# Full text of "Scientific Papers - Vi"

## See other formats

```1918]       ON THE DISPERSAL OF  LIGHT BY  A DIELECTRIC  CYLINDER
561
As might have been expected, the modulus, representing the amplitude of vibration, is greater in the second case, that is in the direction of the primary ray produced.
For other angles, except 90°, the calculation is longer on account of the factor cos m&. The angles chosen as about sufficient are 0, 30°, 60°, 90° and their supplements. For 2 or 3 of the larger z's the angle 45° and its supplement were added. The results are embodied in Table II, and a plot of most of them is given in Fig. 1, where the abscissa is the angle 0 and the ordinate the corresponding modulus from the table. The curve marked N corresponds to (22) and that marked N' to (26). A few points have been derived from values not tabulated. From the nature of the functions represented both curves are horizontal at the limits 0° and 180°.
When z = '8, the curves show the characteristics of a very thin cylinder. At 90° N' nearly vanishes, indicating that in this direction little light is scattered whose vibrations are perpendicular to the axis. When z= T2, the maximum polarization is still pretty complete, but the direction in which it occurs is at a smaller angle d. For z — T6 the polarization is reversed over most of the range between 45° and 90°. By the time z has risen to 2'4> a good deal of complication enters, at any rate for the curve N.
TABLE II.
6	[ 3 in (22)	Modulus	[ ] in (2G)	Modulus
0	•10222 -ix '01823	•1038	- -05808 + ix -00295	•0582
30	•1027-5 -tx '01 824	•1044	- '05048 + 1 x -00255	•0505
60	•10421 -ix -01824	•1058	- -02925 + tx -00147	•0293
90	•10622- i x -01825	•1078	+ -00080 -ix -00001	•0008
120 '	•10825 -i x -01826	•1098	•03207 -tx -001 49	•0321
150	•10975 -ix '01826	•1113	•05574- ix -00257	•0558
180	•1 1030- ix -01827	•1118	•06456 - 1 x -00297	•0646
e	[ 1 in (22)	Modulus	[  ]in{26)	Modulus
0	•22476 -ix 18576	•2916	- -16535 + ix O3618	•1693
30	•23303-ix -18625	•2983	~ -14502 -H'x -031 19	•1483
60	•25625 -ix '18768	•3176	- -08356 + ix -01746	•0854
90	•28936- tx -18940	•3458	+ -01 535 -ix -00154	•0154
120	•32415 -ix '19122	•3763	•13288- ix -02082	•1345
150	•36071 -ix -19255	•4001	•231 58 -.ix -03511	•2342
180	•36068-ix -19304	•4091	•27053 -ix -04038	•2735
R. VI.
36) must be taken with the opposite sign from (18) of § 341.   W. P. S.] J Reports for 1913, p. 115; 1914, p. 75. also agreesion.again, as in (1), so that the vibration is A sin2 6 + C cos2 6, reducing to G simply, if A = G. This is the result for a single particle whose axis is at W. What we are aiming
```