Numerical Data

A P P E N D I X VI

Numerical Data for Some Two-Group Systems

T h e following tables give the resonance frequencies and relative intensities of the A

B , A

B , A

B , A

B

, and A

B

systems for a num- ber of values of J/8. All resonance frequencies are given in units of the internal chemical shift δ = ω

— ω

, with ω

> ω

. In the Α

Β

case, the origin has been taken at ^(ω

-\- ω

) and only the positive half of the (symmetrical) spectrum is given; in all other cases the origin is at ω

.

In general, the study of complex spectra is materially simplified with the assistance of high-speed computing devices. T h e reader interested in such matters should consult the following references:

1. J. D . Swalen and C. A. Reilly, / . Chem. Phys. 3 7 , 21 (1962). "Analysis of Complex N M R Spectra. An Iterative Method."

2. D . R. Whitman, / . Chem. Phys. 3 6 , 2085 (1962). "Computer Assignment Technique for Analysis of High Resolution N M R Spectra."

3. S. Castellano and A. A. Bothner-By, / . Chem. Phys. 41, 3863 (1964).

"Analysis of N M R Spectra by Least Squares."

4. R. C. Ferguson and D . W. Marquardt, / . Chem. Phys. 41, 2087 (1964). "Computer Analysis of N M R Spectra: Magnetic Equivalence Factoring."

493

494 APPENDIX VI

L i n e F r e q u e n c i e s And R e l a t i v e I n t e n s i t i e s F o r The A

B S p i n S y s t e m

JZJL I n t e n s i t y F r e q u e n c y I n t e n s i t y F r e q u e n c y

A .

0 . 0 0 2 . 0 0 0 0 0 2 . 0 0 0 0 0 2 . 0 0 0 0 0 2 . 0 0 0 0 0

1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0

0 . 0 5 1.89640

1 . 9 0 3 8 6 2 . 1 0 3 6 1 2 . 0 9 6 1 5

1 . 0 2 6 2 8 1 . 0 2 4 9 4 0 . 9 7 5 0 6 0 . 9 7 6 2 2

B

B

1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0

0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0

10361 99254 90386 00000

0 . 0 4 8 7 2 - 0 . 0 0 2 5 0 - 0 . 0 5 1 2 2 0 . 0 0 0 0 0

0 . 0 0 0 0 0 2 . 0 0 0 0 0 0 . 0 0 0 0 0 2 . 0 0 2 5 0

0 . 1 0 1 . 7 8 6 3 2 1 . 8 1 5 6 8 2 . 2 1 3 6 6 2 . 1 8 4 3 0

1 . 0 5 5 2 3 1 . 0 4 9 5 1 0 . 9 5 0 4 9 0 . 9 5 4 7 4

0 . 1 5 ,67123

,73556 ,32866 ,26433

1 . 0 8 7 0 1 1 . 0 7 3 3 6 0 . 9 2 6 6 4 0 . 9 3 5 3 7 21368

97064 81570 00000

0 . 0 9 4 7 7 - 0 . 0 0 9 9 7 - 0 . 1 0 4 7 4 0 . 0 0 0 0 0

1 . 3 2 8 7 7 0 . 9 3 5 6 8 0 . 7 3 5 6 7 1 . 0 0 0 0 0

0 . 1 3 7 9 9 - 0 . 0 2 2 3 7 - 0 . 1 6 0 3 7 0 . 0 0 0 0 0

0 . 0 0 0 0 2 2 . 0 0 9 9 7 0 . 0 0 0 1 1 2.02237

0 . 2 0 55300

66324 44667 33643

1 . 1 2 1 7 0 1 . 0 9 6 1 9 0 . 9 0 3 8 1 0 . 9 1 7 8 9

0 . 2 5 1.43377

1 . 5 9 8 2 6 2 . 5 6 5 4 8 2 . 4 0 1 0 0

1 . 1 5 9 3 6 1 . 1 1 7 7 6 0 . 8 8 2 2 4 0 . 9 0 2 1 2 1 . 4 4 7 0 0

0 . 8 8 9 7 6 0 . 6 6 3 5 7 1.00000

17830 03959 21789 00000

1 . 5 6 6 2 3 0 . 8 3 5 5 2 0 . 5 9 9 0 0 1 . 0 0 0 0 0

0 . 2 1 5 6 4 - 0 . 0 6 1 4 9 - 0 . 2 7 7 1 2 0 . 0 0 0 0 0

0 . 0 0 0 3 4 2 . 0 3 9 5 9 0 . 0 0 0 7 4 2 . 0 6 1 4 9

A

0 . 3 0 1 . 3 1 5 7 9 1 . 5 4 0 0 4 2 . 6 8 2 8 4 2 . 4 5 8 5 9

1.20000 1 . 1 3 7 8 8 0 . 8 6 2 1 2 0 . 8 8 7 8 8

0 . 3 5 .20117

.48796 .79660 .50981

1.24355 1.15645 0 . 8 4 3 5 5 0 . 8 7 5 0 0

B

B

1 . 6 8 4 2 1 0 . 7 7 5 7 5 0 . 5 4 1 4 1 1 . 0 0 0 0 0

0 . 2 5 0 0 0 - 0 . 0 8 7 8 8 - 0 . 3 3 7 8 8 0 . 0 0 0 0 0

79883 71321 49020 00000

0 . 2 8 1 4 5 0 . 1 1 8 5 5 0 . 4 0 0 0 0 0 . 0 0 0 0 0

0 . 0 0 1 3 7 2 . 0 8 7 8 8 0 . 0 0 2 2 3 2 . 1 1 8 5 5

DATA FOR T W O - G R O U P SYSTEMS 495

J / 6

0 . 4 0

A Β g

I n t e n s i t y F r e q u e n c y

1 . 0 9 1 7 5 1 . 4 4 1 4 2 2 . 9 0 4 9 6 2 . 5 5 5 2 9

1 . 9 0 8 2 5 0 . 6 5 0 3 3 0 . 4 4 4 7 1 1 . 0 0 0 0 0

0 . 0 0 3 2 9

1 . 2 8 9 9 0 1 . 1 7 3 4 3 0 . 8 2 6 5 7 0 . 8 6 3 3 2

0 . 3 1 0 1 0 - 0 . 1 5 3 2 2 - 0 . 4 6 3 3 2 0 . 0 0 0 0 0

2 . 1 5 3 2 2

JZL.

0 . 4 5

I n t e n s i t y F r e q u e n c y

0 . 9 8 8 9 4 1 . 3 9 9 8 4 3 . 0 0 6 5 6 2 . 5 9 5 6 6

2 . 0 1 1 0 7 0 . 5 8 9 1 0 0 . 4 0 4 3 4 1 . 0 0 0 0 0

0 . 0 0 4 5 0

1 . 3 3 8 9 0 1 . 1 8 8 8 2 0 . 8 1 1 1 8 0 . 8 5 2 7 2

0 . 3 3 6 1 0 - 0 . 1 9 1 6 3 - 0 . 5 2 7 7 2 0 . 0 0 0 0 0

2 . 1 9 1 6 3

0 . 5 0 0 . 8 9 3 6 6 1 . 3 6 2 7 0 3 . 1 0 0 5 4 2 . 6 3 1 5 1

2 . 1 0 6 3 4 0 . 5 3 0 9 7 0 . 3 6 8 5 0 1 . 0 0 0 0 0

0 . 0 0 5 8 0

1 . 3 9 0 3 9 1 . 2 0 2 6 8 0 . 7 9 7 3 2 0 . 8 4 3 0 7

0 . 3 5 9 6 1 - 0 . 2 3 3 4 6 - 0 . 5 9 3 0 7 0 . 0 0 0 0 0

2 . 2 3 3 4 6

0 . 5 5 0 . 8 0 6 4 1 1 . 3 2 9 5 3 3 . 1 8 6 4 7 2 . 6 6 3 3 5

. 1 9 3 5 9 , 4 7 6 8 8 , 3 3 6 6 5 , 0 0 0 0 0

0 . 0 0 7 1 2

1 . 4 4 4 1 5 1 . 2 1 5 1 1 0 . 7 8 4 8 9 0 . 8 3 4 2 6

0 . 3 8 0 8 5 - 0 . 2 7 8 4 2 - 0 . 6 5 9 2 6 0 . 0 0 0 0 0

2 . 2 7 8 4 2

0 . 6 0 7 2 7 2 7

2 9 9 9 1 2 6 4 3 3 6 9 1 6 9

2 . 2 7 2 7 3 0 . 4 2 7 3 7 0 . 3 0 8 3 1 1 . 0 0 0 0 0

0 . 0 0 8 4 0

5 0 0 0 0 2 2 6 2 1 7 7 3 7 9 8 2 6 2 1

4 0 0 0 0 3 2 6 2 1 7 2 6 2 1

0 . 6 5

0 . 0 0 0 0 0

2 . 3 2 6 2 1

0 . 6 5 6 0 3 1 . 2 7 3 4 5 3 . 3 3 4 3 6 2 . 7 1 6 9 5

2 . 3 4 3 9 7 0 . 3 8 2 5 8 0 . 2 8 3 0 6 1 . 0 0 0 0 0

0 . 0 0 9 6 0

1 . 5 5 7 7 2 1 . 2 3 6 1 0 0 . 7 6 3 9 0 0 . 8 1 8 8 2

0 . 4 1 7 2 8 - 0 . 3 7 6 5 5 - 0 . 7 9 3 8 2 0 . 0 0 0 0 0

2 . 3 7 6 5 5

A .

0 . 7 0 0 . 5 9 2 2 7 1 . 2 4 9 8 2 3 . 3 9 7 0 4 2 . 7 3 9 5 0

2 . 4 0 7 7 3 0 . 3 4 2 4 5 0 . 2 6 0 5 0 1 . 0 0 0 0 0

1 . 6 1 7 1 4 1 . 2 4 4 9 0 0 . 7 5 5 1 0 0 . 8 1 2 0 3

0 . 4 3 2 8 6 - 0 . 4 2 9 1 7 - 0 . 8 6 2 0 3 0 . 0 0 0 0 0

0 . 7 5 0 . 5 3 5 4 2 1 . 2 2 8 6 8 3 . 4 5 2 9 4 2 . 7 5 9 6 8

2 . 4 6 4 5 8 0 . 3 0 6 7 4 0 . 2 4 0 3 2 1 . 0 0 0 0 0

1 . 6 7 8 0 5 1 . 2 5 2 7 2 0 . 7 4 7 2 8 0 . 8 0 5 7 8

0 . 4 4 6 9 5 - 0 . 4 8 3 8 3 - 0 . 9 3 0 7 8 0 . 0 0 0 0 0

0 . 0 1 0 6 9 2 . 4 2 9 1 7 0 . 0 1 1 6 4 2 . 4 8 3 8 3

496 APPENDIX VI

I n t e n s i t y F r e q u e n c y I n t e n s i t y F r e q u e n c y

A

a

0 , 8 0 0 . 4 8 4 8 7 1 . 2 0 9 7 8 3 . 5 0 2 6 9 2 . 7 7 7 7 8

1 . 7 4 0 3 1 1 . 2 5 9 6 9 0 . 7 4 0 3 1 0 . 8 0 0 0 0

0 . 8 5 0 . 4 3 9 9 8 1 . 1 9 2 8 4 3 . 5 4 6 9 1 2 . 7 9 4 0 5

1 . 8 0 3 7 6 1 . 2 6 5 8 9 0 . 7 3 4 1 1 0 . 7 9 4 6 5 2 . 5 1 5 1 3

0 . 2 7 5 0 9 0 . 2 2 2 2 2 1 . 0 0 0 0 0

0 . 4 5 9 6 9 - 0 . 5 4 0 3 1 - 1 . 0 0 0 0 0 0 . 0 0 0 0 0

2 . 5 6 0 0 2 0 . 2 4 7 1 4 0 . 2 0 5 9 5 1 . 0 0 0 0 0

0 . 4 7 1 2 4 - 0 . 5 9 8 4 1 - 1 . 0 6 9 6 5 0 . 0 0 0 0 0

0 . 0 1 2 4 5 2 . 5 4 0 3 1 0 . 0 1 3 1 1 2 . 5 9 8 4 1

0 . 9 0 0 . 4 0 0 1 4 1 . 1 7 7 6 6 3 . 5 8 6 2 3 2 . 8 0 8 7 1

1 . 8 6 8 2 7 1 . 2 7 1 4 2 0 . 7 2 8 5 8 0 . 7 8 9 6 9

0 . 9 5 0 . 3 6 4 7 7 1 . 1 6 4 0 1 3 . 6 2 1 2 0 2 . 8 2 1 9 6

1 . 9 3 3 7 2 1 . 2 7 6 3 6 0 . 7 2 3 6 4 0 . 7 8 5 0 8 2 . 5 9 9 8 6

0 . 2 2 2 4 9 0 . 1 9 1 2 9 1 . 0 0 0 0 0

4 8 1 7 3 6 5 7 9 6 1 3 9 6 9 00000

2 . 6 3 5 2 3 0 . 2 0 0 7 6 0 . 1 7 8 0 4 1 . 0 0 0 0 0

0 . 4 9 1 2 8 - 0 . 7 1 8 7 9 - 1 . 2 1 0 0 8 0 . 0 0 0 0 0

0 . 0 1 3 6 3 2 . 6 5 7 9 6 0 . 0 1 4 0 3 2 . 7 1 8 7 9

Α

1 . 0 0 0 . 3 3 3 3 3 1 . 1 5 1 7 4 3 . 6 5 2 3 5 2 . 8 3 3 9 5

2 . 0 0 0 0 0 1 . 2 8 0 7 8 0 . 7 1 9 2 2 0 . 7 8 0 7 8

2 . 0 0 0 8 5 7 9 0 4 5 9 5 9 0 3 5 4 9 4 3 3 8

, 4 1 4 2 1 , 3 1 7 8 4 , 6 8 2 1 6 , 7 3 2 0 5 2 . 6 6 6 6 7

0 . 1 8 1 6 0 0 . 1 6 6 0 5 1 . 0 0 0 0 0

0 . 5 0 0 0 0 - 0 . 7 8 0 7 8 - 1 . 2 8 0 7 8 0 . 0 0 0 0 0

. 9 1 4 2 1 . 0 3 9 8 4 . 0 5 6 6 2 .00000

0 . 5 8 5 7 9 - 2 . 1 4 6 2 6 - 2 . 7 3 2 0 5 0 . 0 0 0 0 0

0 . 0 1 4 3 2 2 . 7 8 0 7 8 0 . 0 1 0 6 7 4 . 1 4 6 2 6

A

a Α

3 . 0 0 0 . 0 3 6 9 9 1 . 0 2 1 2 5 3 . 9 5 6 5 1 2 . 9 7 2 2 5

. 8 8 6 0 0 . 3 2 6 2 1 , 6 7 3 7 9 , 7 1 2 2 1

4 . 0 0 0 . 0 2 0 3 4 1 . 0 1 2 1 2 3 . 9 7 5 4 3 2 . 9 8 3 6 5

6 . 3 7 2 2 8 1 . 3 2 9 2 8 0 . 6 7 0 7 2 0 . 7 0 1 5 6 2 . 9 6 3 0 2

0 . 0 1 5 7 4 0 . 0 2 7 7 5 1 . 0 0 0 0 0

0 . 6 1 4 0 0 - 3 . 5 9 8 2 2 - 4 . 2 1 2 2 1 0 . 0 0 0 0 0

2 . 9 7 9 6 6 0 . 0 0 8 2 2 0 . 0 1 6 3 5 1 . 0 0 0 0 0

0 . 6 2 7 7 2 - 5 . 0 7 3 8 4 - 5 . 7 0 1 5 6 0 , 0 0 0 0 0

0 . 0 0 6 5 0 5 . 5 9 8 2 2 0 . 0 0 4 2 3 7 . 0 7 3 8 4

DATA FOR T W O - G R O U P SYSTEMS 497

A

B

5 . 0 0

I n t e n s i t y F r e q u e n c y

0 . 0 1 2 8 1 1 . 0 0 7 8 1 3 . 9 8 4 2 5 2 . 9 8 9 2 5

7 . 8 6 4 2 1 1 . 3 3 0 7 3 0 . 6 6 9 2 7 0 . 6 9 4 9 3

J / 6 I n t e n s i t y F r e q u e n c y

1 0 . 0 0 0 . 0 0 3 0 9 1 . 0 0 1 9 7 3 . 9 9 6 0 5 2 . 9 9 7 1 7

1 5 . 3 4 8 4 7 1 . 3 3 2 6 8 0 . 6 6 7 3 2 0 . 6 8 1 1 5

2 . 9 8 7 1 9 0 . 0 0 5 0 1 0 . 0 1 0 7 5 1 . 0 0 0 0 0

0 . 6 3 5 7 9 - 6 . 5 5 9 1 4 - 7 . 1 9 4 9 3 0 . 0 0 0 0 0

, 9 9 6 9 1 , 0 0 1 1 2 , 0 0 2 8 3 . 0 0 0 0 0

0 . 6 5 1 5 3 - 1 4 . 0 2 9 6 1 - 1 4 . 6 8 1 1 5 0 . 0 0 0 0 0

0 . 0 0 2 9 4 8 . 5 5 9 1 4 0 . 0 0 0 8 6 1 6 . 0 2 9 6 1

A

0 . 0 0 0 0 0 1 . 0 0 0 0 0 4 . 0 0 0 0 0 3 . 0 0 0 0 0

3 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 1 . 0 0 0 0 0

1 . 3 3 3 3 3 0 . 6 6 6 6 7 0 . 6 6 6 6 7

0 . 6 6 6 6 7

0 . 0 0 0 0 0

0 . 0 0 0 0 0

498 APPENDIX VI

L i n e F r e q u e n c i e s And R e l a t i v e I n t e n s i t i e s F o r The A

B S p i n System

I n t e n s i t y F r e q u e n c y I n t e n s i t y F r e q u e n c y 0 . 0 0 3 . 0 0 0 0 0

4 . 0 0 0 0 0 3 . 0 0 0 0 0 3 . 0 0 0 0 0 4 . 0 0 0 0 0 3 . 0 0 0 0 0 2 . 0 0 0 0 0 2 . 0 0 0 0 0

1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0

0 . 0 5 ,83863

,80099 ,86104 ,16141 ,19900 ,13899 ,90012 .09988

1.02697 1 . 0 2 5 5 2 1 . 0 2 4 2 9 0 . 9 7 4 4 8 0 . 9 7 5 7 1 0 . 9 7 6 7 8 1 . 0 2 5 6 2 0 . 9 7 5 6 2

B

1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 2 . 0 0 0 0 0 2 . 0 0 0 0 0

0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0

1.16137 1 . 0 3 7 6 5 0 . 9 4 0 0 0 0 . 8 6 1 0 1 2 . 0 9 9 8 8 1 . 9 0 0 1 2

0 . 0 7 3 0 3 0 . 0 2 0 5 4 - 0 . 0 2 9 2 8 - 0 . 0 7 6 7 8 0 . 0 2 4 3 8 - 0 . 0 2 5 6 2 0 . 0 0 0 0 0

0 . 0 0 0 0 0 2 . 0 0 0 0 0 2 . 0 0 0 0 0

0 . 0 0 0 0 1

0 . 0 0 0 0 0 1 . 9 7 9 4 6 2 . 0 2 9 2 8

A

A

e

A7

0 . 1 0 2 . 6 5 4 6 5 3 . 6 0 7 6 7 2 . 7 4 2 7 1 3 . 3 4 5 2 5 4 . 3 9 2 1 8 3 . 2 5 7 2 4 1 . 8 0 0 9 9 2 . 1 9 9 0 1

1 . 0 5 8 2 6 1 . 0 5 1 6 4 1.04687 0 . 9 4 8 3 6 0 . 9 5 3 1 3 0 . 9 5 6 7 8 1 . 0 5 2 4 9 0 . 9 5 2 4 9

0 . 1 5 2 . 4 5 0 0 4 3 . 4 2 4 8 1 2 . 6 4 2 6 9 3 . 5 4 9 4 8 4 . 5 7 4 4 9 3 . 3 5 7 1 0 1 . 7 0 3 3 2 2 . 2 9 6 6 8

1 . 0 9 4 4 1 1 . 0 7 7 6 1 1 . 0 6 7 4 8 0 . 9 2 2 3 9 0 . 9 3 2 5 2 0 . 9 3 9 4 9 1 . 0 8 0 5 9 0 . 9 3 0 5 9 1 . 3 4 5 3 5

1 . 0 4 6 9 8 0 . 8 6 5 0 6 0 . 7 4 2 7 6 2 . 1 9 9 0 1 1 . 8 0 0 9 9

0 . 1 4 1 7 4 0 . 0 3 1 8 4 - 0 . 0 6 6 6 8 - 0 . 1 5 6 7 8 0 . 0 4 7 5 1 - 0 . 0 5 2 4 9

1 . 5 4 9 9 6 1 . 0 2 5 2 2 0 . 7 8 2 6 2 0 . 6 4 2 9 0 2 . 2 9 6 6 8 1 . 7 0 3 3 2

0 . 2 0 5 5 9 0 . 0 3 3 5 8 - 0 . 1 1 1 5 1 - 0 . 2 3 9 4 9 0 . 0 6 9 4 1 - 0 . 0 8 0 5 9 0 . 0 0 0 0 9

0 . 0 0 0 0 5 96816

06668

0 . 0 0 0 4 9 0 . 0 0 0 2 1

1 . 9 6 6 4 3

2 . 1 1 1 5 1

D A T A F O R T W O - G R O U P S Y S T E M S

J / 6 I n t e n s i t y F r e q u e n c y J / 6 I n t e n s i t y F r e q u e n c e

Al 0 . 2 0 2 . 2 2 9 4 2 1 . 1 3 5 8 9 0 . 2 5 2 . 0 0 0 0 0 1 . 1 8 3 0 1

Aa 3 . 2 5 5 6 7 1 . 1 0 2 6 3 3 . 1 0 1 9 8 1 . 1 2 6 0 0

A3 2 . 5 5 8 3 3 1 . 0 8 5 9 8 2 . 4 8 7 1 7 1 . 1 0 2 4 2

A4 3 . 7 6 9 0 4 0 . 8 9 7 3 7 3 . 9 9 6 4 1 0 . 8 7 4 0 0

A6 4 . 7 4 2 2 6 0 . 9 1 4 0 2 4 . 8 9 3 4 5 0 . 8 9 7 5 8

Αβ 3 . 4 4 1 1 5 0 . 9 2 4 5 0 3 . 5 1 1 8 6 0 . 9 1 1 4 4

A7 1 . 6 0 7 7 7 1 . 1 0 9 9 0 1 . 5 1 4 9 3 1 . 1 4 0 3 9

A8 2 . 3 9 2 2 3 0 . 9 0 9 9 0 2 . 4 8 5 0 7 0 . 8 9 0 3 9

B i 1 . 7 7 0 5 8 0 . 2 6 4 1 1 2 . 0 0 0 0 0 0 . 3 1 6 9 9

B2 0 . 9 7 3 7 5 0 . 0 2 5 5 9 0 . 8 9 8 0 2 0 . 0 0 7 9 7

B3 0 . 6 9 8 8 9 - 0 . 1 6 3 0 2 0 . 6 1 8 4 1 - 0 . 2 2 0 4 5

B4 0 . 5 5 8 8 5 - 0 . 3 2 4 5 0 0 . 4 8 8 1 4 - 0 . 4 1 1 4 4

B5 2 . 3 9 2 2 3 0 . 0 9 0 1 0 2 . 4 8 5 0 7 0 . 1 0 9 6 1

Be 1 . 6 0 7 7 7 - 0 . 1 0 9 9 0 1 . 5 1 4 9 3 - 0 . 1 4 0 3 9

Ml 0 . 0 0 1 5 5 1 . 9 7 4 4 1 0 . 0 0 3 5 9 1 . 9 9 2 0 3

0 . 0 0 0 5 2 2 . 1 6 3 0 2 0 . 0 0 0 9 8 2 . 2 2 0 4 5

Al 0 . 3 0 1 . 7 7 0 5 8 1 . 2 3 5 8 9 0 . 3 5 1 . 5 4 9 9 7 1 . 2 9 4 4 1

A2 2 . 9 6 4 2 5 1 . 1 4 7 2 1 2 . 8 4 2 1 6 1 . 1 6 5 9 2

A3 2 . 4 2 7 0 3 1 . 1 1 6 9 0 2 . 3 7 6 0 6 1 . 1 2 9 6 0

A4 4 . 2 2 2 6 6 0 . 8 5 2 7 9 4 . 4 3 9 1 2 0 . 8 3 4 0 8

AB 5 . 0 2 7 4 5 0 . 8 8 3 1 0 5 . 1 4 4 7 5 0 . 8 7 0 4 0

Αβ 3 . 5 7 1 4 3 0 . 9 0 0 0 0 3 . 6 2 1 7 7 0 . 8 8 9 9 3

A7 1 . 4 2 5 3 0 1 . 1 7 2 0 2 1 . 3 3 9 3 0 1 . 2 0 4 7 4

Ae 2 . 5 7 4 7 0 0 . 8 7 2 0 2 2 . 6 6 0 7 0 0 . 8 5 4 7 4

Bl 2 . 2 2 9 4 2 0 . 3 6 4 1 1 2 . 4 5 0 0 4 0 . 4 0 5 5 9

Ba 0 . 8 0 6 3 4 - 0 . 0 1 8 9 9 0 . 7 0 7 8 0 - 0 . 0 5 4 7 4

B3 0 . 5 4 3 9 8 - 0 . 2 8 3 1 0 0 . 4 7 7 0 2 - 0 . 3 5 0 2 6

» 4 0 . 4 2 8 5 7 - 0 . 5 0 0 0 0 0 . 3 7 8 2 3 - 0 . 5 8 9 9 3

B6 2 . 5 7 4 7 0 0 . 1 2 7 9 8 2 . 6 6 0 7 0 Ö . 1 4 5 2 6

Be 1 . 4 2 5 3 0 - 0 . 1 7 2 0 2 1 . 3 3 9 3 0 - 0 . 2 0 4 7 4

Ml 0 . 0 0 6 7 6 2 . 0 1 8 9 9 0 . 0 1 0 9 2 2 . 0 5 4 7 4

M2 0 . 0 0 1 5 5 2 . 2 8 3 1 0 0 . 0 0 2 1 8 2 . 3 5 0 2 6

500

A3 Β

I n t e n s i t y F r e q u e n c y J / £ I n t e n s i t y F r e q u e n c \

Αχ 0 . 4 0 1 . 3 4 5 3 5 1 . 3 5 8 2 6 0 . 4 5 1 . 1 6 1 3 7 1 . 4 2 6 9 7

Aa 2 . 7 3 4 9 3 1 . 1 8 2 0 5 2 . 6 4 1 5 1 1 . 1 9 5 7 1

A3 2 . 3 3 2 7 1 1 . 1 4 0 7 1 2 . 2 9 5 7 0 1 . 1 5 0 4 2

Α4 4 . 6 3 8 9 8 0 . 8 1 7 9 5 4 . 8 1 8 0 7 0 . 8 0 4 2 9

ΑΒ 5 . 2 4 6 5 8 0 . 8 5 9 2 9 5 . 3 3 4 5 1 0 . 8 4 9 5 8

Αβ 3 . 6 6 4 4 8 0 . 8 8 1 0 2 3 . 7 0 0 8 8 0 . 8 7 3 1 0

A7 1 . 2 5 7 2 2 1 . 2 3 8 5 2 1 . 1 7 9 2 7 1 . 2 7 3 2 9

Αβ 2 . 7 4 2 7 8 0 . 8 3 8 5 2 2 . 8 2 0 7 3 0 . 8 2 3 2 9

Βχ 2 . 6 5 4 6 5 0 . 4 4 1 7 4 2 . 8 3 8 6 3 0 . 4 7 3 0 3

B8 0 . 6 1 0 4 1 - 0 . 0 9 8 5 7 0 . 5 1 9 8 6 - 0 . 1 4 9 6 5

B3 0 . 4 1 7 9 0 - 0 . 4 2 1 3 4 0 . 3 6 6 3 7 - 0 . 4 9 5 7 9

B4 0 . 3 3 5 5 2 - 0 . 6 8 1 0 2 0 . 2 9 9 1 2 - 0 . 7 7 3 1 0

B5 2 . 7 4 2 7 8 0 . 1 6 1 4 8 2 . 8 2 0 7 3 0 . 1 7 6 7 1

Be 1 . 2 5 7 2 2 - 0 . 2 3 8 5 2 1 . 1 7 9 2 7 - 0 . 2 7 3 2 9

Ml 0 . 0 1 5 6 8 2 . 0 9 8 5 7 0 . 0 2 0 5 6 2 . 1 4 9 6 5

0 . 0 0 2 8 1 2 . 4 2 1 3 4 0 . 0 0 3 4 2 2 . 4 9 5 7 9

Ai 0 . 5 0 1 . 0 0 0 0 0 1 . 5 0 0 0 0 0 . 5 5 0 . 8 6 1 0 1 1 . 5 7 6 7 8

A8 2 . 5 6 0 6 6 1 . 2 0 7 1 1 2 . 4 9 1 0 6 1 . 2 1 6 5 2

A3 2 . 2 6 3 9 9 1 . 1 5 8 9 2 2 . 2 3 6 6 9 1 . 1 6 6 3 7

A4 4 . 9 7 4 8 7 0 . 7 9 2 8 9 5 . 1 0 9 9 3 0 . 7 8 3 4 8

AB 5 . 4 1 0 2 5 0 . 8 4 1 0 8 5 . 4 7 5 4 5 0 . 8 3 3 6 3

Ae 3 . 7 3 2 0 5 0 . 8 6 6 0 3 3 . 7 5 8 8 8 0 . 8 5 9 6 7

A7 1 . 1 0 5 5 7 1 . 3 0 9 0 2 1 . 0 3 6 1 6 1 . 3 4 5 6 4

Ae 2 . 8 9 4 4 3 0 . 8 0 9 0 2 2 . 9 6 3 8 4 0 . 7 9 5 6 4

Bi 3 . 0 0 0 0 0 0 . 5 0 0 0 0 3 . 1 3 8 9 9 0 . 5 2 3 2 2

Ba 0 . 4 3 9 3 4 - 0 . 2 0 7 1 1 0 . 3 6 9 9 5 - 0 . 2 7 0 0 9

B3 0 . 3 2 1 8 0 - 0 . 5 7 3 1 3 0 . 2 8 3 4 3 - 0 . 6 5 2 9 7

B4 0 . 2 6 7 9 5 - 0 . 8 6 6 0 3 0 . 2 4 1 1 2 - 0 . 9 5 9 6 7

BB 2 . 8 9 4 4 3 0 . 1 9 0 9 8 2 . 9 6 3 8 4 0 . 2 0 4 3 6

Be 1 . 1 0 5 5 7 - 0 . 3 0 9 0 2 1 . 0 3 6 1 6 - 0 . 3 4 5 6 4

Ml 0 . 0 2 5 1 3 2 . 2 0 7 1 1 0 . 0 2 9 0 6 2 . 2 7 0 0 9

M2 0 . 0 0 3 9 6 2 . 5 7 3 1 3 0 . 0 0 4 4 3 2 . 6 5 2 9 7

DATA FOR T W O - G R O U P SYSTEMS 501

I n t e n s i t y

0 . 7 4 2 7 6 2 . 4 3 1 3 5 2 . 2 1 3 0 9 5 . 2 2 5 0 3 5 . 5 3 1 6 2 3 . 7 8 2 0 8 0 . 9 7 1 0 1 3 . 0 2 8 9 9

3 . 2 5 7 2 4 0 . 3 1 1 4 1 0 . 2 5 0 4 6 0 . 2 1 7 9 2 3 . 0 2 8 9 9 0 . 9 7 1 0 1

0 . 0 3 2 2 1 0 . 0 0 4 8 2

0 . 5 5 8 8 5 2 . 3 3 6 4 5 2 . 1 7 4 7 6 5 . 4 0 5 0 7 5 . 6 2 2 1 0 3 . 8 1 9 8 7 0 . 8 5 3 0 8 3 . 1 4 6 9 2

3 . 4 4 1 1 5 0 . 2 2 2 4 0 0 . 1 9 7 7 7 0 . 1 8 0 1 3 3 . 1 4 6 9 2 0 . 8 5 3 0 8

0 . 0 3 6 0 8 0 . 0 0 5 3 7

A

B

F r e q u e n c y

1 . 6 5 6 7 8 1 . 2 2 4 2 5 1 . 1 7 2 9 1 0 . 7 7 5 7 5 0 . 8 2 7 0 9 0 . 8 5 3 9 4 1 . 3 8 3 1 0 0 . 7 8 3 1 0

0 . 5 4 3 2 2 - 0 . 3 3 7 8 0 - 0 . 7 3 4 9 6 - 1 . 0 5 3 9 4 0 . 2 1 6 9 0 - 0 . 3 8 3 1 0

2 . 3 3 7 8 0 2 . 7 3 4 9 6

1 . 8 2 4 5 0 1 . 2 3 5 7 3 1 . 1 8 3 8 0 0 . 7 6 4 2 7 0 . 8 1 6 2 0 0 . 8 4 4 0 3 1 . 4 6 0 3 3 0 . 7 6 0 3 3

0 . 5 7 5 5 0 - 0 . 4 8 4 7 3 - 0 . 9 0 4 2 6 - 1 . 2 4 4 0 3 0 . 2 3 9 6 7 - 0 . 4 6 0 3 3

2 . 4 8 4 7 3 2 . 9 0 4 2 6

J / 6 I n t e n s i t y

0 . 6 5 0 . 6 4 2 9 0 2 . 3 8 0 2 2 2 . 1 9 2 6 1 5 . 3 2 2 5 7 5 . 5 8 0 1 2 3 . 8 0 2 2 5 0 . 9 1 0 0 2 3 . 0 8 9 9 8

3 . 3 5 7 1 0 0 . 2 6 2 6 8 0 . 2 2 2 1 4 0 . 1 9 7 7 5 3 . 0 8 9 9 8 0 . 9 1 0 0 2

0 . 0 3 4 5 3 0 . 0 0 5 1 3

0 . 7 5 0 . 4 8 8 1 4 2 . 2 9 8 9 3 2 . 1 5 9 1 4 5 . 4 7 4 8 9 5 . 6 5 8 5 7 3 . 8 3 5 3 3 0 . 8 0 0 0 0 3 . 2 0 0 0 0

3 . 5 1 1 8 6 0 . 1 8 9 2 1 0 . 1 7 6 7 6 0 . 1 6 4 6 7 3 . 2 0 0 0 0 0 . 8 0 0 0 0

0 . 0 3 6 9 7 0 . 0 0 5 5 3

F r e q u e n c y

1 . 7 3 9 4 9 1 . 2 3 0 5 7 1 . 1 7 8 6 9 0 . 7 6 9 4 3 0 . 8 2 1 3 1 0 . 8 4 8 7 5 1 . 4 2 1 3 4 0 . 7 7 1 3 4

0 . 5 6 0 5 1 - 0 . 4 0 9 5 5 - 0 . 8 1 8 8 1 - 1 . 1 4 8 7 5 0 . 2 2 8 6 6 - 0 . 4 2 1 3 4

2 . 4 0 9 5 5 2 . 8 1 8 8 1

1 . 9 1 1 4 4 1 . 2 3 9 9 5 1 . 1 8 8 3 4 0 . 7 6 0 0 5 0 . 8 1 1 6 6 0 . 8 3 9 7 2 1 . 5 0 0 0 0 0 . 7 5 0 0 0

0 . 5 8 8 5 6 - 0 . 5 6 2 8 3 - 0 . 9 9 1 1 1 - 1 . 3 3 9 7 2 0 . 2 5 0 0 0 - 0 . 5 0 0 0 0

2 . 5 6 2 8 3 2 . 9 9 1 1 1

502 APPENDIX VI

A o B

A a A3 A4 A5 Ae A7 Aa

J / L .

0 . 8 0

I n t e n s i t y F r e q u e n c y

0 . 4 2 8 5 7 2 . 2 6 6 7 1 2 . 1 4 5 4 1 5 . 5 3 4 1 4 5 . 6 9 0 3 5 3 . 8 4 8 9 5 0 . 7 5 0 6 1 3 . 2 4 9 3 9

2 . 0 0 0 0 0 1 . 2 4 3 4 0 1 . 1 9 2 3 8 0 . 7 5 6 6 0 0 . 8 0 7 6 2 0 . 8 3 5 7 8 1 . 5 4 0 3 1 0 . 7 4 0 3 1

0 . 8 5

I n t e n s i t y F r e q u e n c y

0 . 3 7 8 2 3 2 . 2 3 8 9 6 2 . 1 3 3 3 0 5 . 5 8 4 6 0 5 . 7 1 8 1 6 3 . 8 6 1 0 0 0 . 7 0 4 7 0 3 . 2 9 5 3 0

2 . 0 8 9 9 3 1 . 2 4 6 2 2 1 . 1 9 6 0 0 0 . 7 5 3 7 8 0 . 8 0 4 0 0 0 . 8 3 2 1 6 1 . 5 8 1 2 2 0 . 7 3 1 2 2

B3 B 4

3 . 5 7 1 4 3 0 . 1 6 1 8 6 0 . 1 5 8 5 9 0 . 1 5 1 0 5 3 . 2 4 9 3 9 0 . 7 5 0 6 1

0 . 6 0 0 0 0 - 0 . 6 4 3 4 0 - 1 . 0 7 9 1 8 - 1 . 4 3 5 7 8 0 . 2 5 9 6 9 - 0 . 5 4 0 3 1

3 . 6 2 1 7 7 0 . 1 3 9 2 7 0 . 1 4 2 8 4 0 . 1 3 9 0 0 3 . 2 9 5 3 0 0 . 7 0 4 7 0

0 . 6 1 0 0 7 - 0 . 7 2 6 0 9 - 1 . 1 6 8 3 1 - 1 . 5 3 2 1 6 0 . 2 6 8 7 8 - 0 . 5 8 1 2 2

0 . 0 3 7 2 9 0 . 0 0 5 6 4

2 . 6 4 3 4 0 3 . 0 7 9 1 8

0 . 0 3 7 1 7 0 . 0 0 5 7 0

2 . 7 2 6 0 9 3 . 1 6 8 3 1

0 . 9 0 0 . 3 3 5 5 2 2 . 2 1 4 9 7 2 . 1 2 2 5 7 5 . 6 2 7 7 7 5 . 7 4 2 5 9 3 . 8 7 1 7 1 0 . 6 6 2 0 7 3 . 3 3 7 9 3

2 . 1 8 1 0 2 1 . 2 4 8 5 4 1 . 1 9 9 2 6 0 . 7 5 1 4 6 0 . 8 0 0 7 4 0 . 8 2 8 8 2 1 . 6 2 2 6 8

0 . 9 5

0 . 7 2 2 6 8

0 . 2 9 9 1 2 2 . 1 9 4 1 6 2 . 1 1 3 0 3 5 . 6 6 4 8 8 5 . 7 6 4 1 3 3 . 8 8 1 2 7 0 . 6 2 2 5 0 3 . 3 7 7 5 0

2 . 2 7 3 1 0 1 . 2 5 0 4 4 1 . 3 0 2 1 9 0 . 7 4 9 5 6 0 . 7 9 8 7 1 0 . 8 2 5 7 4 1 . 6 6 4 6 6 0 . 7 1 4 6 6

B8 B3 B4 B e

3 . 6 6 4 4 8 0 . 1 2 0 5 5 0 . 1 2 9 1 2 0 . 1 2 8 2 9 3 . 3 3 7 9 3 0 . 6 6 2 0 7

0 . 6 1 8 9 8 - 0 . 8 1 0 5 9 - 1 . 2 5 8 3 8 - 1 . 6 2 8 8 2 0 . 2 7 7 3 2 - 0 . 6 2 2 6 8

3 . 7 0 0 8 8 0 . 1 0 4 9 6 0 . 1 1 7 1 4 0 . 1 1 8 7 3 3 . 3 7 7 5 0 0 . 6 2 2 5 0

0 . 6 2 6 9 0 - 0 . 8 9 6 6 5 - 1 . 3 4 9 2 8 - 1 . 7 2 5 7 4 0 . 2 8 5 3 4 - 0 . 6 6 4 6 6

0 . 0 3 6 7 1 0 . 0 0 5 7 2

2 . 8 1 0 5 9 3 . 2 5 8 3 8

0 . 0 3 6 0 0 0 . 0 0 5 7 0

2 . 8 9 6 6 5 3 . 3 4 9 2 8

A *

A .

A7

Î Ù L . 1 . 0 0

3 . 0 0

D A T A F O R T W O - G R O U P S Y S T E M S

503

I n t e n s i t y F r e q u e n c y J / 6 I n t e n s i t y F r e q u e n c y

0 . 2 6 7 9 5 2 . 3 6 6 0 3 2 . 0 0 0 . 0 5 8 5 5 4 . 3 0 2 7 8

2 . 1 7 6 0 4 1 . 2 5 2 0 1 2 . 0 4 3 5 2 1 . 2 5 8 7 8

2 . 1 0 4 5 2 1 . 2 0 4 8 4 2 . 0 3 2 5 9 1 . 2 2 9 7 4

5 . 6 9 6 9 4 0 . 7 4 7 9 9 5 . 9 2 5 2 5 0 . 7 4 1 2 2

5 . 7 8 3 1 9 0 . 7 9 5 1 6 5 . 9 3 6 8 3 0 . 7 7 0 2 6

3 . 8 8 9 8 2 0 . 8 2 2 8 8 3 . 9 6 3 9 6 0 . 7 9 1 2 9

0 . 5 8 5 7 9 1 . 7 0 7 1 1 0 . 2 1 1 1 5 2 . 6 1 8 0 3

3 . 4 1 4 2 1 0 . 7 0 7 1 1 3 . 7 8 8 8 5 0 . 6 1 8 0 3

3 . 7 3 2 0 5 0 . 6 3 3 9 7 3 . 9 4 1 4 5 0 . 6 9 7 2 2

0 . 0 9 1 9 1 - 0 . 9 8 4 0 6 0 . 0 1 5 0 3 - 2 . 8 6 4 3 3

0 . 1 0 6 6 3 - 1 . 4 4 0 9 1 0 . 0 2 7 1 3 - 3 . 3 5 2 8 4

0 . 1 1 0 1 8 - 1 . 8 2 2 8 8 0 . 0 3 6 0 4 - 3 . 7 9 1 2 9

3 . 4 1 4 2 1 0 . 2 9 2 8 9 3 . 7 8 8 8 5 0 . 3 8 1 9 7

0 . 5 8 5 7 9 - 0 . 7 0 7 1 1 0 . 2 1 1 1 5 - 1 . 6 1 8 0 3

0 . 0 3 5 1 1 2 . 9 8 4 0 6 0 . 0 1 6 2 0 4 . 8 6 4 3 3

0 . 0 0 5 6 6 3 . 4 4 0 9 1 0 . 0 0 3 4 5 5 . 3 5 2 8 4

0 . 0 2 4 3 4 6 . 2 8 3 8 8 4 . 0 0 0 . 0 1 3 2 0 8 . 2 7 4 9 2

2 . 0 1 8 8 4 1 . 2 5 7 5 0 2 . 0 1 0 4 2 1 . 2 5 6 2 1

2 . 0 1 5 4 8 1 . 2 3 7 3 4 2 . 0 0 8 9 8 1 . 2 4 0 8 7

5 . 9 6 7 2 9 0 . 7 4 2 5 0 5 . 9 8 1 7 8 0 . 7 4 3 7 9

5 . 9 7 0 7 5 0 . 7 6 2 6 6 5 . 9 8 3 2 4 0 . 7 5 9 1 3

3 . 9 8 2 4 8 0 . 7 7 8 7 2 3 . 9 8 9 7 0 0 . 7 7 2 0 0

0 . 1 0 2 6 3 3 . 5 8 1 1 4 0 . 0 5 9 7 2 4 . 5 6 1 5 5

3 . 8 9 7 3 7 0 . 5 8 1 1 4 3 . 9 4 0 2 9 0 . 5 6 1 5 5

3 . 9 7 5 6 6 0 . 7 1 6 1 2 3 . 9 8 6 8 0 0 . 7 2 5 0 8

0 . 0 0 5 5 0 - 4 . 8 2 5 2 6 0 . 0 0 2 7 8 - 6 . 8 0 6 0 5

0 . 0 1 1 7 3 - 5 . 3 2 0 1 0 0 . 0 0 6 4 6 - 7 . 3 0 3 1 3

0 . 0 1 7 5 2 - 5 . 7 7 8 7 2 0 . 0 1 0 3 0 - 7 . 7 7 2 0 0

3 . 8 9 7 3 7 0 . 4 1 8 8 6 3 . 9 4 0 2 9 0 . 4 3 8 4 5

0 . 1 0 2 6 3 - 2 . 5 8 1 1 4 0 . 0 5 9 7 2 - 3 . 5 6 1 5 5

0 . 0 0 8 3 7 6 . 8 2 5 2 6 0 . 0 0 5 0 2 8 . 8 0 6 0 5

0 . 0 0 2 0 4 7 . 3 2 0 1 0 0 . 0 0 1 3 2 9 . 3 0 3 1 3

504 APPENDIX VI

A3B

I n t e n s i t y F r e q u e n c y I n t e n s i t y F r e q u e n c y

5 . 0 0

B3 B4 B5

0 . 0 0 8 2 6 1 0 . 2 6 9 7 0 1 0 . 0 0 0 . 0 0 1 9 7 2 0 . 2 5 9 6 1

2 . 0 0 6 6 0 1 . 2 5 5 2 4 2 . 0 0 1 6 1 1 . 2 5 2 8 8

2 . 0 0 5 8 5 1 . 2 4 2 8 9 2 . 0 0 1 5 1 1 . 2 4 6 6 5

5 . 9 8 8 4 1 0 . 7 4 4 7 6 5 . 9 9 7 1 4 0 . 7 4 7 1 2

5 . 9 8 9 1 6 0 . 7 5 7 1 1 5 . 9 9 7 2 4 0 . 7 5 3 3 5

3 . 9 9 3 2 3 0 . 7 6 7 8 3 3 . 9 9 8 2 2 0 . 7 5 9 1 4

0 . 0 3 8 8 4 5 . 5 4 9 5 1 0 . 0 0 9 9 3 1 0 . 5 2 4 9 4

3 . 9 6 1 1 6 0 . 5 4 9 5 1 3 . 9 9 0 0 7 0 . 5 2 4 9 4

3 . 9 9 1 7 4 0 . 7 3 0 3 0 3 . 9 9 8 0 3 0 . 7 4 0 3 9

0 . 0 0 1 6 6 - 8 . 7 9 4 6 3 0 . 0 0 0 3 6 - 1 8 . 7 7 2 1 0

0 . 0 0 4 0 7 - 9 . 2 9 2 7 6 0 . 0 0 0 9 8 - 1 9 . 2 7 1 6 3

0 . 0 0 6 7 7 - 9 . 7 6 7 8 3 0 . 0 0 1 7 8 - 1 9 . 7 5 9 1 4

3 . 9 6 1 1 6 0 . 4 5 0 4 9 3 . 9 9 0 0 7 0 . 4 7 5 0 6

0 . 0 3 8 8 4 - 4 . 5 4 9 5 1 0 . 0 0 9 9 3 - 9 . 5 2 4 9 4

0 . 0 0 3 3 3 1 0 . 7 9 4 6 3 0 . 0 0 0 8 9 2 0 . 7 7 2 1 0

0 . 0 0 0 9 1 1 1 . 2 9 2 7 6 0 . 0 0 0 2 7 2 1 . 2 7 1 6 3

A4

Ae A7

B P B3 B4 B

6

0 . 0 0 0 0 0

00

2 . 0 0 0 0 0 1 . 2 5 0 0 0 2 . 0 0 0 0 0 1 . 2 5 0 0 0 6 . 0 0 0 0 0 0 . 7 5 0 0 0 6 . 0 0 0 0 0 0 . 7 5 0 0 0 4 . 0 0 0 0 0 0 . 7 5 0 0 0

0 . 0 0 0 0 0

00

4 . 0 0 0 0 0 0 . 5 0 0 0 0

4 . 0 0 0 0 0 0 . 7 5 0 0 0

0 . 0 0 0 0 0

— 00

0 . 0 0 0 0 0

— 00

0 . 0 0 0 0 0

- 0 0

0 . 0 0 0 0 0

— 00

0 . 0 0 0 0 0

00

0 . 0 0 0 0 0

OO

D A T A F O R T W O - G R O U P S Y S T E M S 505

L i n e F r e q u e n c i e s a n d R e l a t i v e I n t e n s i t i e s F o r t h e A4B S p i n S y s t e m

'JL

6 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 6 . 0 0 0 0 0 6 . 0 0 0 0 0

1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

J / 6 I n t e n s i t y F r e q u e n c y

0 . 0 5 3 . 7 7 6 3 5 5 . 6 9 0 8 0 5 . 7 1 2 9 0 3 . 8 2 1 1 9 4 . 2 2 3 6 4 6 . 3 0 9 1 8 6 . 2 8 7 0 8 4 . 1 7 8 8 0 5 . 6 8 9 1 8 5 . 7 1 1 5 6 6 . 3 1 0 8 1 6 . 2 8 8 4 3

1 . 0 2 7 6 9 1 . 0 2 6 1 4 1 . 0 2 4 8 1 1 . 0 2 3 6 8 0 . 9 7 3 8 6 0 . 9 7 5 1 9 0 . 9 7 6 3 2 0 . 9 7 7 3 2 1 . 0 2 6 2 8 1 . 0 2 4 9 4 0 . 9 7 5 0 6 0 . 9 7 6 2 2

1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 1 . 0 0 0 0 0 3 . 0 0 0 0 0 3 . 0 0 0 0 0 3 . 0 0 0 0 0 2 . 0 0 0 0 0

0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0

1 . 2 2 3 6 5 1 . 0 8 5 5 5 0 . 9 7 7 9 1 0 . 8 9 1 7 2 0 . 8 2 1 2 0 3 . 3 1 0 8 2 2 . 9 7 7 6 2 2 . 7 1 1 5 7 2 . 0 0 0 0 0

0 . 0 9 7 3 1 0 . 0 4 3 4 7 - 0 . 0 0 7 4 8 - 0 . 0 5 5 9 7 - 0 . 1 0 2 3 2 0 . 0 4 8 7 2 - 0 . 0 0 2 5 0 - 0 . 0 5 1 2 2 0 . 0 0 0 0 0

0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0

2 . 0 0 0 0 0 2 . 0 0 0 0 0 2 . 0 0 0 0 0 2 . 0 0 0 0 0

0 . 0 0 0 0 1 0 . 0 0 0 0 1 0 . 0 0 0 0 1 0 . 0 0 0 0 0

1 . 9 5 6 5 3 2 . 0 0 7 4 8 2 . 0 5 5 9 7 2 . 0 0 2 5 0

506 A P P E N D I X V I

A . B

I n t e n s i t y F r e q u e n c y J / 6 I n t e n s i t y F r e q u e n c y

Αχ

A

A

A

0 . 1 0 3 . 5 0 2 0 5 5 . 3 7 2 3 4 5 . 4 5 6 3 9 3 . 6 7 9 4 2 4 . 4 9 7 7 1 6 . 6 2 7 2 2 6 . 5 4 3 3 4 4 . 3 2 0 5 0 5 . 3 5 8 9 6 5 . 4 4 7 0 4 6 . 6 4 0 9 7 6 . 5 5 2 8 9

1 . 0 6 1 6 1 1 . 0 5 3 9 3 1 . 0 4 8 5 6 1 . 0 4 4 5 3 0 . 9 4 6 0 7 0 . 9 5 1 4 4 0 . 9 5 5 4 7 0 . 9 5 8 6 3 1 . 0 5 5 2 3 1 . 0 4 9 5 1 0 . 9 5 0 4 9 0 . 9 5 4 7 4

0 . 1 5 3 . 1 7 6 8 6 5 . 0 5 9 0 1 5 . 2 3 3 8 2 3 . 5 6 7 0 5 4 . 8 2 1 7 1 6 . 9 3 8 7 3 6 . 7 6 5 0 7 4 . 4 3 2 6 8 5 . 0 1 3 6 9 5 . 2 0 6 6 7 6 . 9 8 5 9 6 6 . 7 9 2 9 9

1 . 1 0 3 0 2 1 . 0 8 2 1 3 1 . 0 7 0 3 8 1 . 0 6 2 5 7 0 . 9 1 7 8 7 0 . 9 2 9 6 2 0 . 9 3 7 4 3 0 . 9 4 3 1 0 1 . 0 8 7 0 1 1 . 0 7 3 3 6 0 . 9 2 6 6 4 0 . 9 3 5 3 7

B i

B

B

B

Be B

B

1 . 4 9 7 9 5 1 . 1 2 9 7 0 0 . 9 1 6 2 0 0 . 7 7 7 1 6 0 . 6 7 9 5 0 3 . 6 4 1 0 4 2 . 9 1 1 9 2 2 . 4 4 7 1 1 2 . 0 0 0 0 0

0 . 1 8 8 3 9 0 . 0 7 2 8 6 - 0 . 0 2 9 6 3 - 0 . 1 2 2 7 3 - 0 . 2 0 8 6 3 0 . 0 9 4 7 7 - 0 . 0 0 9 9 7 - 0 . 1 0 4 7 4 0 . 0 0 0 0 0

1 . 8 2 3 1 4 1 . 1 1 7 8 6 0 . 8 2 6 6 1 0 . 6 6 7 6 1 0 . 5 6 7 3 2 3 . 9 8 6 3 1 2 . 8 0 7 0 3 2 . 2 0 7 0 1 2 . 0 0 0 0 0

0 . 2 7 1 9 8 0 . 0 8 6 8 3 - 0 . 0 6 5 6 8 - 0 . 1 9 8 6 3 - 0 . 3 1 8 1 0 0 . 1 3 7 9 9 - 0 . 0 2 2 3 7 - 0 . 1 6 0 3 7 0 . 0 0 0 0 0

Μχ M * M3 MA

0 . 0 0 0 2 4 0 . 0 0 0 2 0 0 . 0 0 0 0 8 0 . 0 0 0 0 7

1 . 9 2 7 1 4 2 . 0 2 9 6 3 2 . 1 2 2 7 3 2 . 0 0 9 9 7

0 . 0 0 1 4 3 0 . 0 0 0 8 4 0 . 0 0 0 2 7 0 . 0 0 0 3 4

1 . 9 1 3 1 7 2 . 0 6 5 6 8 2 . 1 9 8 6 3 2 . 0 2 2 3 7

DATA FOR T W O - G R O U P SYSTEMS

A

B

J / 6 I n t e n s i t y F r e q u e n c y J / 6 I n t e n s i t y F r e q u e n c y 0. 20

A

A

A

A

A

A

A

A

Α

ο A n Ai a

2 . 8 1 0 0 9 4 . 7 6 3 2 9 5 . 0 4 4 5 9 3 . 4 7 7 5 8 5 . 1 8 5 1 3 7 . 2 2 9 8 1 6 . 9 5 2 7 1 4 . 5 2 1 8 4 4 . 6 5 9 0 0 4 . 9 8 9 7 1 7 . 3 3 9 9 9 7 . 0 0 9 2 9

1 . 1 5 3 1 1 1 . 1 0 9 2 3 1 . 0 8 9 7 3 1 . 0 7 7 9 9 0 . 8 9 0 7 7 0 . 9 1 0 2 7 0 . 9 2 2 0 1 0 . 9 3 U 0 7 1 . 1 2 1 7 0 1 . 0 9 6 1 9 0 . 9 0 3 8 1 0 . 9 1 7 8 9

0 . 2 5 2 . 4 2 1 9 1 4 . 4 9 3 8 1 . 8 8 5 7 8 . 4 0 5 8 5 . 5 6 6 7 4 . 4 9 0 8 6 . 1 0 9 2 6 4 . 5 9 3 1 8 4 . 3 0 1 3 2 4 . 7 9 4 7 8 7 . 6 9 6 4 5 7 . 2 0 2 9 9

1 . 2 1 2 7 0 1 . 1 3 3 8 0 1 . 1 0 6 4 3 1 . 0 9 1 1 1 0 . 8 6 6 2 0 0 . 8 9 3 5 7 0 . 9 0 8 8 9 0 . 9 1 9 0 4 1 . 1 5 9 3 6 1 . 1 1 7 7 6 0 . 8 8 2 2 4 0 . 9 0 2 1 2

Bi B

B

B5 Be B

B

B

2 . 1 8 9 9 1 1 . 0 4 6 7 9 0 . 7 2 3 4 9 0 . 5 6 9 1 3 0 . 4 7 8 1 6 4 . 3 4 1 0 0 2 . 6 6 9 2 9 1 . 9 9 0 7 1 2 . 0 0 0 0 0

0 . 3 4 6 8 9 0 . 0 8 4 5 4 - 0 . 1 1 4 4 3 - 0 . 2 8 2 1 5 - 0 . 4 3 0 0 7 0 . 1 7 8 3 0 - 0 . 0 3 9 5 9 - 0 . 2 1 7 8 9 0 . 0 0 0 0 0

2 . 5 7 8 0 9 0 . 9 2 8 1 1 0 . 6 1 9 3 7 0 . 4 8 3 9 1 0 . 4 0 6 8 2 4 . 6 9 8 6 8 2 . 5 0 6 5 4 1 . 7 9 7 0 1 2 . 0 0 0 0 0

0 . 4 1 2 3 0 0 . 0 6 5 8 0 - 0 . 1 7 4 4 3 - 0 . 3 7 1 9 8 - 0 . 5 4 4 0 4 0 . 2 1 5 6 4 - 0 . 0 6 1 4 9 - 0 . 2 7 7 1 2 0 . 0 0 0 0 0

Mi 0 . 0 0 4 7 8

0 . 0 0 2 1 2 0 . 0 0 0 5 8 0 . 0 0 1 0 1

1 . 9 1 5 4 6 2 . 1 1 4 4 3 2 . 2 8 2 1 5 2 . 0 3 9 5 9

0 . 0 1 1 3 4 0 . 0 0 3 9 9 0 . 0 0 0 9 7 0 . 0 0 2 2 3

1 . 9 3 4 2 0

2 . 1 7 4 4 3

2 . 3 7 1 9 8

2 . 0 6 1 4 9

508 APPENDIX VI

A . B

I n t e n s i t y F r e q u e n c y J / 6 I n t e n s i t y F r e q u e n c y

A i Aa A3 A 4 AB Ae A7 Ae A9 Αχ 0 A . i Αχ 3

0 . 3 0 2 . 0 3 9 2 8 4 . 2 5 5 2 3 4 . 7 5 3 5 5 3 . 3 4 7 8 8 5 . 9 3 9 6 9 . 7 1 7 5 5 , 2 3 8 8 8 . 6 5 0 7 3 . 9 4 7 3 7 . 6 2 0 1 2 8 . 0 4 8 5 1 7 . 3 7 5 7 5

1 . 2 8 1 9 7 1 . 1 5 4 8 3 1 . 1 2 0 5 6 1 . 1 0 2 2 5 0 . 8 4 5 1 7 0 . 8 7 9 4 4 0 . 8 9 7 7 5 0 . 9 0 9 6 2 1 . 2 0 0 0 0 1 . 1 3 7 8 8 0 . 8 6 2 1 2 0 . 8 8 7 8 8

0 . 3 5 1 . 6 8 7 3 0 4 . 0 4 9 2 5 4 . 6 4 3 8 8 3 . 3 0 0 6 3 6 . 2 8 0 2 6 7 . 9 0 9 8 8 7 . 3 4 5 9 0 4 . 6 9 7 5 8 3 . 6 0 3 5 2 4 . 4 6 3 8 9 8 . 3 8 9 7 8 7 . 5 2 9 4 1

1 . 3 6 0 4 7 1 . 1 7 1 9 3 1 . 1 3 2 3 6 1 . 1 1 1 7 3 0 . 8 2 8 0 7 0 . 8 6 7 6 4 0 . 8 8 8 2 7 0 . 9 0 1 4 9 1 . 2 4 3 5 5 1 . 1 5 6 4 5 0 . 8 4 3 5 5 0 . 8 7 5 0 0

B i B2 B3 B4 B8 B e B7 B8 B g

2 . 9 6 0 7 2 0 . 7 8 4 0 5 0 . 5 2 2 7 2 0 . 4 1 1 8 5 0 . 3 4 9 2 7 5 . 0 5 2 6 3 2 . 3 2 7 2 5 1 . 6 2 4 2 5 2 . 0 0 0 0 0

0 . 4 6 8 0 3 0 . 0 3 1 2 2 - 0 . 2 4 4 1 7 - 0 . 4 6 6 9 8 - 0 . 6 5 9 6 2 0 . 2 5 0 0 0 - 0 . 0 8 7 8 8 - 0 . 3 3 7 8 8 0 . 0 0 0 0 0

3 . 3 1 2 7 0 0 . 6 3 8 0 5 0 . 4 3 7 8 1 0 . 3 5 1 6 8 . 3 0 2 4 2 . 3 9 6 4 8 . 1 3 9 6 3 . 4 7 0 5 9 . 0 0 0 0 0

0 . 5 1 4 5 3 - 0 . 0 1 7 8 7 - 0 . 3 2 2 1 6 - 0 . 5 6 6 2 5 - 0 . 7 7 6 4 9 0 . 2 8 1 4 5 - 0 . 1 1 8 5 5 - 0 . 4 0 0 0 0 0 . 0 0 0 0 0

Mi

M3

0 . 0 2 1 0 3 0 . 0 0 6 1 9 0 . 0 0 1 3 9 0 . 0 0 4 1 2

1 . 9 6 8 7 8 2 . 2 4 4 1 7 2 . 4 6 6 9 8 2 . 0 8 7 8 8

0 . 0 3 2 4 4 0 . 0 0 8 4 3 0 . 0 0 1 7 9 0 . 0 0 6 7 0

2 . 0 1 7 8 7 2 . 3 2 2 1 6 2 . 5 6 6 2 5 2 . 1 1 8 5 5

DATA FOR T W O - G R O U P SYSTEMS 509

Α . Β

I n t e n s i t y F r e q u e n c y J / 6 I n t e n s i t y F r e q u e n c y

1 . 3 8 1 9 7 3 . 8 7 5 2 9 4 . 5 5 3 0 5 3 . 2 6 1 8 0 6 . 5 7 4 4 6 8 . 0 7 0 6 8 7 . 4 3 4 3 6 4 . 7 3 6 0 7 3 . 2 7 5 2 6 4 . 3 2 4 2 5 8 . 7 1 4 8 7 7 . 6 6 5 8 7

1 . 4 4 7 2 1 1 . 1 8 5 2 4 1 . 1 4 2 1 4 1 . 1 1 9 8 3 0 . 8 1 4 7 6 0 . 8 5 7 8 6 0 . 8 8 0 1 7 0 . 8 9 4 4 3 1 . 2 8 9 9 0 1 . 1 7 3 4 3 0 . 8 2 6 5 7 0 . 8 6 3 3 2

0 . 4 5 1 . 1 2 8 3 6 3 . 7 3 0 9 6 4 . 4 7 7 7 3 3 . 2 2 9 6 0 6 . 8 1 8 8 1 8 . 2 0 4 0 5 7 . 5 0 7 6 9 4 . 7 6 7 9 7 2 . 9 6 6 8 1 4 . 1 9 9 5 0 9 . 0 1 9 6 8 7 . 7 8 6 9 9

1 . 5 4 0 9 4 1 . 1 9 5 2 8 1 . 1 5 0 2 3 1 . 1 2 6 7 8 0 . 8 0 4 7 2 0 . 8 4 9 7 7 0 . 8 7 3 2 2 0 . 8 8 8 2 4 1 . 3 3 8 9 0 1 . 1 8 8 8 2 0 . 8 1 1 1 8 0 . 8 5 2 7 2

3 . 6 1 8 0 3 0 . 5 0 6 6 8 0 . 3 6 5 8 1 0 . 3 0 1 7 1 0 . 2 6 3 9 3 5 . 7 2 4 7 4 1 . 9 5 1 0 0 1 . 3 3 4 1 3 2 . 0 0 0 0 0

0 . 5 5 2 7 9 - 0 . 0 7 9 6 7 - 0 . 4 0 7 0 5 - 0 . 6 6 9 0 2 . 8 9 4 4 3 . 3 1 0 1 0 . 1 5 3 2 2 . 4 6 3 3 2 . 0 0 0 0 0

3 . 8 7 1 6 4 0 . 3 9 7 4 0 0 . 3 0 6 0 6 0 . 2 6 0 2 8 0 . 2 3 2 0 3 6 . 0 3 3 1 9 1 . 7 6 7 3 0 1 . 2 1 3 0 1 2 . 0 0 0 0 0

0 . 5 8 4 0 6 - 0 . 1 5 2 1 7 - 0 . 4 9 7 6 8 - 0 . 7 7 4 7 0 . 0 1 3 2 4 . 3 3 6 1 0 . 1 9 1 6 3 . 5 2 7 7 2 . 0 0 0 0 0

0 . 0 4 3 5 7 0 . 0 1 0 4 6 0 . 0 0 2 1 4 0 . 0 0 9 8 8

2 . 0 7 9 6 7 2 . 4 0 7 0 5 2 . 6 6 9 0 2 2 . 1 5 3 2 2

0 . 0 5 2 8 3 0 . 0 1 2 1 5 0 . 0 0 2 4 3 0 . 0 1 3 5 1

2 . 1 5 2 1 7 2 . 4 9 7 6 8 2 . 7 7 4 7 0 2 . 1 9 1 6 3

A P P E N D I X VI

A

B

J/6 Intensity Frequency J/6 Intensity Frequency Ai A ²

A ³ A ⁴ A ⁵ A ^e A ⁷ A ⁸ A ^e Αι ο Αχί Ai a

0.50 4.41512 8.31437 0.92352 3.61272 3.20270 7.01702 7.56877 79464 68098 08808 30161 89451

64039 20268 15693 13278 79732 84307 86722 88278 1.39039 1.20268 0.79732 0.84307

0.55 4.36288 8.40569 0.76051 3.51651 3.18005 7.17604 7.61994 .81712 .41923 .98858 .55941 .99006

1.74442 1.20804 1.16249 1.13799 0.79196 0.83751 0.86201 0.87794 1.44415 1.21511 0.78489 0.83426

Β . B ² B ³ B ⁴ B ^B Be B ⁷ B ^e Bo

4.07648 0.31080 0.25706 0.22587 0.20536 6.31902 1.59290 1.10549 2.00000

0.60961 -0.23346 -0.59307 -0.88278 -1.13278 0.35961 -0.23346 -0.59307 0.00000

4.23949 0.24401 0.21707 0.19718 0.18288 6.58077 1.43065 1.00994 2.00000

0.63058 -0.32187 -0.69240 -0.99288 -1.25294 0.38085 -0.27842 -0.65926 0.00000 Mi M ^a

Ma M ⁴ 0.05947 0.01345 0.00265 0.01740 2.23346 2.88278 2.59307 2.23346 0.06345 0.01436 0.00282 0.02136 2.32187 2.69240 2.99288 2.27842

DATA FOR TWO-GROUP SYSTEMS

J/6 Intensity Frequency J/6 Intensity Frequency A,B A Ai A A A ^{a 3 5 4}

A ^e A ⁷ A ⁸ A ⁹ A ¹⁰ An A ^x a

0.60 4.31908 4.83622 8.07507 0.63148 3.43838 3.16084 8.48153 7.66306 2.18182 3.89972 9.79297 7.30336

1.85208 1.21186 1.16713 1.14254 0.78814 0.83287 0.85746 0.87361 1.50000 1.22621 0.77379 0.82621

0.65 10.00308 0.52921 4.28216 7.40564 8.54482 7.69962 4.85256 8.15083 3.37482 3.14443 1.96810 3.82035

1.96262 1.21455 1.17102 1.14653 0.78545 0.82898 0.85347 0.86973 1.55772 1.23610 0.76390 0.81882 Bi B ²

B ³ B4 B ⁵

B

B ⁷ Be B ⁹

4.36852 0.19310 0.18447 0.17316 0.16378 6.81818 1.28210 0.92493 2.00000

0.64792 -0.41602 -0.79501 -1.10468 -1.37361 0.40000 -0.32621 -0.72621 0.00000

47079 15439 15781 15294 03190 14744 1.14775 0.84917 2.00000

66238 51479 90036 ,21792 ,49473 ,41728 79382 37655 0.00000 M ^a

Ms M ^A 0.02521 0.06517 0.01492 0.00294 2.41602 2.79501 3.10468 2.32621 0.06515 0.01521 0.00302 0.02881 2.51479 2.90036 3.21792 2.37655

512 A P P E N D I X V I

A4B

J / 6 I n t e n s i t y F r e q u e n c y J / 6 I n t e n s i t y F r e q u e n c y

Aa A3

A7 Ae Ae

0 . 7 0 0 . 4 4 7 7 4 3 . 3 2 2 9 0 4 . 2 5 0 8 7 3 , 1 3 0 3 2 7 . 4 8 8 3 6 8 . 5 9 7 9 3 7 . 7 3 0 8 1 4 . 8 6 6 6 2 1 . 7 7 6 8 1 3 . 7 4 9 4 4 1 0 . 1 9 1 1 2 8 . 2 1 8 4 9

2 . 0 7 5 4 5 1 . 2 1 6 4 1 1 . 1 7 4 3 0 1 . 1 5 0 0 6 0 . 7 8 3 5 9 0 . 8 2 5 7 0 0 . 8 4 9 9 4 0 . 8 6 6 2 2 1 . 6 1 7 1 4 1 . 2 4 4 9 0 0 . 7 5 5 1 0 0 . 8 1 2 0 3

0 . 7 5 0 . 3 8 2 3 4 3 . 2 8 0 2 4 4 . 2 2 4 2 0 3 . 1 1 8 1 2 7 . 5 5 5 8 2 8 . 6 4 2 7 8 7 . 7 5 7 5 9 4 . 8 7 8 8 2 1 . 6 0 6 2 6 3 . 6 8 6 0 5 1 0 . 3 5 8 8 2 8 . 2 7 9 0 3

2 . 1 9 0 1 0 1 . 2 1 7 6 6 1 . 1 7 7 0 9 1 . 1 5 3 1 9 0 . 7 8 2 3 4 0 . 8 2 2 9 1 0 . 8 4 6 8 1 0 . 8 6 3 0 4 1 . 6 7 8 0 5 1 . 2 5 2 7 2 0 . 7 4 7 2 8 0 . 8 0 5 7 8

B i B3 B3 B . B5 Be B7 Be B o

4 . 5 5 2 2 6 0 . 1 2 4 8 4 0 . 1 3 5 9 3 0 . 1 3 5 8 1 0 . 1 3 3 3 8 7 . 2 2 3 1 9 1 . 0 2 7 3 6 0 . 7 8 1 5 1 2 . 0 0 0 0 0

0 . 6 7 4 5 5 - 0 . 6 1 7 3 0 - 1 . 0 0 8 0 1 - 1 . 3 3 2 3 8 - 1 . 6 1 6 2 2 0 . 4 3 2 8 6 - 0 . 4 2 9 1 7 - 0 . 8 6 2 0 3 0 . 0 0 0 0 0

4 . 6 1 7 6 6 0 . 1 0 2 1 0 0 . 1 1 7 8 7 0 . 1 2 1 2 3 0 . 1 2 1 1 8 7 . 3 9 3 7 4 0 . 9 2 0 2 1 0 . 7 2 0 9 7 2 . 0 0 0 0 0

0 . 6 8 4 9 0 - 0 . 7 2 2 8 6 - 1 . 1 1 7 6 1 - 1 . 4 4 7 8 9 - 1 . 7 3 8 0 4 0 . 4 4 6 9 5 - 0 . 4 8 3 8 3 - 0 . 9 3 0 7 8 0 . 0 0 0 0 0

Mi Ma

M3

MA

0 . 0 6 3 9 0 0 . 0 1 5 2 6 0 . 0 0 3 0 5 0 . 0 3 2 0 7

2 . 6 1 7 3 0 3 . 0 0 8 0 1 3 . 3 3 2 3 8 2 . 4 2 9 1 7

0 . 0 6 1 8 4 0 . 0 1 5 1 5 0 . 0 0 3 0 6 0 . 0 3 4 9 2

2 . 7 2 2 8 6 3 . 1 1 7 6 1 3 . 4 4 7 8 9 2 . 4 8 3 8 3

DATA FOR T W O - G R O U P SYSTEMS 513

A

B

J / 6 I N T E N S I T Y F R E Q U E N C Y J / 6 I N T E N S I T Y F R E Q U E N C Y

ΑΧ A

A

A4 A

A

A

A

A

ΑΧ Ο A N ΑΧ A

0 . 8 0 0 . 3 2 9 3 9 3 . 2 4 4 9 4 4 . 2 0 1 3 5 3 . 1 0 7 5 1 7 . 6 1 1 3 2 8 . 6 8 0 8 7 7 . 7 8 0 7 1 4 . 8 8 9 4 5 1 . 4 5 4 6 1 3 . 6 2 9 3 3 1 0 . 5 0 8 0 5 8 . 3 3 3 3 3

2 . 3 0 6 2 3 1 . 2 1 8 4 7 1 . 1 7 9 4 6 1 . 1 5 5 9 9 0 . 7 8 1 5 3 0 . 8 2 0 5 4 0 . 8 4 4 0 1 0 . 8 6 0 1 5 1 . 7 4 0 3 1 1 . 2 5 9 6 9 0 . 7 4 0 3 1 0 . 8 0 0 0 0

0 . 8 5 0 . 2 8 6 1 3 3 . 2 1 5 5 3 4 . 1 8 1 6 5 3 . 0 9 8 2 3 7 . 6 5 7 4 0 8 . 7 1 3 4 4 7 . 8 0 0 7 8 4 . 8 9 8 7 6 1 . 3 1 9 9 5 3 . 5 7 8 5 3 1 0 . 6 4 0 7 3 8 . 3 8 2 1 5

2 . 4 2 3 5 5 1 . 2 1 8 9 5 1 . 1 8 1 5 1 1 . 1 5 8 4 9 0 . 7 8 1 0 5 0 . 8 1 8 4 9 0 . 8 4 1 5 1 0 . 8 5 7 5 0 1 . 8 0 3 7 6 1 . 2 6 5 8 9 0 . 7 3 4 1 1 0 . 7 * 4 6 5

Bi B

B

B4 B

Β

B

B

Β

4 . 6 7 0 6 1 0 . 0 8 4 4 5 0 . 1 0 2 8 8 0 . 1 0 8 7 4 0 . 1 1 0 5 5 7 . 5 4 5 3 9 0 . 8 2 5 2 8 0 . 6 6 6 6 7 2 . 0 0 0 0 0

0 . 6 9 3 7 7 - 0 . 8 3 0 9 2 - 1 . 2 2 8 8 5 - 1 . 5 6 4 3 1 - 1 . 8 6 0 1 5 0 . 4 5 9 6 9 - 0 . 5 4 0 3 1 - 1 . 0 0 0 0 0 0 . 0 0 0 0 0

4 . 7 1 3 8 7 0 . 0 7 0 6 0 0 . 0 9 0 3 5 . 0 9 7 9 9 . 1 0 1 2 4 . 6 8 0 0 5 . 7 4 1 4 2 . 6 1 7 8 5 2 . 0 0 0 0 0

0 . 7 0 1 4 5 - 0 . 9 4 1 0 5 - 1 . 3 4 1 5 1 - 1 . 6 8 1 5 1 - 1 . 9 8 2 5 0 0 . 4 7 1 2 4 - 0 . 5 9 8 4 1 - 1 . 0 6 9 6 5 0 . 0 0 0 0 0

ML MA MA

0 . 0 5 9 2 8 0 . 0 1 4 9 0 0 . 0 0 3 0 4 0 . 0 3 7 3 4

2 . 8 3 0 9 2 3 . 2 2 8 8 5 3 . 5 6 4 3 1 2 . 5 4 0 3 1

0 . 0 5 6 4 7 0 . 0 1 4 5 6 0 . 0 0 3 0 1 0 . 0 3 9 3 2

2 . 9 4 1 0 5

3 . 3 4 1 5 1

3 . 6 8 1 5 1

2 . 5 9 8 4 1

514 APPENDIX VI

Α . Β

J / 6 I N T E N S I TY F R E Q U E N CY J / 6 I N T E N S I TY F R E Q U E N CY

Α Χ AA A3 A4 A5 AE A7 AE A9 A1 0 A N

A ! A

0 . 9 0 0 . 2 5 0 46 3 . 1 9 0 85 4 . 1 6 4 58 3 . 0 9 0 07 7 . 6 9 5 99 8 . 7 4 1 45 7 . 8 1 8 30 4 . 9 0 6 97 1 . 2 0 0 43 3 . 5 3 2 96 1 0 . 7 5 8 67 8 . 4 2 6 14

2 . 5 4 1 86 1 . 2 1 9 20 1 . 1 8 3 27 1 . 1 6 0 75 0 . 7 8 0 80 0 . 8 1 6 73 0 . 8 3 9 25 0 . 8 5 5 08 1 . 8 6 8 27 1 . 2 7 1 42 0 . 7 2 8 58 0 . 7 8 9 69

0 . 9 5 0 . 2 2 0 80 3 . 1 6 9 99 4 . 1 4 97 2 3 . 0 8 2 86 7 . 7 2 8 58 8 . 7 6 5 68 7 . 8 3 3 66 4 . 9 1 4 24 1 . 0 9 4 31 3 . 4 9 2 04 1 0 . 8 6 3 60 8 . 4 6 5 87

2 . 6 6 0 98 1 . 2 1 9 28 1 . 1 8 4 80 1 . 1 6 2 79 0 . 7 8 0 72 0 . 8 1 5 20 0 . 8 3 7 21 0 . 8 5 2 84 1 . 9 3 3 72 1 . 2 7 6 36 0 . 7 2 3 64 0 . 7 8 5 08

B I BA B3 B 4 B5 B E B7 B E B9

4 . 7 4 9 54 0 . 0 5 9 62 0 . 0 7 9 81 0 . 0 8 8 67 0 . 0 9 3 03 7 . 7 9 9 57 0 . 6 6 7 46 0 . 5 7 3 86 2 . 0 0 0 00

0 . 7 0 8 14 - 1 . 0 5 2 91 - 1 . 4 5 5 38 - 1 . 7 9 9 40 - 2 . 1 0 5 08 0 . 4 8 1 73 - 0 . 6 5 7 96 - 1 . 1 3 9 69 0 . 0 0 0 00

4 . 7 7 9 20 0 . 0 5 0 81 0 . 0 7 0 89 0 . 0 8 0 57 0 . 0 8 5 76 7 . 9 0 5 69 0 . 6 0 2 27 0 . 5 3 4 13 2 . 0 0 0 00

0 . 7 1 4 02 - 1 . 1 6 6 23 - 1 . 5 7 0 31 - 1 . 9 1 7 90 - 2 . 2 2 7 84 0 . 4 9 1 28 - 0 . 7 1 8 79 - 1 . 2 1 0 08 0 . 0 0 0 00

M I

M 3 M4

0 . 0 5 3 54 0 . 0 1 4 16 0 . 0 0 2 96 0 . 0 4 0 90

3 . 0 5 2 91 3 . 4 5 5 38 3 . 7 9 9 40 2 . 6 5 7 96

0 . 0 5 0 62 0 . 0 1 3 71 0 . 0 0 2 90 0 . 0 4 2 10

3 . 1 6 6 23 3 . 5 7 0 31 3 . 9 1 7 90 2 . 7 1 8 79

DATA FOR T W O - G R O U P SYSTEMS

A . B

J / 6 I n t e n s i t y F r e q u e n c y J / 6 I n t e n s i t y F r e q u e n c y

1 . 0 0

A . A5 Ae A7 Ae A9 A , .

