . . ; 10,10; . . . ; 33 , 33 ; . . all 
in pairs after zero 2. Thus diagram 2 shows zero 1 considerably- 
advanced leftwards (that is, outwards) ; and zero 2 beginning its 
outward progress. Diagram 3 shows zeros 1 and 2 each advanced 
arther outwards, 1 farther than 2. Diagram 4 shows all the zeros 
which have come into existence at time These are zeros 1 
and 2, both farther outwards than at time Ji r, and a pair, 3,3, 
which have come into existence shortly before the time 
The outer of these two travels outwards and the inner inwards. 
Some time later 4 , 4 come into existence between 3 and 3 : later 
still 5 , 5 come into existence between 4 and 4. 
In diagram 5, zero 1 has passed out of range leftwards : but we 
see distinctly the outward zeros 2, 3, 4, 5, 6, 7, 8, 9, and 
indications of the inward zeros 9,8. The whole train of zeros 
for time 4 Jtt, .shown and ideally continued - to the middle by 
numbers, is 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 8, 7, 6, 5, 4, 3; 
sixteen in all. 
Zero 3 has passed out of the range of diagram 6, but we see in 
it distinctly the outward zeros 4,5,.... 12, and an indication 
of the pair 33 , 33 , which has come into existence before the time 
8 Jit. The whole train of zeros for time S^Ar, indicated by 
numbers, is 1 , 2 , .... 32, 33, 33, 32, .... 4, 3; sixty- 
four in all. 
(2) Illustrations of the Indefinite Extension and Multiplica- 
tion of a Group of Two-Dimensional, Deep-Sea Waves 
Initially Finite in Kumber. §§ 114-117. 
§ 114. The water is left at rest and free, after being initially 
displaced to a configuration of a finite number of sinusoidal 
mountains and valleys — five mountains and four valleys ; in the 
diagrams placed before the Society. The initial group of waves, 
shown in diagram 1, of fig. 35, is formed by placing side by side, 
at distances equal to 2 (taken as unity), nine of the curves of 
diagram 1, fig. 34, alternately positive and negative. Diagrams 
2 and 3, of fig. 35, are made by corresponding superpositions of 
