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Full text of "Scientific Papers - Vi"

1917]
AND  ON THE THEORY OF  FOUCAULT S  TEST
TABLE II.
K6& = 0,    0& = 500.
465
0/0	I .	<Pie	I	*\9	I	*/*	I
o-ooo	9-87	\    0-980	31-13	1-001	56-28	1-05	13-76
0.-250	10-13	!    0-990	35-78	1-002	52-89	1-10	9-24
0-500	11-08	1    0-992	39-98	1-004	44-09	1-20	5-76
0-800	14-71	.    0-994	46-81	1-006	35-27	1-50	2-59
0-900	18-51	i    0-996	54-13	1-008	29-03	2-00	1-21
0-950	23-27	i    0-998	58-81	1-010	26-14	oc	0
		0-999	59-36	1-020	20-89		
		!    1-000	58-50				
TABLE III.
= 7T,       K0& = 500.
tie	I	W	I
o-oo	0-32	1-OL	8-98
0-50	0-48	1-02	6-57
0-91	2-46	1-23	0-58
0-98	7-55	1-55	0-13
0-99	9-90	1-86	0-05
1-00	25-51	00	o-oo
In the practical use of Foucault's method the general field would be darkened much more than has been supposed above where half the whole light passes. We may suppose that the screening just cuts off the central band, as well as all on one side of it, so that 0a = TT. In this case (7) becomes
sin T[Si (0 + 0) + Si (0- 0) - Si (1 + 0/0) TT- Si (l-0/0)7r]
+ cos T[Ci (0 - 0) - Ci (0 + 0) + Ci (1 + ft 6) IT- Ci (1 - 0/0) TT].
......... (28)
We will apply it to the case already considered, where 0 = 500, as before omitting Ci (0 4- </>)  and equating Si (Q + 0)  to \TT. Thus
I = [^TT + Si 500 (1 - 0/0) - Si (1+ 0/0) 7T - Si (1 - 0/0) 7T]2
+ [Ci 500 (1 - 0/0) + Ci (1 + 0/0) TT - Ci (1 - 0/0) -nj.
......... (29)
When 0 = oo , 1 = 0.    When 0=0,
When 0=0, / =
_ Si (27r)]2 + [log (500/Tr) + Ci (2-Tr)]2 = 25'51 ;
R. vi.
30(a)  |TT and Ci (x) are approximately periodic in period 2?r and of order ar1. It is hardly worth while to include these fluctuations, which would manifest themselves as rather feeble and narrow bands, superposed upon the general ground, and we may thus content ourselves with (25). If we apply this to  10, we get