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Full text of "Scientific Papers - Vi"

172                             ON THE  PASSAGE  OF WAVES  THROUGH
For the general value of a, (43) is perhaps best expressed in terms o equal to ij/6.    With introduction of the values of h, we have
7rkebQ    [7      .     ikb\(     .        . .       ,                ..    ,
-             ,   I 7 + log-j- )lcos8a +  cos4 a +  cos" a +--)
15         -45      ,    ,   5 \
cos " + Tcos a +16J
37     B. _23     4   _159     2   _J73_ These expressions are the values of
for the various values of 17.
We now suppose that kb = 1.    The values for other particular cases as kb = ^, may then easily be deduced.    For cos a = 0, from (44) we ha
,     A L     11       13.1          1      5.3.1        "1
"4- lOfT__11__________h_______________________________________i
L-                                 *            *                                    ^j
,   :i i    i  11      i    73
J- rrr   \------_  _   ---------- .-------L
1     *J    I   Cko A            ro      ^ n r*rv    I
_224    22.4232    22.42.62192
= -TT (7 + log j) [1 - 012500 + 0-00586 + 0-00013] \            **/
+ TT [0-06250 - 0-00537 + 0-00016] = TT (y + log^ x 0-88073 + TT x 0'05729
=  [-0-65528 +1-3834 i]........................................
since             7 = Q'577215,        log 2 = 0'693147,        log i = %7ri.
In like manner, if kb = -|, we get still with cos a = 0,
^ (7 + % I) [1 - 0-03125 + 0-00037] + TT [0'01562 - Q'00033]
If kb = 2, we have
7 + log |) [1 - 0-5 + 0-0938 - 0-0087 + 0-0005]
+ TT [0-25 - 0-0859 + 0-0102 - 0-0006] = TT [+01058 + 0-9199 i]................, 1)