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Full text of "Scientific Papers - Vi"

182                             ON THE  PASSAGE  OF WAVES THKOTJGH
and when cos a = + 1,
-TT das
_                   ,
= i +         7 + log -j-s
4
_ W L
512 f
16
6!=
429
the last term, deduced from A14, A16, being approximate.
For   the   values   of   -•jr~^d^/dx   we   find   from   (91),   (90),   (92 kb = ^, 1, V2, 2:
TABLE V.
	ft6 = 4	Jtb = l	*& = ^/2	ft& = 2
cos a =0 eos2a=^ cos2a=l	0 -8448+0 -0974 i 0-8778 +0-0958 i 0 -9] 03 + 0 -0944 i	0-5615 + 0-3807 i 0-6998 + 0-3583?: 0-8353 + 0-3364?;	0-3123 + 0-7383 1 0-8587 + 0-5783^	0-0102+1-38 0-518 +1-15 1-020 +0-8€
These numbers correspond to the value of "W expressed in (82).
We have now, in pursuance of our method, to seek a second solution another form of W. The first which suggests itself with M* = 1 cloei answer the purpose. For (81) then gives as the leading term
_ <ty=r     y-'n     ]»  =   25 dss     |_(2/-7?)2 + <J-&    fr-y2'  ..................^
becoming infinite when tj — ±b.
A like objection is encountered if ^ = 62 — 7/1    In this case
,_^) + 7?}Jl.
o
-- - = 2
dx The first part gives 4& simply when x becomes zero.    And
f(y-<n)dy  =         -          2
8
sothat
(£
V
becoming infinite when ?;= + &.
So far as this difficulty is concerned we might take ^ = (62 -another form seems preferable, that is
.(9
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