for marine navigation - madden maritime · for marine navigation latitudes 45°—60°, inclusive...

PUB. NO. 229VOL. 4

SIGHT REDUCTION TABLESFOR

MARINE NAVIGATIONLATITUDES 45°—60°, Inclusive

NATIONAL IMAGERY AND MAPPING AGENCY

Page II

INTERPOLATION TABLE

Altitude Difference (d) DoubleSecond

Diff.andCorr.


Diff.andCorr.

Dec.Inc. Tens Decimals Units


10′ 20′ 30′ 40′ 50′ ⇓ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′ 10′ 20′ 30′ 40′ 50′ ⇓ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′

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 0.1 0.1 8.0 1.3 2.6 4.0 5.3 6.6 .0 0.0 0.1 0.3 0.4 0.6 0.7 0.8 1.0 1.1 1.3

1.64.88.0

11.214.517.720.924.127.330.533.736.9

0.10.20.30.40.50.60.70.80.91.01.1

0.1 0.0 0.0 0.0 0.0 0.1 .1 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.10.048.2

8.1 1.3 2.7 4.0 5.4 6.7 .1 0.0 0.2 0.3 0.4 0.6 0.7 0.9 1.0 1.1 1.30.2 0.0 0.0 0.1 0.1 0.1 .2 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.0 8.2 1.3 2.7 4.1 5.4 6.8 .2 0.0 0.2 0.3 0.5 0.6 0.7 0.9 1.0 1.2 1.30.3 0.0 0.1 0.1 0.2 0.2 .3 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 8.3 1.4 2.8 4.1 5.5 6.9 .3 0.0 0.2 0.3 0.5 0.6 0.8 0.9 1.0 1.2 1.30.4 0.1 0.1 0.2 0.3 0.3 .4 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 8.4 1.4 2.8 4.2 5.6 7.0 .4 0.1 0.2 0.3 0.5 0.6 0.8 0.9 1.0 1.2 1.3

0.5 0.1 0.2 0.3 0.3 0.4 .5 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 8.5 1.4 2.8 4.3 5.7 7.1 .5 0.1 0.2 0.4 0.5 0.6 0.8 0.9 1.1 1.2 1.30.6 0.1 0.2 0.3 0.4 0.5 .6 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1

16.248.6

8.6 1.4 2.9 4.3 5.7 7.2 .6 0.1 0.2 0.4 0.5 0.7 0.8 0.9 1.1 1.2 1.40.7 0.1 0.3 0.4 0.5 0.6 .7 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.1 8.7 1.5 2.9 4.4 5.8 7.3 .7 0.1 0.2 0.4 0.5 0.7 0.8 0.9 1.1 1.2 1.40.8 0.2 0.3 0.4 0.6 0.7 .8 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 8.8 1.5 3.0 4.4 5.9 7.4 .8 0.1 0.3 0.4 0.5 0.7 0.8 1.0 1.1 1.2 1.40.9 0.2 0.3 0.5 0.6 0.8 .9 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 8.9 1.5 3.0 4.5 6.0 7.5 .9 0.1 0.3 0.4 0.6 0.7 0.8 1.0 1.1 1.3 1.4

1.0 0.1 0.3 0.5 0.6 0.8 .0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.2 9.0 1.5 3.0 4.5 6.0 7.5 .0 0.0 0.2 0.3 0.5 0.6 0.8 0.9 1.1 1.3 1.41.1 0.2 0.3 0.5 0.7 0.9 .1 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 9.1 1.5 3.0 4.5 6.0 7.6 .1 0.0 0.2 0.3 0.5 0.6 0.8 1.0 1.1 1.3 1.41.2 0.2 0.4 0.6 0.8 1.0 .2 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2

8.224.641.0

9.2 1.5 3.0 4.6 6.1 7.6 .2 0.0 0.2 0.3 0.5 0.7 0.8 1.0 1.1 1.3 1.51.3 0.2 0.4 0.6 0.9 1.1 .3 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 9.3 1.5 3.1 4.6 6.2 7.7 .3 0.0 0.2 0.4 0.5 0.7 0.8 1.0 1.2 1.3 1.51.4 0.2 0.5 0.7 0.9 1.2 .4 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.1

0.2

9.4 1.6 3.1 4.7 6.3 7.8 .4 0.1 0.2 0.4 0.5 0.7 0.9 1.0 1.2 1.3 1.5

1.44.27.19.9

12.715.518.421.224.026.829.732.535.3

1.5 0.3 0.5 0.8 1.0 1.3 .5 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 9.5 1.6 3.2 4.8 6.3 7.9 .5 0.1 0.2 0.4 0.6 0.7 0.9 1.0 1.2 1.3 1.5

0.10.20.30.40.50.60.70.80.91.01.11.2

1.6 0.3 0.5 0.8 1.1 1.3 .6 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 9.6 1.6 3.2 4.8 6.4 8.0 .6 0.1 0.3 0.4 0.6 0.7 0.9 1.0 1.2 1.4 1.51.7 0.3 0.6 0.9 1.2 1.4 .7 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 9.7 1.6 3.3 4.9 6.5 8.1 .7 0.1 0.3 0.4 0.6 0.7 0.9 1.1 1.2 1.4 1.51.8 0.3 0.6 0.9 1.2 1.5 .8 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 9.8 1.7 3.3 4.9 6.6 8.2 .8 0.1 0.3 0.4 0.6 0.8 0.9 1.1 1.2 1.4 1.61.9 0.4 0.7 1.0 1.3 1.6 .9 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 9.9 1.7 3.3 5.0 6.6 8.3 .9 0.1 0.3 0.5 0.6 0.8 0.9 1.1 1.3 1.4 1.6

2.0 0.3 0.6 1.0 1.3 1.6 .0 0.0 0.0 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.4 10.0 1.6 3.3 5.0 6.6 8.3 .0 0.0 0.2 0.3 0.5 0.7 0.9 1.0 1.2 1.4 1.62.1 0.3 0.7 1.0 1.4 1.7 .1 0.0 0.0 0.1 0.1 0.2 0.2 0.3 0.3 0.3 0.4 10.1 1.7 3.3 5.0 6.7 8.4 .1 0.0 0.2 0.4 0.5 0.7 0.9 1.1 1.2 1.4 1.62.2 0.3 0.7 1.1 1.4 1.8 .2 0.0 0.0 0.1 0.1 0.2 0.2 0.3 0.3 0.3 0.4

5.015.025.035.1

0.10.20.3

10.2 1.7 3.4 5.1 6.8 8.5 .2 0.0 0.2 0.4 0.6 0.7 0.9 1.1 1.3 1.4 1.62.3 0.4 0.8 1.1 1.5 1.9 .3 0.0 0.1 0.1 0.1 0.2 0.2 0.3 0.3 0.3 0.4 10.3 1.7 3.4 5.1 6.9 8.6 .3 0.1 0.2 0.4 0.6 0.8 0.9 1.1 1.3 1.5 1.62.4 0.4 0.8 1.2 1.6 2.0 .4 0.0 0.1 0.1 0.1 0.2 0.2 0.3 0.3 0.3 0.4 10.4 1.7 3.5 5.2 6.9 8.7 .4 0.1 0.2 0.4 0.6 0.8 0.9 1.1 1.3 1.5 1.6

2.5 0.4 0.8 1.3 1.7 2.1 .5 0.0 0.1 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0.4 10.5 1.8 3.5 5.3 7.0 8.8 .5 0.1 0.3 0.4 0.6 0.8 1.0 1.1 1.3 1.5 1.72.6 0.4 0.9 1.3 1.7 2.2 .6 0.0 0.1 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0.4 10.6 1.8 3.5 5.3 7.1 8.8 .6 0.1 0.3 0.5 0.6 0.8 1.0 1.2 1.3 1.5 1.72.7 0.5 0.9 1.4 1.8 2.3 .7 0.0 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.4 0.4 10.7 1.8 3.6 5.4 7.2 8.9 .7 0.1 0.3 0.5 0.6 0.8 1.0 1.2 1.3 1.5 1.72.8 0.5 1.0 1.4 1.9 2.4 .8 0.0 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.4 0.4 10.8 1.8 3.6 5.4 7.2 9.0 .8 0.1 0.3 0.5 0.7 0.8 1.0 1.2 1.4 1.5 1.72.9 0.5 1.0 1.5 2.0 2.5 .9 0.0 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.4 0.4 10.9 1.9 3.7 5.5 7.3 9.1 .9 0.2 0.3 0.5 0.7 0.9 1.0 1.2 1.4 1.6 1.7

3.0 0.5 1.0 1.5 2.0 2.5 .0 0.0 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0.5 0.5 11.0 1.8 3.6 5.5 7.3 9.1 .0 0.0 0.2 0.4 0.6 0.8 1.0 1.1 1.3 1.5 1.71.33.86.38.9

11.414.016.519.021.624.126.729.231.734.3

0.10.20.30.40.50.60.70.80.91.01.11.21.3

3.1 0.5 1.0 1.5 2.0 2.6 .1 0.0 0.1 0.1 0.2 0.2 0.3 0.4 0.4 0.5 0.5

3.610.918.225.532.840.1

0.10.20.30.40.5

11.1 1.8 3.7 5.5 7.4 9.2 .1 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.73.2 0.5 1.0 1.6 2.1 2.6 .2 0.0 0.1 0.1 0.2 0.2 0.3 0.4 0.4 0.5 0.5 11.2 1.8 3.7 5.6 7.4 9.3 .2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.83.3 0.5 1.1 1.6 2.2 2.7 .3 0.0 0.1 0.1 0.2 0.3 0.3 0.4 0.4 0.5 0.5 11.3 1.9 3.8 5.6 7.5 9.4 .3 0.1 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.83.4 0.6 1.1 1.7 2.3 2.8 .4 0.0 0.1 0.1 0.2 0.3 0.3 0.4 0.4 0.5 0.5 11.4 1.9 3.8 5.7 7.6 9.5 .4 0.1 0.3 0.5 0.7 0.8 1.0 1.2 1.4 1.6 1.8

3.5 0.6 1.2 1.8 2.3 2.9 .5 0.0 0.1 0.1 0.2 0.3 0.3 0.4 0.4 0.5 0.6 11.5 1.9 3.8 5.8 7.7 9.6 .5 0.1 0.3 0.5 0.7 0.9 1.1 1.2 1.4 1.6 1.83.6 0.6 1.2 1.8 2.4 3.0 .6 0.0 0.1 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.6 11.6 1.9 3.9 5.8 7.7 9.7 .6 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.6 1.83.7 0.6 1.3 1.9 2.5 3.1 .7 0.0 0.1 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.6 11.7 2.0 3.9 5.9 7.8 9.8 .7 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.93.8 0.7 1.3 1.9 2.6 3.2 .8 0.0 0.1 0.2 0.2 0.3 0.3 0.4 0.5 0.5 0.6 11.8 2.0 4.0 5.9 7.9 9.9 .8 0.2 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.93.9 0.7 1.3 2.0 2.6 3.3 .9 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0.5 0.5 0.6 11.9 2.0 4.0 6.0 8.0 10.0 .9 0.2 0.4 0.6 0.7 0.9 1.1 1.3 1.5 1.7 1.9

4.0 0.6 1.3 2.0 2.6 3.3 .0 0.0 0.1 0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 12.0 2.0 4.0 6.0 8.0 10.0 .0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.5 1.7 1.94.1 0.7 1.3 2.0 2.7 3.4 .1 0.0 0.1 0.2 0.2 0.3 0.4 0.5 0.5 0.6 0.7

2.98.614.420.225.931.737.5

0.10.20.30.40.50.6

12.1 2.0 4.0 6.0 8.0 10.1 .1 0.0 0.2 0.4 0.6 0.9 1.1 1.3 1.5 1.7 1.94.2 0.7 1.4 2.1 2.8 3.5 .2 0.0 0.1 0.2 0.2 0.3 0.4 0.5 0.5 0.6 0.7 12.2 2.0 4.0 6.1 8.1 10.1 .2 0.0 0.2 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.94.3 0.7 1.4 2.1 2.9 3.6 .3 0.0 0.1 0.2 0.2 0.3 0.4 0.5 0.5 0.6 0.7 12.3 2.0 4.1 6.1 8.2 10.2 .3 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.94.4 0.7 1.5 2.2 2.9 3.7 .4 0.0 0.1 0.2 0.3 0.3 0.4 0.5 0.6 0.6 0.7 12.4 2.1 4.1 6.2 8.3 10.3 .4 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 2.0

4.5 0.8 1.5 2.3 3.0 3.8 .5 0.0 0.1 0.2 0.3 0.3 0.4 0.5 0.6 0.6 0.7 12.5 2.1 4.2 6.3 8.3 10.4 .5 0.1 0.3 0.5 0.7 0.9 1.1 1.4 1.6 1.8 2.0 1.23.55.88.1

10.512.815.117.419.822.124.426.729.131.433.736.0

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5

4.6 0.8 1.5 2.3 3.1 3.8 .6 0.0 0.1 0.2 0.3 0.3 0.4 0.5 0.6 0.6 0.7 12.6 2.1 4.2 6.3 8.4 10.5 .6 0.1 0.3 0.5 0.7 1.0 1.2 1.4 1.6 1.8 2.04.7 0.8 1.6 2.4 3.2 3.9 .7 0.1 0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.7 12.7 2.1 4.3 6.4 8.5 10.6 .7 0.1 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.04.8 0.8 1.6 2.4 3.2 4.0 .8 0.1 0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.7 12.8 2.2 4.3 6.4 8.6 10.7 .8 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.04.9 0.9 1.7 2.5 3.3 4.1 .9 0.1 0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.7 12.9 2.2 4.3 6.5 8.6 10.8 .9 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.9 2.1

5.0 0.8 1.6 2.5 3.3 4.1 .0 0.0 0.1 0.2 0.3 0.4 0.5 0.5 0.6 0.7 0.82.47.212.016.821.626.431.236.0

13.0 2.1 4.3 6.5 8.6 10.8 .0 0.0 0.2 0.4 0.7 0.9 1.1 1.3 1.6 1.8 2.05.1 0.8 1.7 2.5 3.4 4.2 .1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.7 0.8

0.10.20.30.40.50.60.7

13.1 2.2 4.3 6.5 8.7 10.9 .1 0.0 0.2 0.5 0.7 0.9 1.1 1.4 1.6 1.8 2.05.2 0.8 1.7 2.6 3.4 4.3 .2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.8 13.2 2.2 4.4 6.6 8.8 11.0 .2 0.0 0.3 0.5 0.7 0.9 1.2 1.4 1.6 1.8 2.15.3 0.9 1.8 2.6 3.5 4.4 .3 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 13.3 2.2 4.4 6.6 8.9 11.1 .3 0.1 0.3 0.5 0.7 1.0 1.2 1.4 1.6 1.9 2.15.4 0.9 1.8 2.7 3.6 4.5 .4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 13.4 2.2 4.5 6.7 8.9 11.2 .4 0.1 0.3 0.5 0.8 1.0 1.2 1.4 1.7 1.9 2.1

5.5 0.9 1.8 2.8 3.7 4.6 .5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 13.5 2.3 4.5 6.8 9.0 11.3 .5 0.1 0.3 0.6 0.8 1.0 1.2 1.5 1.7 1.9 2.15.6 0.9 1.9 2.8 3.7 4.7 .6 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 13.6 2.3 4.5 6.8 9.1 11.3 .6 0.1 0.4 0.6 0.8 1.0 1.3 1.5 1.7 1.9 2.25.7 1.0 1.9 2.9 3.8 4.8 .7 0.1 0.2 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 13.7 2.3 4.6 6.9 9.2 11.4 .7 0.2 0.4 0.6 0.8 1.1 1.3 1.5 1.7 2.0 2.25.8 1.0 2.0 2.9 3.9 4.9 .8 0.1 0.2 0.3 0.3 0.4 0.5 0.6 0.7 0.8 0.9 13.8 2.3 4.6 6.9 9.2 11.5 .8 0.2 0.4 0.6 0.9 1.1 1.3 1.5 1.8 2.0 2.25.9 1.0 2.0 3.0 4.0 5.0 .9 0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7 0.8 0.9 13.9 2.4 4.7 7.0 9.3 11.6 .9 0.2 0.4 0.7 0.9 1.1 1.3 1.6 1.8 2.0 2.2

6.0 1.0 2.0 3.0 4.0 5.0 .0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.8 0.9 1.02.16.210.414.518.622.826.931.135.2

14.0 2.3 4.6 7.0 9.3 11.6 .0 0.0 0.2 0.5 0.7 1.0 1.2 1.4 1.7 1.9 2.2

1.13.25.37.59.6

11.713.916.018.120.322.424.526.728.830.933.135.2

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.6

6.1 1.0 2.0 3.0 4.0 5.1 .1 0.0 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 1.0 0.10.20.30.40.50.60.70.8

14.1 2.3 4.7 7.0 9.4 11.7 .1 0.0 0.3 0.5 0.7 1.0 1.2 1.5 1.7 2.0 2.26.2 1.0 2.0 3.1 4.1 5.1 .2 0.0 0.1 0.2 0.3 0.5 0.6 0.7 0.8 0.9 1.0 14.2 2.3 4.7 7.1 9.4 11.8 .2 0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.7 2.0 2.26.3 1.0 2.1 3.1 4.2 5.2 .3 0.0 0.1 0.2 0.4 0.5 0.6 0.7 0.8 0.9 1.0 14.3 2.4 4.8 7.1 9.5 11.9 .3 0.1 0.3 0.6 0.8 1.0 1.3 1.5 1.8 2.0 2.26.4 1.1 2.1 3.2 4.3 5.3 .4 0.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 14.4 2.4 4.8 7.2 9.6 12.0 .4 0.1 0.3 0.6 0.8 1.1 1.3 1.5 1.8 2.0 2.3

6.5 1.1 2.2 3.3 4.3 5.4 .5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 14.5 2.4 4.8 7.3 9.7 12.1 .5 0.1 0.4 0.6 0.8 1.1 1.3 1.6 1.8 2.1 2.36.6 1.1 2.2 3.3 4.4 5.5 .6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 14.6 2.4 4.9 7.3 9.7 12.2 .6 0.1 0.4 0.6 0.9 1.1 1.4 1.6 1.8 2.1 2.36.7 1.1 2.3 3.4 4.5 5.6 .7 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.1 14.7 2.5 4.9 7.4 9.8 12.3 .7 0.2 0.4 0.7 0.9 1.1 1.4 1.6 1.9 2.1 2.36.8 1.2 2.3 3.4 4.6 5.7 .8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0 1.1 14.8 2.5 5.0 7.4 9.9 12.4 .8 0.2 0.4 0.7 0.9 1.2 1.4 1.6 1.9 2.1 2.46.9 1.2 2.3 3.5 4.6 5.8 .9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.9 1.0 1.1 14.9 2.5 5.0 7.5 10.0 12.5 .9 0.2 0.5 0.7 0.9 1.2 1.4 1.7 1.9 2.2 2.4

