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Full text of "Scientific Papers - Vi"

1913]                         FINE  SLITS IN  THIN  OPAQUE  SCREENS
If kb = 1 and cos a = + 1, we have from (45)
_i?       1    35         1      231
222 + 22.42 8     2:!.42.62 16
1         6436 __   __1_____19.17.6435
22. 42. 62. 82 128     227i2T62. 8s. 10"2   10. 9 .128
1    97           1      7303 .     38-084                 170'64
1 1
224 ' 22.4296    22.42.62960   '22.42.62.82     2s. 42. 62. 82.102
= TT (y + log^) [1 - 0-375 + 0-068359 - 0-006266 + 0-000341 - 0'000012]
V     4v
- TT [0-0625 + 0-015788 - 0-003302 + 0'000258 + 0-000012]
= TT [-0-63141 +1-0798 i]......................................................(51)
Similarly, if kb = fa we have
TT (7 + log |) [1 - 0-09375 + 0-00427 - 0-00010]
- TT [0-01562 + 0-00099 - 0-00005]
= TT [-l-3842 + l-4301i].........................................(52)
And if kb = 2, with diminished accuracy,
TT (7 + log |) [1 - 1-5 + 1-094 - 0-401 + 0'087 - 0-012 + O'OOl]
- TT [0-25 + 0-253 - 0-211 + 0-066 - 0-012 + O'OOl] = TT [- 0-378 + 0-422 i]. '...................................................(53)
As an intermediate value of a we will select cosy a = fa    For kb — 1, from (46)
TT (7 + log™) [1 - 0-25 + 0-03320 - 0-00222 + ...]
+ TT [0 - 0-01286 + 0-001522 + ...] = TT [-0-6432 + 1-22681].................................................(54)
Also, when kb = fa
TT[~ 1-4123 + 1-4759?;].........................(55)
When kb = 2, only a rough value is afforded by (46), viz.,
TT [-0-16 + 0-61 i]............................(56)
The accompanying table exhibits the various numerical results, the factor TT being omitted.
TABLE II.
	*6 = J	kb = l	kb = 2
cos a=0 cos2a=i|f cos2 a = 1	- 1-4405 + 1-5223 i - 1-4123 + 1-4759 i - 1-3842 + 1 -4301 i	-0-65528 + 1-3834 1 -0-6432 +l-2268t -0-63141 + 1 -0798 i	+ 0-1058 + 0-9199 i -0-16    +0-61 i -0-378  +0-422?: