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Full text of "Scientific Papers - Vi"

468        ON  METHODS FOR DETECTING  SMALL OPTICAL  RETARDATIONS
neglect Ci (9 ± </>) £2 and equate Si (6 ± <jb) £3 to \TT.   A similar simp' is admissible for Si(<p|2)» Ci(<£f?!i), unless <$>JQ is very small. When (f) = 0, (34) gives
sin T [cos p {-rr - 2 Si (TT)} + sin p {2 log (500/7r) + 2 Ci (TT)]], in which
TT - 2 Si (TT) = -'5623,    Ci (TT) ='0738,    log (500/7r) = 5'0691
Thus for the intensity
/(0) = [- -5623 cos p + 10-2874sin PJ..............
If p = 0, we fall back upon a former result ('3162).   If p = ITT, /((
Interest attaches mainly to small values of p, and we see that t depends upon the sign of p, A positive p means that the retardatic first aperture takes place on the side opposite to that covered by th at the second aperture. As regards magnitude, we must remembe stands "for an angular retardation icp, or 27r/o/X; so that, for example above represents a linear retardation X./8, and a total relative ret between the two halves of the first aperture equal to \/4.
The second column of Table IV gives the general expression vibration in terms of p for various values of <p/6, followed by the valu intensity (/) for sin p = ± 1/10 and sin p — ± 1/V2.
TABLE IV.
K6      = TT,       K0      = 500.
0 e	.formula for Vibration	__   j		I	
		sin p "		sin />	
		+ •1	-•1	H-l/v/2	—
0	sin T { - -56 cos p + 10-29 sin p}	•22	2-53	47-3	
•001	sin 7'{--56cosp + 10-16sinp} + cos Tx '99 sin p	•22	2-50	46-6	
•010	sin T {- -56 cosp + 5-53 sin p} •fees fx 3-10 sin p   -	•10	1-34	17-2	
•050	sin jP{--55cosp + 2'71sin p} + cos7T{--10cosp + 2-83sinp}	•11	•83	6-0	
•100	' sin T { - -53 cos p + 1 '37 sin p} f _cos T{- -20 cos p + 2'52 siu p}	•16	•66	3-0	
•250	sin T { - -37 cos p - '1 7 siu p} + cos T { - -46 cos p + 1-66 sin p}	•23	•52	•86	
•500	sin 7T{ + -16cosp->67sinp} + cos T { - -67 cos p + -64 sin p}	•38	•59	•13