7.0 1.1 2.3 3.5 4.6 5.8 .0 0.0 0.1 0.2 0.4 0.5 0.6 0.7 0.9 1.0 1.1 1.85.59.112.816.520.123.827.431.134.7

0.10.20.30.40.50.60.70.80.9

15.0 2.5 5.0 7.5 10.0 12.5 .0 0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 2.1 2.37.1 1.2 2.3 3.5 4.7 5.9 .1 0.0 0.1 0.3 0.4 0.5 0.6 0.8 0.9 1.0 1.1 15.1 2.5 5.0 7.5 10.0 12.6 .1 0.0 0.3 0.5 0.8 1.1 1.3 1.6 1.8 2.1 2.47.2 1.2 2.4 3.6 4.8 6.0 .2 0.0 0.1 0.3 0.4 0.5 0.6 0.8 0.9 1.0 1.1 15.2 2.5 5.0 7.6 10.1 12.6 .2 0.1 0.3 0.6 0.8 1.1 1.3 1.6 1.9 2.1 2.47.3 1.2 2.4 3.6 4.9 6.1 .3 0.0 0.2 0.3 0.4 0.5 0.7 0.8 0.9 1.0 1.2 15.3 2.5 5.1 7.6 10.2 12.7 .3 0.1 0.3 0.6 0.9 1.1 1.4 1.6 1.9 2.1 2.47.4 1.2 2.5 3.7 4.9 6.2 .4 0.0 0.2 0.3 0.4 0.5 0.7 0.8 0.9 1.0 1.2 15.4 2.6 5.1 7.7 10.3 12.8 .4 0.1 0.4 0.6 0.9 1.1 1.4 1.7 1.9 2.2 2.4

7.5 1.3 2.5 3.8 5.0 6.3 .5 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 1.1 1.2 15.5 2.6 5.2 7.8 10.3 12.9 .5 0.1 0.4 0.6 0.9 1.2 1.4 1.7 1.9 2.2 2.57.6 1.3 2.5 3.8 5.1 6.3 .6 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 1.1 1.2 15.6 2.6 5.2 7.8 10.4 13.0 .6 0.2 0.4 0.7 0.9 1.2 1.4 1.7 2.0 2.2 2.57.7 1.3 2.6 3.9 5.2 6.4 .7 0.1 0.2 0.3 0.5 0.6 0.7 0.8 1.0 1.1 1.2 15.7 2.6 5.3 7.9 10.5 13.1 .7 0.2 0.4 0.7 1.0 1.2 1.5 1.7 2.0 2.2 2.57.8 1.3 2.6 3.9 5.2 6.5 .8 0.1 0.2 0.3 0.5 0.6 0.7 0.8 1.0 1.1 1.2 15.8 2.7 5.3 7.9 10.6 13.2 .8 0.2 0.5 0.7 1.0 1.2 1.5 1.8 2.0 2.3 2.57.9 1.4 2.7 4.0 5.3 6.6 .9 0.1 0.2 0.4 0.5 0.6 0.7 0.9 1.0 1.1 1.2 15.9 2.7 5.3 8.0 10.6 13.3 .9 0.2 0.5 0.7 1.0 1.3 1.5 1.8 2.0 2.3 2.6

10′ 20′ 30′ 40′ 50′ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′ 10′ 20′ 30′ 40′ 50′ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′

The Double-Second-Difference correction (Corr.) is always to be added to the tabulated altitude.

INTERPOLATION TABLEAltitude Difference (d) Double

SecondDiff.andCorr.


Diff.andCorr.



10′ 20′ 30′ 40′ 50′ ⇓ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′ 10′ 20′ 30′ 40′ 50′ ⇓ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′

16.0 2.6 5.3 8.0 10.6 13.3 .0 0.0 0.3 0.5 0.8 1.1 1.4 1.6 1.9 2.2 2.5

1.03.04.96.98.910.812.814.816.718.720.722.724.626.628.630.532.534.5

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.7

24.0 4.0 8.0 12.0 16.0 20.0 .0 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.9 3.3 3.7 0.82.54.15.87.49.1

10.712.314.015.617.318.920.622.223.925.527.228.830.432.133.735.4

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.02.1

16.1 2.7 5.3 8.0 10.7 13.4 .1 0.0 0.3 0.6 0.9 1.1 1.4 1.7 2.0 2.2 2.5 24.1 4.0 8.0 12.0 16.0 20.1 .1 0.0 0.4 0.9 1.3 1.7 2.1 2.5 2.9 3.3 3.716.2 2.7 5.4 8.1 10.8 13.5 .2 0.1 0.3 0.6 0.9 1.2 1.4 1.7 2.0 2.3 2.5 24.2 4.0 8.0 12.1 16.1 20.1 .2 0.1 0.5 0.9 1.3 1.7 2.1 2.5 2.9 3.3 3.816.3 2.7 5.4 8.1 10.9 13.6 .3 0.1 0.4 0.6 0.9 1.2 1.5 1.7 2.0 2.3 2.6 24.3 4.0 8.1 12.1 16.2 20.2 .3 0.1 0.5 0.9 1.3 1.8 2.2 2.6 3.0 3.4 3.816.4 2.7 5.5 8.2 10.9 13.7 .4 0.1 0.4 0.7 0.9 1.2 1.5 1.8 2.0 2.3 2.6 24.4 4.1 8.1 12.2 16.3 20.3 .4 0.2 0.6 1.0 1.4 1.8 2.2 2.6 3.0 3.4 3.8

16.5 2.8 5.5 8.3 11.0 13.8 .5 0.1 0.4 0.7 1.0 1.2 1.5 1.8 2.1 2.3 2.6 24.5 4.1 8.2 12.3 16.3 20.4 .5 0.2 0.6 1.0 1.4 1.8 2.2 2.7 3.1 3.5 3.916.6 2.8 5.5 8.3 11.1 13.8 .6 0.2 0.4 0.7 1.0 1.3 1.5 1.8 2.1 2.4 2.6 24.6 4.1 8.2 12.3 16.4 20.5 .6 0.2 0.7 1.1 1.5 1.9 2.3 2.7 3.1 3.5 3.916.7 2.8 5.6 8.4 11.2 13.9 .7 0.2 0.5 0.7 1.0 1.3 1.6 1.8 2.1 2.4 2.7 24.7 4.1 8.3 12.4 16.5 20.6 .7 0.3 0.7 1.1 1.5 1.9 2.3 2.7 3.1 3.6 4.016.8 2.8 5.6 8.4 11.2 14.0 .8 0.2 0.5 0.8 1.0 1.3 1.6 1.9 2.1 2.4 2.7 24.8 4.2 8.3 12.4 16.6 20.7 .8 0.3 0.7 1.1 1.6 2.0 2.4 2.8 3.2 3.6 4.016.9 2.9 5.7 8.5 11.3 14.1 .9 0.2 0.5 0.8 1.1 1.3 1.6 1.9 2.2 2.4 2.7 24.9 4.2 8.3 12.5 16.6 20.8 .9 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0

17.0 2.8 5.6 8.5 11.3 14.1 .0 0.0 0.3 0.6 0.9 1.2 1.5 1.7 2.0 2.3 2.6 25.0 4.1 8.3 12.5 16.6 20.8 .0 0.0 0.4 0.8 1.3 1.7 2.1 2.5 3.0 3.4 3.817.1 2.8 5.7 8.5 11.4 14.2 .1 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 25.1 4.2 8.3 12.5 16.7 20.9 .1 0.0 0.5 0.9 1.3 1.7 2.2 2.6 3.0 3.4 3.917.2 2.8 5.7 8.6 11.4 14.3 .2 0.1 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 25.2 4.2 8.4 12.6 16.8 21.0 .2 0.1 0.5 0.9 1.4 1.8 2.2 2.6 3.1 3.5 3.917.3 2.9 5.8 8.6 11.5 14.4 .3 0.1 0.4 0.7 1.0 1.3 1.5 1.8 2.1 2.4 2.7 25.3 4.2 8.4 12.6 16.9 21.1 .3 0.1 0.6 1.0 1.4 1.8 2.3 2.7 3.1 3.5 4.017.4 2.9 5.8 8.7 11.6 14.5 .4 0.1 0.4 0.7 1.0 1.3 1.6 1.9 2.2 2.4 2.7 25.4 4.2 8.5 12.7 16.9 21.2 .4 0.2 0.6 1.0 1.4 1.9 2.3 2.7 3.1 3.6 4.0

17.5 2.9 5.8 8.8 11.7 14.6 .5 0.1 0.4 0.7 1.0 1.3 1.6 1.9 2.2 2.5 2.8 25.5 4.3 8.5 12.8 17.0 21.3 .5 0.2 0.6 1.1 1.5 1.9 2.3 2.8 3.2 3.6 4.017.6 2.9 5.9 8.8 11.7 14.7 .6 0.2 0.5 0.8 1.0 1.3 1.6 1.9 2.2 2.5 2.8 25.6 4.3 8.5 12.8 17.1 21.3 .6 0.3 0.7 1.1 1.5 2.0 2.4 2.8 3.2 3.7 4.117.7 3.0 5.9 8.9 11.8 14.8 .7 0.2 0.5 0.8 1.1 1.4 1.7 2.0 2.2 2.5 2.8 25.7 4.3 8.6 12.9 17.2 21.4 .7 0.3 0.7 1.1 1.6 2.0 2.4 2.8 3.3 3.7 4.117.8 3.0 6.0 8.9 11.9 14.9 .8 0.2 0.5 0.8 1.1 1.4 1.7 2.0 2.3 2.6 2.9 25.8 4.3 8.6 12.9 17.2 21.5 .8 0.3 0.8 1.2 1.6 2.0 2.5 2.9 3.3 3.7 4.217.9 3.0 6.0 9.0 12.0 15.0 .9 0.3 0.6 0.8 1.1 1.4 1.7 2.0 2.3 2.6 2.9 25.9 4.4 8.7 13.0 17.3 21.6 .9 0.4 0.8 1.2 1.7 2.1 2.5 2.9 3.4 3.8 4.2