0 . 1 9 5 9 1 3 . 1 5 2 2 3 4 . 1 3 6 7 1 3 . 0 7 6 4 7 7 . 7 5 6 3 2 8 . 7 8 6 7 6 7 . 8 4 7 2 1 4 . 9 2 0 6 9 1 . 0 0 0 0 0 3 . 4 5 5 2 1 1 0 . 9 5 7 0 5 8 . 5 0 1 8 4

2 . 7 8 0 7 8 1 . 2 1 9 2 2 1 . 1 8 6 1 4 1 . 1 6 4 6 4 0 . 7 8 0 7 8 0 . 8 1 3 8 6 0 . 8 3 5 3 6 0 . 8 5 0 7 8 2 . 0 0 0 0 0 1 . 2 8 0 7 8 0 . 7 1 9 2 2 0 . 7 8 0 7 8

2 . 0 0 0 . 0 4 0 3 3 3 . 0 3 4 0 3 4 . 0 3 7 2 4 3 . 0 2 3 6 1 7 . 9 4 3 2 0 8 . 9 4 3 5 0 7 . 9 5 5 2 5 4 . 9 7 4 8 7 0 . 2 5 7 3 6 3 . 1 3 7 8 5 1 1 . 7 1 0 6 2 8 . 8 3 0 1 3

5 . 2 3 6 0 7 1 . 2 1 3 4 2 1 . 1 9 6 2 6 1 . 1 8 2 6 8 0 . 7 8 6 5 8 0 . 8 0 3 7 4 0 . 8 1 7 3 2 0 . 8 2 8 4 3 3 . 4 1 4 2 1 1 . 3 1 7 8 4 0 . 6 8 2 1 6 0 . 7 3 2 0 5

B i Ba B3 B . B6 Be B7 B e Be

4 . 8 0 4 0 9 0 . 0 4 3 6 8 0 . 0 6 3 2 9 0 . 0 7 3 4 8 0 . 0 7 9 3 1 8 . 0 0 0 0 0 0 . 5 4 4 7 9 0 . 4 9 8 1 6 2 . 0 0 0 0 0

0 . 7 1 9 2 2 - 1 . 2 8 0 7 8 - 1 . 6 8 6 1 4 - 2 . 0 3 6 9 2 - 2 . 3 5 0 7 8 0 . 5 0 0 0 0 - 0 . 7 8 0 7 8 - 1 . 2 8 0 7 8 0 . 0 0 0 0 0

4 . 9 5 9 6 7 0 . 0 0 6 2 9 0 . 0 1 3 2 7 0 . 0 1 9 6 2 0 . 0 2 5 1 3 8 . 7 4 2 6 4 0 . 1 1 9 5 1 0 . 1 6 9 8 7 2 . 0 0 0 0 0

0 . 7 6 3 9 3 - 3 . 6 8 5 5 6 - 4 . 0 9 5 2 4 - 4 . 4 7 4 1 8 - 4 . 8 2 8 4 3 0 . 5 8 5 7 9 - 2 . 1 4 6 2 6 - 2 . 7 3 2 0 5 0 . 0 0 0 0 0

Mi Ma Ma MA

0 . 0 4 7 7 7 0 . 0 1 3 2 4 0 . 0 0 2 8 4 0 . 0 4 2 9 5

3 . 2 8 0 7 8 3 . 6 8 6 1 4 4 . 0 3 6 9 2 2 . 7 8 0 7 8

0 . 0 1 6 4 8 0 . 0 0 5 9 9 0 . 0 0 1 5 2 0 . 0 3 2 0 2

5 . 6 8 5 5 6 6 . 0 9 5 2 4 6 . 4 7 4 1 8 4 . 1 4 6 2 6

APPENDIX VI

A

B

J/6 Intensity Frequency j/δ Intensity Frequency 0. 01664 7.72311 4.00 0. , 3. 01438 1.20962 3. ,00787 1.20744 00900 10.21699 4. 01683 1.19831 3. 01124 1.18866 7. 97552 0.79038 4. ,00953 1.19905 7. , 3. ,00654 1.19160 98646 0.79256 8. 97462 0.80169 8. 98567 0.80095 7. 97913 0.81134 7. , 98799 0.80840 4. 98790 0.81971 4. ,99291 0.81507 0. 11096 4.88600 0. , 06102 6.37228 3. 06374 1.32621 3. ,03636 1.32928 11. 86954 0.67379 8. 91676 0.71221 11. , 8. , 92629 0.67072 95095 0.70156

4.98336 0.00226 0.00539 0.00876 0.01210 8.88904 0.04722 0.08324 2.00000

0.77689

•6.15584

•6.56377

•6.95075

•7.31971 0.61400

•3.59822

•4.21221 0.00000

4.99100 0.00114 0.00288 0.00492 0.00709 8.93898 0.02466 0.04905 2.00000

0.78301 -8.64142 -9.04790 -9.43855 -9.81507 -5.07384 -5.70156 0.62772 0.00000

0.00784 0.00316 0.00087

0.01951 8.15584 8.56377 8.95075 5.59822 0.00453 0.00193 0.00055 0.01269 10.64142 11.04790 11.43855 7.07 384

D A T A F O R T W O - G R O U P S Y S T E M S

AAB

J / 6 I n t e n s i t y F r e q u e n c y J / 6 I n t e n s i t y F r e q u e n c y

A i A2 A3

* 4 A5 A6 A7 Ae A9 A ,

5 . 0 0 0 . 0 0 5 6 3 1 2 . 7 1 3 4 3 1 0 . 0 0 0 . 0 0 1 3 4 2 5 . 2 0 6 5 6

3 . 0 0 4 9 5 1 . 2 0 6 0 5 3 . 0 0 1 2 0 1 . 2 0 3 1 2

4 . 0 0 6 1 1 1 . 1 9 9 3 9 4 . 0 0 1 5 3 1 . 1 9 9 8 5

3 . 0 0 4 2 7 1 . 1 9 3 3 3 3 . 0 0 1 1 1 1 . 1 9 6 7 3

7 . 9 9 1 4 3 0 . 7 9 3 9 5 7 . 9 9 7 9 0 0 . 7 9 6 8 8

8 . 9 9 0 8 1 0 . 8 0 0 6 1 8 . 9 9 7 7 0 0 . 8 0 0 1 5

7 . 9 9 2 2 1 0 . 8 0 6 6 7 7 . 9 9 8 0 0 0 . 8 0 3 2 7

4 . 9 9 5 3 5 0 . 8 1 2 2 0 4 . 9 9 8 7 8 0 . 8 0 6 2 5

0 . 0 3 8 4 4 7 . 8 6 4 2 1 0 . 0 0 9 2 7 1 5 . 3 4 8 4 7

3 . 0 2 3 4 3 1 . 3 3 0 7 3 3 . 0 0 5 9 1 1 . 3 3 2 6 8

1 1 . 9 5 2 7 4 0 . 6 6 9 2 7 1 1 . 9 8 8 1 6 0 . 6 6 7 3 2

8 . 9 6 7 7 6 0 . 6 9 4 9 3 8 . 9 9 1 5 2 0 . 6 8 1 1 5

B i Ba B3

B4

B5 Be B7 B e B9

4 . 9 9 4 3 7 0 . 0 0 0 6 8 0 . 0 0 1 7 8 0 . 0 0 3 1 4 0 . 0 0 4 6 5 8 . 9 6 1 5 6 0 . 0 1 5 0 2 0 . 0 3 2 2 4 2 . 0 0 0 0 0

0 . 7 8 6 5 7 - 1 1 . 1 3 2 9 1 - 1 1 . 5 3 8 3 5 - 1 1 . 9 3 1 0 7 - 1 2 . 3 1 2 2 0 0 . 6 3 5 7 9 - 6 . 5 5 9 1 4 - 7 . 1 9 4 9 3 0 . 0 0 0 0 0

4 . 9 9 8 6 6 0 . 0 0 0 1 5 0 . 0 0 0 4 1 0 . 0 0 0 7 8 0 . 0 0 1 2 2 8 . 9 9 0 7 3 0 . 0 0 3 3 6 0 . 0 0 8 4 8 2 . 0 0 0 0 0

0 . 7 9 3 4 4 - 2 3 . 6 1 6 2 3 - 2 4 . 0 1 9 1 9 - 2 4 . 4 1 5 7 7 - 2 4 . 8 0 6 2 5 0 . 6 5 1 5 3 - 1 4 . 0 2 9 6 1 - 1 4 . 6 8 1 1 5 0 . 0 0 0 0 0

Mi M2

Ms

0 . 0 0 2 9 4 0 . 0 0 1 2 9 0 . 0 0 0 3 8 0 . 0 0 8 8 2

1 3 . 1 3 2 9 1 1 3 . 5 3 8 3 5 1 3 . 9 3 1 0 7 8 . 5 5 9 1 4

0 . 0 0 0 7 5 0 . 0 0 0 3 5 0 . 0 0 0 1 1 0 . 0 0 2 5 7

2 5 . 6 1 6 2 3 2 6 . 0 1 9 1 9 2 6 . 4 1 5 7 7 1 6 . 0 2 9 6 1

518 APPENDIX

J / 6 I n t e n s i t y F r e q u e n c y

A i Aa A3 A 4 A5 A

e

A7 Ae A9 Αχ ο A n Ax 2

0 . 0 0 0 0 0 3 . 0 0 0 0 0 4 . 0 0 0 0 0 3 . 0 0 0 0 0 8 . 0 0 0 0 0 9 . 0 0 0 0 0 8 . 0 0 0 0 0 5 . 0 0 0 0 0 0 . 0 0 0 0 0 3 . 0 0 0 0 0 1 2 . 0 0 0 0 0 9 . 0 0 0 0 0

1 . 2 0 0 0 0 1 . 2 0 0 0 0 1 . 2 0 0 0 0 0 . 8 0 0 0 0 0 . 8 0 0 0 0 0 . 8 0 0 0 0 0 . 8 0 0 0 0

1 . 3 3 3 3 3 0 . 6 6 6 6 6 0 . 6 6 6 6 6

B i Bs B3 B 4 B5 Β b ; Be B9

5 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 9 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 2 . 0 0 0 0 0

0 . 8 0 0 0 0

0 . 6 6 6 6 6

0 . 0 0 0 0 0

Mi M2 M3 M 4

0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0 0 . 0 0 0 0 0