0.92.84.66.58.310.212.013.915.717.619.421.323.125.026.828.730.532.334.2

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.8

18.0 3.0 6.0 9.0 12.0 15.0 .0 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.2 2.5 2.8 26.0 4.3 8.6 13.0 17.3 21.6 .0 0.0 0.4 0.9 1.3 1.8 2.2 2.6 3.1 3.5 4.0 0.82.44.05.77.38.9

10.512.113.715.417.018.620.221.823.425.126.728.329.931.533.134.7

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.02.1

18.1 3.0 6.0 9.0 12.0 15.1 .1 0.0 0.3 0.6 1.0 1.3 1.6 1.9 2.2 2.5 2.8 26.1 4.3 8.7 13.0 17.4 21.7 .1 0.0 0.5 0.9 1.4 1.8 2.3 2.7 3.1 3.6 4.018.2 3.0 6.0 9.1 12.1 15.1 .2 0.1 0.4 0.7 1.0 1.3 1.6 1.9 2.2 2.5 2.8 26.2 4.3 8.7 13.1 17.4 21.8 .2 0.1 0.5 1.0 1.4 1.9 2.3 2.7 3.2 3.6 4.118.3 3.0 6.1 9.1 12.2 15.2 .3 0.1 0.4 0.7 1.0 1.3 1.6 1.9 2.3 2.6 2.9 26.3 4.4 8.8 13.1 17.5 21.9 .3 0.1 0.6 1.0 1.5 1.9 2.3 2.8 3.2 3.7 4.118.4 3.1 6.1 9.2 12.3 15.3 .4 0.1 0.4 0.7 1.0 1.4 1.7 2.0 2.3 2.6 2.9 26.4 4.4 8.8 13.2 17.6 22.0 .4 0.2 0.6 1.1 1.5 1.9 2.4 2.8 3.3 3.7 4.2

18.5 3.1 6.2 9.3 12.3 15.4 .5 0.2 0.5 0.8 1.1 1.4 1.7 2.0 2.3 2.6 2.9 26.5 4.4 8.8 13.3 17.7 22.1 .5 0.2 0.7 1.1 1.5 2.0 2.4 2.9 3.3 3.8 4.218.6 3.1 6.2 9.3 12.4 15.5 .6 0.2 0.5 0.8 1.1 1.4 1.7 2.0 2.3 2.7 3.0 26.6 4.4 8.9 13.3 17.7 22.2 .6 0.3 0.7 1.1 1.6 2.0 2.5 2.9 3.4 3.8 4.218.7 3.1 6.3 9.4 12.5 15.6 .7 0.2 0.5 0.8 1.1 1.4 1.8 2.1 2.4 2.7 3.0 26.7 4.5 8.9 13.4 17.8 22.3 .7 0.3 0.8 1.2 1.6 2.1 2.5 3.0 3.4 3.8 4.318.8 3.2 6.3 9.4 12.6 15.7 .8 0.2 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 26.8 4.5 9.0 13.4 17.9 22.4 .8 0.4 0.8 1.2 1.7 2.1 2.6 3.0 3.4 3.9 4.318.9 3.2 6.3 9.5 12.6 15.8 .9 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.1 26.9 4.5 9.0 13.5 18.0 22.5 .9 0.4 0.8 1.3 1.7 2.2 2.6 3.0 3.5 3.9 4.4

19.0 3.1 6.3 9.5 12.6 15.8 .0 0.0 0.3 0.6 1.0 1.3 1.6 1.9 2.3 2.6 2.9 27.0 4.5 9.0 13.5 18.0 22.5 .0 0.0 0.5 0.9 1.4 1.8 2.3 2.7 3.2 3.7 4.119.1 3.2 6.3 9.5 12.7 15.9 .1 0.0 0.4 0.7 1.0 1.3 1.7 2.0 2.3 2.6 3.0 27.1 4.5 9.0 13.5 18.0 22.6 .1 0.0 0.5 1.0 1.4 1.9 2.3 2.8 3.3 3.7 4.219.2 3.2 6.4 9.6 12.8 16.0 .2 0.1 0.4 0.7 1.0 1.4 1.7 2.0 2.3 2.7 3.0 27.2 4.5 9.0 13.6 18.1 22.6 .2 0.1 0.5 1.0 1.5 1.9 2.4 2.8 3.3 3.8 4.219.3 3.2 6.4 9.6 12.9 16.1 .3 0.1 0.4 0.7 1.1 1.4 1.7 2.0 2.4 2.7 3.0 27.3 4.5 9.1 13.6 18.2 22.7 .3 0.1 0.6 1.1 1.5 2.0 2.4 2.9 3.3 3.8 4.319.4 3.2 6.5 9.7 12.9 16.2 .4 0.1 0.5 0.8 1.1 1.4 1.8 2.1 2.4 2.7 3.1 27.4 4.6 9.1 13.7 18.3 22.8 .4 0.2 0.6 1.1 1.6 2.0 2.5 2.9 3.4 3.8 4.3

19.5 3.3 6.5 9.8 13.0 16.3 .5 0.2 0.5 0.8 1.1 1.5 1.8 2.1 2.4 2.8 3.1 27.5 4.6 9.2 13.8 18.3 22.9 .5 0.2 0.7 1.1 1.6 2.1 2.5 3.0 3.4 3.9 4.419.6 3.3 6.5 9.8 13.1 16.3 .6 0.2 0.5 0.8 1.2 1.5 1.8 2.1 2.5 2.8 3.1 27.6 4.6 9.2 13.8 18.4 23.0 .6 0.3 0.7 1.2 1.6 2.1 2.6 3.0 3.5 3.9 4.419.7 3.3 6.6 9.9 13.2 16.4 .7 0.2 0.6 0.9 1.2 1.5 1.9 2.2 2.5 2.8 3.2 27.7 4.6 9.3 13.9 18.5 23.1 .7 0.3 0.8 1.2 1.7 2.2 2.6 3.1 3.5 4.0 4.419.8 3.3 6.6 9.9 13.2 16.5 .8 0.3 0.6 0.9 1.2 1.6 1.9 2.2 2.5 2.9 3.2 27.8 4.7 9.3 13.9 18.6 23.2 .8 0.4 0.8 1.3 1.7 2.2 2.7 3.1 3.6 4.0 4.519.9 3.4 6.7 10.0 13.3 16.6 .9 0.3 0.6 0.9 1.3 1.6 1.9 2.2 2.6 2.9 3.2 27.9 4.7 9.3 14.0 18.6 23.3 .9 0.4 0.9 1.3 1.8 2.2 2.7 3.2 3.6 4.1 4.5

20.0 3.3 6.6 10.0 13.3 16.6 .0 0.0 0.3 0.7 1.0 1.4 1.7 2.0 2.4 2.7 3.1

0.92.64.46.27.99.711.413.214.916.718.520.222.023.725.527.329.030.832.534.3

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.9

28.0 4.6 9.3 14.0 18.6 23.3 .0 0.0 0.5 0.9 1.4 1.9 2.4 2.8 3.3 3.8 4.3 0.82.44.05.67.28.8

10.412.013.615.216.818.420.021.623.224.826.428.029.631.232.834.4

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.02.1

20.1 3.3 6.7 10.0 13.4 16.7 .1 0.0 0.4 0.7 1.1 1.4 1.7 2.1 2.4 2.8 3.1 28.1 4.7 9.3 14.0 18.7 23.4 .1 0.0 0.5 1.0 1.5 1.9 2.4 2.9 3.4 3.8 4.320.2 3.3 6.7 10.1 13.4 16.8 .2 0.1 0.4 0.8 1.1 1.4 1.8 2.1 2.5 2.8 3.1 28.2 4.7 9.4 14.1 18.8 23.5 .2 0.1 0.6 1.0 1.5 2.0 2.5 2.9 3.4 3.9 4.420.3 3.4 6.8 10.1 13.5 16.9 .3 0.1 0.4 0.8 1.1 1.5 1.8 2.2 2.5 2.8 3.2 28.3 4.7 9.4 14.1 18.9 23.6 .3 0.1 0.6 1.1 1.6 2.0 2.5 3.0 3.5 3.9 4.420.4 3.4 6.8 10.2 13.6 17.0 .4 0.1 0.5 0.8 1.2 1.5 1.8 2.2 2.5 2.9 3.2 28.4 4.7 9.5 14.2 18.9 23.7 .4 0.2 0.7 1.1 1.6 2.1 2.6 3.0 3.5 4.0 4.5

20.5 3.4 6.8 10.3 13.7 17.1 .5 0.2 0.5 0.9 1.2 1.5 1.9 2.2 2.6 2.9 3.2 28.5 4.8 9.5 14.3 19.0 23.8 .5 0.2 0.7 1.2 1.7 2.1 2.6 3.1 3.6 4.0 4.520.6 3.4 6.9 10.3 13.7 17.2 .6 0.2 0.5 0.9 1.2 1.6 1.9 2.3 2.6 2.9 3.3 28.6 4.8 9.5 14.3 19.1 23.8 .6 0.3 0.8 1.2 1.7 2.2 2.7 3.1 3.6 4.1 4.620.7 3.5 6.9 10.4 13.8 17.3 .7 0.2 0.6 0.9 1.3 1.6 1.9 2.3 2.6 3.0 3.3 28.7 4.8 9.6 14.4 19.2 23.9 .7 0.3 0.8 1.3 1.8 2.2 2.7 3.2 3.7 4.1 4.620.8 3.5 7.0 10.4 13.9 17.4 .8 0.3 0.6 1.0 1.3 1.6 2.0 2.3 2.7 3.0 3.3 28.8 4.8 9.6 14.4 19.2 24.0 .8 0.4 0.9 1.3 1.8 2.3 2.8 3.2 3.7 4.2 4.720.9 3.5 7.0 10.5 14.0 17.5 .9 0.3 0.6 1.0 1.3 1.7 2.0 2.4 2.7 3.0 3.4 28.9 4.9 9.7 14.5 19.3 24.1 .9 0.4 0.9 1.4 1.9 2.3 2.8 3.3 3.8 4.2 4.7

21.0 3.5 7.0 10.5 14.0 17.5 .0 0.0 0.4 0.7 1.1 1.4 1.8 2.1 2.5 2.9 3.2 29.0 4.8 9.6 14.5 19.3 24.1 .0 0.0 0.5 1.0 1.5 2.0 2.5 2.9 3.4 3.9 4.421.1 3.5 7.0 10.5 14.0 17.6 .1 0.0 0.4 0.8 1.1 1.5 1.8 2.2 2.5 2.9 3.3 29.1 4.8 9.7 14.5 19.4 24.2 .1 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.521.2 3.5 7.0 10.6 14.1 17.6 .2 0.1 0.4 0.8 1.1 1.5 1.9 2.2 2.6 2.9 3.3 29.2 4.8 9.7 14.6 19.4 24.3 .2 0.1 0.6 1.1 1.6 2.1 2.6 3.0 3.5 4.0 4.521.3 3.5 7.1 10.6 14.2 17.7 .3 0.1 0.5 0.8 1.2 1.5 1.9 2.3 2.6 3.0 3.3 29.3 4.9 9.8 14.6 19.5 24.4 .3 0.1 0.6 1.1 1.6 2.1 2.6 3.1 3.6 4.1 4.621.4 3.6 7.1 10.7 14.3 17.8 .4 0.1 0.5 0.9 1.2 1.6 1.9 2.3 2.7 3.0 3.4 29.4 4.9 9.8 14.7 19.6 24.5 .4 0.2 0.7 1.2 1.7 2.2 2.7 3.1 3.6 4.1 4.6

21.5 3.6 7.2 10.8 14.3 17.9 .5 0.2 0.5 0.9 1.3 1.6 2.0 2.3 2.7 3.0 3.4 29.5 4.9 9.8 14.8 19.7 24.6 .5 0.2 0.7 1.2 1.7 2.2 2.7 3.2 3.7 4.2 4.721.6 3.6 7.2 10.8 14.4 18.0 .6 0.2 0.6 0.9 1.3 1.6 2.0 2.4 2.7 3.1 3.4 29.6 4.9 9.9 14.8 19.7 24.7 .6 0.3 0.8 1.3 1.8 2.3 2.8 3.2 3.7 4.2 4.721.7 3.6 7.3 10.9 14.5 18.1 .7 0.3 0.6 1.0 1.3 1.7 2.0 2.4 2.8 3.1 3.5 29.7 5.0 9.9 14.9 19.8 24.8 .7 0.3 0.8 1.3 1.8 2.3 2.8 3.3 3.8 4.3 4.821.8 3.7 7.3 10.9 14.6 18.2 .8 0.3 0.6 1.0 1.4 1.7 2.1 2.4 2.8 3.2 3.5 29.8 5.0 10.0 14.9 19.9 24.9 .8 0.4 0.9 1.4 1.9 2.4 2.9 3.3 3.8 4.3 4.821.9 3.7 7.3 11.0 14.6 18.3 .9 0.3 0.7 1.0 1.4 1.8 2.1 2.5 2.8 3.2 3.5 29.9 5.0 10.0 15.0 20.0 25.0 .9 0.4 0.9 1.4 1.9 2.4 2.9 3.4 3.9 4.4 4.9

22.0 3.6 7.3 11.0 14.6 18.3 .0 0.0 0.4 0.7 1.1 1.5 1.9 2.2 2.6 3.0 3.40.82.54.25.97.69.311.012.714.416.117.819.521.222.824.526.227.929.631.333.034.7

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.0

30.0 5.0 10.0 15.0 20.0 25.0 .0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.6 4.1 4.6 0.82.44.05.67.28.8

10.412.013.615.216.818.420.021.623.224.826.428.029.631.232.834.4

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.02.1

22.1 3.7 7.3 11.0 14.7 18.4 .1 0.0 0.4 0.8 1.2 1.5 1.9 2.3 2.7 3.0 3.4 30.1 5.0 10.0 15.0 20.0 25.1 .1 0.1 0.6 1.1 1.6 2.1 2.6 3.1 3.6 4.1 4.622.2 3.7 7.4 11.1 14.8 18.5 .2 0.1 0.4 0.8 1.2 1.6 1.9 2.3 2.7 3.1 3.4 30.2 5.0 10.0 15.1 20.1 25.1 .2 0.1 0.6 1.1 1.6 2.1 2.6 3.2 3.7 4.2 4.722.3 3.7 7.4 11.1 14.9 18.6 .3 0.1 0.5 0.9 1.2 1.6 2.0 2.4 2.7 3.1 3.5 30.3 5.0 10.1 15.1 20.2 25.2 .3 0.2 0.7 1.2 1.7 2.2 2.7 3.2 3.7 4.2 4.722.4 3.7 7.5 11.2 14.9 18.7 .4 0.1 0.5 0.9 1.3 1.6 2.0 2.4 2.8 3.1 3.5 30.4 5.1 10.1 15.2 20.3 25.3 .4 0.2 0.7 1.2 1.7 2.2 2.7 3.3 3.8 4.3 4.8

22.5 3.8 7.5 11.3 15.0 18.8 .5 0.2 0.6 0.9 1.3 1.7 2.1 2.4 2.8 3.2 3.6 30.5 5.1 10.2 15.3 20.3 25.4 .5 0.3 0.8 1.3 1.8 2.3 2.8 3.3 3.8 4.3 4.822.6 3.8 7.5 11.3 15.1 18.8 .6 0.2 0.6 1.0 1.3 1.7 2.1 2.5 2.8 3.2 3.6 30.6 5.1 10.2 15.3 20.4 25.5 .6 0.3 0.8 1.3 1.8 2.3 2.8 3.4 3.9 4.4 4.922.7 3.8 7.6 11.4 15.2 18.9 .7 0.3 0.6 1.0 1.4 1.8 2.1 2.5 2.9 3.3 3.6 30.7 5.1 10.3 15.4 20.5 25.6 .7 0.4 0.9 1.4 1.9 2.4 2.9 3.4 3.9 4.4 4.922.8 3.8 7.6 11.4 15.2 19.0 .8 0.3 0.7 1.0 1.4 1.8 2.2 2.5 2.9 3.3 3.7 30.8 5.2 10.3 15.4 20.6 25.7 .8 0.4 0.9 1.4 1.9 2.4 2.9 3.5 4.0 4.5 5.022.9 3.9 7.7 11.5 15.3 19.1 .9 0.3 0.7 1.1 1.5 1.8 2.2 2.6 3.0 3.3 3.7 30.9 5.2 10.3 15.5 20.6 25.8 .9 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

23.0 3.8 7.6 11.5 15.3 19.1 .0 0.0 0.4 0.8 1.2 1.6 2.0 2.3 2.7 3.1 3.5 31.0 5.1 10.3 15.5 20.6 25.8 .0 0.0 0.5 1.0 1.6 2.1 2.6 3.1 3.7 4.2 4.723.1 3.8 7.7 11.5 15.4 19.2 .1 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 31.1 5.2 10.3 15.5 20.7 25.9 .1 0.1 0.6 1.1 1.6 2.2 2.7 3.2 3.7 4.3 4.823.2 3.8 7.7 11.6 15.4 19.3 .2 0.1 0.5 0.9 1.3 1.6 2.0 2.4 2.8 3.2 3.6 31.2 5.2 10.4 15.6 20.8 26.0 .2 0.1 0.6 1.2 1.7 2.2 2.7 3.3 3.8 4.3 4.823.3 3.9 7.8 11.6 15.5 19.4 .3 0.1 0.5 0.9 1.3 1.7 2.1 2.5 2.9 3.3 3.6 31.3 5.2 10.4 15.6 20.9 26.1 .3 0.2 0.7 1.2 1.7 2.3 2.8 3.3 3.8 4.4 4.923.4 3.9 7.8 11.7 15.6 19.5 .4 0.2 0.5 0.9 1.3 1.7 2.1 2.5 2.9 3.3 3.7 31.4 5.2 10.5 15.7 20.9 26.2 .4 0.2 0.7 1.3 1.8 2.3 2.8 3.4 3.9 4.4 4.9

23.5 3.9 7.8 11.8 15.7 19.6 .5 0.2 0.6 1.0 1.4 1.8 2.2 2.5 2.9 3.3 3.7 31.5 5.3 10.5 15.8 21.0 26.3 .5 0.3 0.8 1.3 1.8 2.4 2.9 3.4 3.9 4.5 5.023.6 3.9 7.9 11.8 15.7 19.7 .6 0.2 0.6 1.0 1.4 1.8 2.2 2.6 3.0 3.4 3.8 31.6 5.3 10.5 15.8 21.1 26.3 .6 0.3 0.8 1.4 1.9 2.4 2.9 3.5 4.0 4.5 5.023.7 4.0 7.9 11.9 15.8 19.8 .7 0.3 0.7 1.1 1.4 1.8 2.2 2.6 3.0 3.4 3.8 31.7 5.3 10.6 15.9 21.2 26.4 .7 0.4 0.9 1.4 1.9 2.5 3.0 3.5 4.0 4.6 5.123.8 4.0 8.0 11.9 15.9 19.9 .8 0.3 0.7 1.1 1.5 1.9 2.3 2.7 3.1 3.4 3.8 31.8 5.3 10.6 15.9 21.2 26.5 .8 0.4 0.9 1.5 2.0 2.5 3.0 3.6 4.1 4.6 5.123.9 4.0 8.0 12.0 16.0 20.0 .9 0.4 0.7 1.1 1.5 1.9 2.3 2.7 3.1 3.5 3.9 31.9 5.4 10.7 16.0 21.3 26.6 .9 0.5 1.0 1.5 2.0 2.6 3.1 3.6 4.1 4.7 5.2

10′ 20′ 30′ 40′ 50′ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′ 10′ 20′ 30′ 40′ 50′ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′



SecondDiff.andCorr.


Diff.andCorr.



10′ 20′ 30′ 40′ 50′ ⇓ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′ 10′ 20′ 30′ 40′ 50′ ⇓ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′

28.0 4.6 9.3 14.0 18.6 23.3 .0 0.0 0.5 0.9 1.4 1.9 2.4 2.8 3.3 3.8 4.3 0.82.44.05.67.28.810.412.013.615.216.818.420.021.623.224.826.428.029.631.232.834.4

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.02.1

36.0 6.0 12.0 18.0 24.0 30.0 .0 0.0 0.6 1.2 1.8 2.4 3.0 3.6 4.3 4.9 5.50.82.54.25.97.69.3

11.012.714.416.117.819.521.222.824.526.227.929.631.333.034.7

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.0

28.1 4.7 9.3 14.0 18.7 23.4 .1 0.0 0.5 1.0 1.5 1.9 2.4 2.9 3.4 3.8 4.3 36.1 6.0 12.0 18.0 24.0 30.1 .1 0.1 0.7 1.3 1.9 2.5 3.1 3.7 4.3 4.9 5.528.2 4.7 9.4 14.1 18.8 23.5 .2 0.1 0.6 1.0 1.5 2.0 2.5 2.9 3.4 3.9 4.4 36.2 6.0 12.0 18.1 24.1 30.1 .2 0.1 0.7 1.3 1.9 2.6 3.2 3.8 4.4 5.0 5.628.3 4.7 9.4 14.1 18.9 23.6 .3 0.1 0.6 1.1 1.6 2.0 2.5 3.0 3.5 3.9 4.4 36.3 6.0 12.1 18.1 24.2 30.2 .3 0.2 0.8 1.4 2.0 2.6 3.2 3.8 4.4 5.0 5.728.4 4.7 9.5 14.2 18.9 23.7 .4 0.2 0.7 1.1 1.6 2.1 2.6 3.0 3.5 4.0 4.5 36.4 6.1 12.1 18.2 24.3 30.3 .4 0.2 0.9 1.5 2.1 2.7 3.3 3.9 4.5 5.1 5.7

28.5 4.8 9.5 14.3 19.0 23.8 .5 0.2 0.7 1.2 1.7 2.1 2.6 3.1 3.6 4.0 4.5 36.5 6.1 12.2 18.3 24.3 30.4 .5 0.3 0.9 1.5 2.1 2.7 3.3 4.0 4.6 5.2 5.828.6 4.8 9.5 14.3 19.1 23.8 .6 0.3 0.8 1.2 1.7 2.2 2.7 3.1 3.6 4.1 4.6 36.6 6.1 12.2 18.3 24.4 30.5 .6 0.4 1.0 1.6 2.2 2.8 3.4 4.0 4.6 5.2 5.828.7 4.8 9.6 14.4 19.2 23.9 .7 0.3 0.8 1.3 1.8 2.2 2.7 3.2 3.7 4.1 4.6 36.7 6.1 12.3 18.4 24.5 30.6 .7 0.4 1.0 1.6 2.3 2.9 3.5 4.1 4.7 5.3 5.928.8 4.8 9.6 14.4 19.2 24.0 .8 0.4 0.9 1.3 1.8 2.3 2.8 3.2 3.7 4.2 4.7 36.8 6.2 12.3 18.4 24.6 30.7 .8 0.5 1.1 1.7 2.3 2.9 3.5 4.1 4.7 5.4 6.028.9 4.9 9.7 14.5 19.3 24.1 .9 0.4 0.9 1.4 1.9 2.3 2.8 3.3 3.8 4.2 4.7 36.9 6.2 12.3 18.5 24.6 30.8 .9 0.5 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0

29.0 4.8 9.6 14.5 19.3 24.1 .0 0.0 0.5 1.0 1.5 2.0 2.5 2.9 3.4 3.9 4.4 37.0 6.1 12.3 18.5 24.6 30.8 .0 0.0 0.6 1.2 1.9 2.5 3.1 3.7 4.4 5.0 5.629.1 4.8 9.7 14.5 19.4 24.2 .1 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 37.1 6.2 12.3 18.5 24.7 30.9 .1 0.1 0.7 1.3 1.9 2.6 3.2 3.8 4.4 5.1 5.729.2 4.8 9.7 14.6 19.4 24.3 .2 0.1 0.6 1.1 1.6 2.1 2.6 3.0 3.5 4.0 4.5 37.2 6.2 12.4 18.6 24.8 31.0 .2 0.1 0.7 1.4 2.0 2.6 3.2 3.9 4.5 5.1 5.729.3 4.9 9.8 14.6 19.5 24.4 .3 0.1 0.6 1.1 1.6 2.1 2.6 3.1 3.6 4.1 4.6 37.3 6.2 12.4 18.6 24.9 31.1 .3 0.2 0.8 1.4 2.1 2.7 3.3 3.9 4.6 5.2 5.829.4 4.9 9.8 14.7 19.6 24.5 .4 0.2 0.7 1.2 1.7 2.2 2.7 3.1 3.6 4.1 4.6 37.4 6.2 12.5 18.7 24.9 31.2 .4 0.2 0.9 1.5 2.1 2.7 3.4 4.0 4.6 5.2 5.9

29.5 4.9 9.8 14.8 19.7 24.6 .5 0.2 0.7 1.2 1.7 2.2 2.7 3.2 3.7 4.2 4.7 37.5 6.3 12.5 18.8 25.0 31.3 .5 0.3 0.9 1.6 2.2 2.8 3.4 4.1 4.7 5.3 5.929.6 4.9 9.9 14.8 19.7 24.7 .6 0.3 0.8 1.3 1.8 2.3 2.8 3.2 3.7 4.2 4.7 37.6 6.3 12.5 18.8 25.1 31.3 .6 0.4 1.0 1.6 2.2 2.9 3.5 4.1 4.7 5.4 6.029.7 5.0 9.9 14.9 19.8 24.8 .7 0.3 0.8 1.3 1.8 2.3 2.8 3.3 3.8 4.3 4.8 37.7 6.3 12.6 18.9 25.2 31.4 .7 0.4 1.1 1.7 2.3 2.9 3.6 4.2 4.8 5.4 6.129.8 5.0 10.0 14.9 19.9 24.9 .8 0.4 0.9 1.4 1.9 2.4 2.9 3.3 3.8 4.3 4.8 37.8 6.3 12.6 18.9 25.2 31.5 .8 0.5 1.1 1.7 2.4 3.0 3.6 4.2 4.9 5.5 6.129.9 5.0 10.0 15.0 20.0 25.0 .9 0.4 0.9 1.4 1.9 2.4 2.9 3.4 3.9 4.4 4.9 37.9 6.4 12.7 19.0 25.3 31.6 .9 0.6 1.2 1.8 2.4 3.1 3.7 4.3 4.9 5.6 6.2

30.0 5.0 10.0 15.0 20.0 25.0 .0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.6 4.1 4.6 0.82.44.05.67.28.810.412.013.615.216.818.420.021.623.224.826.428.029.631.232.834.4

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.02.1

38.0 6.3 12.6 19.0 25.3 31.6 .0 0.0 0.6 1.3 1.9 2.6 3.2 3.8 4.5 5.1 5.8

0.92.64.46.27.99.7

11.413.214.916.718.520.222.023.725.527.329.030.832.534.3

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.9

30.1 5.0 10.0 15.0 20.0 25.1 .1 0.1 0.6 1.1 1.6 2.1 2.6 3.1 3.6 4.1 4.6 38.1 6.3 12.7 19.0 25.4 31.7 .1 0.1 0.7 1.3 2.0 2.6 3.3 3.9 4.6 5.2 5.830.2 5.0 10.0 15.1 20.1 25.1 .2 0.1 0.6 1.1 1.6 2.1 2.6 3.2 3.7 4.2 4.7 38.2 6.3 12.7 19.1 25.4 31.8 .2 0.1 0.8 1.4 2.1 2.7 3.3 4.0 4.6 5.3 5.930.3 5.0 10.1 15.1 20.2 25.2 .3 0.2 0.7 1.2 1.7 2.2 2.7 3.2 3.7 4.2 4.7 38.3 6.4 12.8 19.1 25.5 31.9 .3 0.2 0.8 1.5 2.1 2.8 3.4 4.0 4.7 5.3 6.030.4 5.1 10.1 15.2 20.3 25.3 .4 0.2 0.7 1.2 1.7 2.2 2.7 3.3 3.8 4.3 4.8 38.4 6.4 12.8 19.2 25.6 32.0 .4 0.3 0.9 1.5 2.2 2.8 3.5 4.1 4.7 5.4 6.0

30.5 5.1 10.2 15.3 20.3 25.4 .5 0.3 0.8 1.3 1.8 2.3 2.8 3.3 3.8 4.3 4.8 38.5 6.4 12.8 19.3 25.7 32.1 .5 0.3 1.0 1.6 2.2 2.9 3.5 4.2 4.8 5.5 6.130.6 5.1 10.2 15.3 20.4 25.5 .6 0.3 0.8 1.3 1.8 2.3 2.8 3.4 3.9 4.4 4.9 38.6 6.4 12.9 19.3 25.7 32.2 .6 0.4 1.0 1.7 2.3 3.0 3.6 4.2 4.9 5.5 6.230.7 5.1 10.3 15.4 20.5 25.6 .7 0.4 0.9 1.4 1.9 2.4 2.9 3.4 3.9 4.4 4.9 38.7 6.5 12.9 19.4 25.8 32.3 .7 0.4 1.1 1.7 2.4 3.0 3.7 4.3 4.9 5.6 6.230.8 5.2 10.3 15.4 20.6 25.7 .8 0.4 0.9 1.4 1.9 2.4 2.9 3.5 4.0 4.5 5.0 38.8 6.5 13.0 19.4 25.9 32.4 .8 0.5 1.2 1.8 2.4 3.1 3.7 4.4 5.0 5.6 6.330.9 5.2 10.3 15.5 20.6 25.8 .9 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 38.9 6.5 13.0 19.5 26.0 32.5 .9 0.6 1.2 1.9 2.5 3.1 3.8 4.4 5.1 5.7 6.4

31.0 5.1 10.3 15.5 20.6 25.8 .0 0.0 0.5 1.0 1.6 2.1 2.6 3.1 3.7 4.2 4.7 39.0 6.5 13.0 19.5 26.0 32.5 .0 0.0 0.7 1.3 2.0 2.6 3.3 3.9 4.6 5.3 5.931.1 5.2 10.3 15.5 20.7 25.9 .1 0.1 0.6 1.1 1.6 2.2 2.7 3.2 3.7 4.3 4.8 39.1 6.5 13.0 19.5 26.0 32.6 .1 0.1 0.7 1.4 2.0 2.7 3.4 4.0 4.7 5.3 6.031.2 5.2 10.4 15.6 20.8 26.0 .2 0.1 0.6 1.2 1.7 2.2 2.7 3.3 3.8 4.3 4.8 39.2 6.5 13.0 19.6 26.1 32.6 .2 0.1 0.8 1.4 2.1 2.8 3.4 4.1 4.7 5.4 6.131.3 5.2 10.4 15.6 20.9 26.1 .3 0.2 0.7 1.2 1.7 2.3 2.8 3.3 3.8 4.4 4.9 39.3 6.5 13.1 19.6 26.2 32.7 .3 0.2 0.9 1.5 2.2 2.8 3.5 4.1 4.8 5.5 6.131.4 5.2 10.5 15.7 20.9 26.2 .4 0.2 0.7 1.3 1.8 2.3 2.8 3.4 3.9 4.4 4.9 39.4 6.6 13.1 19.7 26.3 32.8 .4 0.3 0.9 1.6 2.2 2.9 3.6 4.2 4.9 5.5 6.2

31.5 5.3 10.5 15.8 21.0 26.3 .5 0.3 0.8 1.3 1.8 2.4 2.9 3.4 3.9 4.5 5.0 39.5 6.6 13.2 19.8 26.3 32.9 .5 0.3 1.0 1.6 2.3 3.0 3.6 4.3 4.9 5.6 6.331.6 5.3 10.5 15.8 21.1 26.3 .6 0.3 0.8 1.4 1.9 2.4 2.9 3.5 4.0 4.5 5.0 39.6 6.6 13.2 19.8 26.4 33.0 .6 0.4 1.1 1.7 2.4 3.0 3.7 4.3 5.0 5.7 6.331.7 5.3 10.6 15.9 21.2 26.4 .7 0.4 0.9 1.4 1.9 2.5 3.0 3.5 4.0 4.6 5.1 39.7 6.6 13.3 19.9 26.5 33.1 .7 0.5 1.1 1.8 2.4 3.1 3.8 4.4 5.1 5.7 6.431.8 5.3 10.6 15.9 21.2 26.5 .8 0.4 0.9 1.5 2.0 2.5 3.0 3.6 4.1 4.6 5.1 39.8 6.7 13.3 19.9 26.6 33.2 .8 0.5 1.2 1.8 2.5 3.2 3.8 4.5 5.1 5.8 6.531.9 5.4 10.7 16.0 21.3 26.6 .9 0.5 1.0 1.5 2.0 2.6 3.1 3.6 4.1 4.7 5.2 39.9 6.7 13.3 20.0 26.6 33.3 .9 0.6 1.3 1.9 2.6 3.2 3.9 4.5 5.2 5.9 6.5

32.0 5.3 10.6 16.0 21.3 26.6 .0 0.0 0.5 1.1 1.6 2.2 2.7 3.2 3.8 4.3 4.9 0.82.44.05.77.38.910.512.113.715.417.018.620.221.823.425.126.728.329.931.533.134.7

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.02.1

40.0 6.6 13.3 20.0 26.6 33.3 .0 0.0 0.7 1.3 2.0 2.7 3.4 4.0 4.7 5.4 6.1

0.92.84.66.58.3

10.212.013.915.717.619.421.323.125.026.828.730.532.334.2

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.8

32.1 5.3 10.7 16.0 21.4 26.7 .1 0.1 0.6 1.1 1.7 2.2 2.8 3.3 3.8 4.4 4.9 40.1 6.7 13.3 20.0 26.7 33.4 .1 0.1 0.7 1.4 2.1 2.8 3.4 4.1 4.8 5.5 6.132.2 5.3 10.7 16.1 21.4 26.8 .2 0.1 0.6 1.2 1.7 2.3 2.8 3.4 3.9 4.4 5.0 40.2 6.7 13.4 20.1 26.8 33.5 .2 0.1 0.8 1.5 2.2 2.8 3.5 4.2 4.9 5.5 6.232.3 5.4 10.8 16.1 21.5 26.9 .3 0.2 0.7 1.2 1.8 2.3 2.9 3.4 4.0 4.5 5.0 40.3 6.7 13.4 20.1 26.9 33.6 .3 0.2 0.9 1.6 2.2 2.9 3.6 4.3 4.9 5.6 6.332.4 5.4 10.8 16.2 21.6 27.0 .4 0.2 0.8 1.3 1.8 2.4 2.9 3.5 4.0 4.5 5.1 40.4 6.7 13.5 20.2 26.9 33.7 .4 0.3 0.9 1.6 2.3 3.0 3.6 4.3 5.0 5.7 6.3

32.5 5.4 10.8 16.3 21.7 27.1 .5 0.3 0.8 1.4 1.9 2.4 3.0 3.5 4.1 4.6 5.1 40.5 6.8 13.5 20.3 27.0 33.8 .5 0.3 1.0 1.7 2.4 3.0 3.7 4.4 5.1 5.7 6.432.6 5.4 10.9 16.3 21.7 27.2 .6 0.3 0.9 1.4 1.9 2.5 3.0 3.6 4.1 4.7 5.2 40.6 6.8 13.5 20.3 27.1 33.8 .6 0.4 1.1 1.8 2.4 3.1 3.8 4.5 5.1 5.8 6.532.7 5.5 10.9 16.4 21.8 27.3 .7 0.4 0.9 1.5 2.0 2.5 3.1 3.6 4.2 4.7 5.3 40.7 6.8 13.6 20.4 27.2 33.9 .7 0.5 1.1 1.8 2.5 3.2 3.8 4.5 5.2 5.9 6.532.8 5.5 11.0 16.4 21.9 27.4 .8 0.4 1.0 1.5 2.1 2.6 3.1 3.7 4.2 4.8 5.3 40.8 6.8 13.6 20.4 27.2 34.0 .8 0.5 1.2 1.9 2.6 3.2 3.9 4.6 5.3 5.9 6.632.9 5.5 11.0 16.5 22.0 27.5 .9 0.5 1.0 1.6 2.1 2.7 3.2 3.7 4.3 4.8 5.4 40.9 6.9 13.7 20.5 27.3 34.1 .9 0.6 1.3 2.0 2.6 3.3 4.0 4.7 5.3 6.0 6.7

33.0 5.5 11.0 16.5 22.0 27.5 .0 0.0 0.6 1.1 1.7 2.2 2.8 3.3 3.9 4.5 5.0 41.0 6.8 13.6 20.5 27.3 34.1 .0 0.0 0.7 1.4 2.1 2.8 3.5 4.1 4.8 5.5 6.233.1 5.5 11.0 16.5 22.0 27.6 .1 0.1 0.6 1.2 1.7 2.3 2.8 3.4 4.0 4.5 5.1 41.1 6.8 13.7 20.5 27.4 34.2 .1 0.1 0.8 1.5 2.1 2.8 3.5 4.2 4.9 5.6 6.333.2 5.5 11.0 16.6 22.1 27.6 .2 0.1 0.7 1.2 1.8 2.3 2.9 3.5 4.0 4.6 5.1 41.2 6.8 13.7 20.6 27.4 34.3 .2 0.1 0.8 1.5 2.2 2.9 3.6 4.3 5.0 5.7 6.433.3 5.5 11.1 16.6 22.2 27.7 .3 0.2 0.7 1.3 1.8 2.4 3.0 3.5 4.1 4.6 5.2 41.3 6.9 13.8 20.6 27.5 34.4 .3 0.2 0.9 1.6 2.3 3.0 3.7 4.4 5.0 5.7 6.433.4 5.6 11.1 16.7 22.3 27.8 .4 0.2 0.8 1.3 1.9 2.5 3.0 3.6 4.1 4.7 5.2 41.4 6.9 13.8 20.7 27.6 34.5 .4 0.3 1.0 1.7 2.4 3.0 3.7 4.4 5.1 5.8 6.5

33.5 5.6 11.2 16.8 22.3 27.9 .5 0.3 0.8 1.4 2.0 2.5 3.1 3.6 4.2 4.7 5.3 41.5 6.9 13.8 20.8 27.7 34.6 .5 0.3 1.0 1.7 2.4 3.1 3.8 4.5 5.2 5.9 6.633.6 5.6 11.2 16.8 22.4 28.0 .6 0.3 0.9 1.5 2.0 2.6 3.1 3.7 4.2 4.8 5.4 41.6 6.9 13.9 20.8 27.7 34.7 .6 0.4 1.1 1.8 2.5 3.2 3.9 4.6 5.3 5.9 6.633.7 5.6 11.3 16.9 22.5 28.1 .7 0.4 0.9 1.5 2.1 2.6 3.2 3.7 4.3 4.9 5.4 41.7 7.0 13.9 20.9 27.8 34.8 .7 0.5 1.2 1.9 2.6 3.3 3.9 4.6 5.3 6.0 6.733.8 5.7 11.3 16.9 22.6 28.2 .8 0.4 1.0 1.6 2.1 2.7 3.2 3.8 4.4 4.9 5.5 41.8 7.0 14.0 20.9 27.9 34.9 .8 0.6 1.2 1.9 2.6 3.3 4.0 4.7 5.4 6.1 6.833.9 5.7 11.3 17.0 22.6 28.3 .9 0.5 1.1 1.6 2.2 2.7 3.3 3.9 4.4 5.0 5.5 41.9 7.0 14.0 21.0 28.0 35.0 .9 0.6 1.3 2.0 2.7 3.4 4.1 4.8 5.5 6.2 6.8

34.0 5.6 11.3 17.0 22.6 28.3 .0 0.0 0.6 1.1 1.7 2.3 2.9 3.4 4.0 4.6 5.2 0.82.54.15.87.49.110.712.314.015.617.318.920.622.223.925.527.228.830.432.133.735.4

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.02.1

42.0 7.0 14.0 21.0 28.0 35.0 .0 0.0 0.7 1.4 2.1 2.8 3.5 4.2 5.0 5.7 6.4

1.03.04.96.98.9

10.812.814.816.718.720.722.724.626.628.630.532.534.5

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.7

34.1 5.7 11.3 17.0 22.7 28.4 .1 0.1 0.6 1.2 1.8 2.4 2.9 3.5 4.1 4.7 5.2 42.1 7.0 14.0 21.0 28.0 35.1 .1 0.1 0.8 1.5 2.2 2.9 3.6 4.3 5.0 5.7 6.434.2 5.7 11.4 17.1 22.8 28.5 .2 0.1 0.7 1.3 1.8 2.4 3.0 3.6 4.1 4.7 5.3 42.2 7.0 14.0 21.1 28.1 35.1 .2 0.1 0.8 1.6 2.3 3.0 3.7 4.4 5.1 5.8 6.534.3 5.7 11.4 17.1 22.9 28.6 .3 0.2 0.7 1.3 1.9 2.5 3.0 3.6 4.2 4.8 5.3 42.3 7.0 14.1 21.1 28.2 35.2 .3 0.2 0.9 1.6 2.3 3.0 3.8 4.5 5.2 5.9 6.634.4 5.7 11.5 17.2 22.9 28.7 .4 0.2 0.8 1.4 2.0 2.5 3.1 3.7 4.3 4.8 5.4 42.4 7.1 14.1 21.2 28.3 35.3 .4 0.3 1.0 1.7 2.4 3.1 3.8 4.5 5.2 5.9 6.7

34.5 5.8 11.5 17.3 23.0 28.8 .5 0.3 0.9 1.4 2.0 2.6 3.2 3.7 4.3 4.9 5.5 42.5 7.1 14.2 21.3 28.3 35.4 .5 0.4 1.1 1.8 2.5 3.2 3.9 4.6 5.3 6.0 6.734.6 5.8 11.5 17.3 23.1 28.8 .6 0.3 0.9 1.5 2.1 2.6 3.2 3.8 4.4 4.9 5.5 42.6 7.1 14.2 21.3 28.4 35.5 .6 0.4 1.1 1.8 2.5 3.3 4.0 4.7 5.4 6.1 6.834.7 5.8 11.6 17.4 23.2 28.9 .7 0.4 1.0 1.6 2.1 2.7 3.3 3.9 4.4 5.0 5.6 42.7 7.1 14.3 21.4 28.5 35.6 .7 0.5 1.2 1.9 2.6 3.3 4.0 4.7 5.5 6.2 6.934.8 5.8 11.6 17.4 23.2 29.0 .8 0.5 1.0 1.6 2.2 2.8 3.3 3.9 4.5 5.1 5.6 42.8 7.2 14.3 21.4 28.6 35.7 .8 0.6 1.3 2.0 2.7 3.4 4.1 4.8 5.5 6.2 6.934.9 5.9 11.7 17.5 23.3 29.1 .9 0.5 1.1 1.7 2.2 2.8 3.4 4.0 4.5 5.1 5.7 42.9 7.2 14.3 21.5 28.6 35.8 .9 0.6 1.3 2.1 2.8 3.5 4.2 4.9 5.6 6.3 7.0

35.0 5.8 11.6 17.5 23.3 29.1 .0 0.0 0.6 1.2 1.8 2.4 3.0 3.5 4.1 4.7 5.3 43.0 7.1 14.3 21.5 28.6 35.8 .0 0.0 0.7 1.4 2.2 2.9 3.6 4.3 5.1 5.8 6.535.1 5.8 11.7 17.5 23.4 29.2 .1 0.1 0.7 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 43.1 7.2 14.3 21.5 28.7 35.9 .1 0.1 0.8 1.5 2.2 3.0 3.7 4.4 5.1 5.9 6.635.2 5.8 11.7 17.6 23.4 29.3 .2 0.1 0.7 1.3 1.9 2.5 3.1 3.7 4.3 4.9 5.4 43.2 7.2 14.4 21.6 28.8 36.0 .2 0.1 0.9 1.6 2.3 3.0 3.8 4.5 5.2 5.9 6.735.3 5.9 11.8 17.6 23.5 29.4 .3 0.2 0.8 1.4 2.0 2.5 3.1 3.7 4.3 4.9 5.5 43.3 7.2 14.4 21.6 28.9 36.1 .3 0.2 0.9 1.7 2.4 3.1 3.8 4.6 5.3 6.0 6.735.4 5.9 11.8 17.7 23.6 29.5 .4 0.2 0.8 1.4 2.0 2.6 3.2 3.8 4.4 5.0 5.6 43.4 7.2 14.5 21.7 28.9 36.2 .4 0.3 1.0 1.7 2.5 3.2 3.9 4.6 5.4 6.1 6.8

35.5 5.9 11.8 17.8 23.7 29.6 .5 0.3 0.9 1.5 2.1 2.7 3.3 3.8 4.4 5.0 5.6 43.5 7.3 14.5 21.8 29.0 36.3 .5 0.4 1.1 1.8 2.5 3.3 4.0 4.7 5.4 6.2 6.935.6 5.9 11.9 17.8 23.7 29.7 .6 0.4 0.9 1.5 2.1 2.7 3.3 3.9 4.5 5.1 5.7 43.6 7.3 14.5 21.8 29.1 36.3 .6 0.4 1.2 1.9 2.6 3.3 4.1 4.8 5.5 6.2 7.035.7 6.0 11.9 17.9 23.8 29.8 .7 0.4 1.0 1.6 2.2 2.8 3.4 4.0 4.6 5.1 5.7 43.7 7.3 14.6 21.9 29.2 36.4 .7 0.5 1.2 2.0 2.7 3.4 4.1 4.9 5.6 6.3 7.035.8 6.0 12.0 17.9 23.9 29.9 .8 0.5 1.1 1.7 2.2 2.8 3.4 4.0 4.6 5.2 5.8 43.8 7.3 14.6 21.9 29.2 36.5 .8 0.6 1.3 2.0 2.8 3.5 4.2 4.9 5.7 6.4 7.135.9 6.0 12.0 18.0 24.0 30.0 .9 0.5 1.1 1.7 2.3 2.9 3.5 4.1 4.7 5.3 5.9 43.9 7.4 14.7 22.0 29.3 36.6 .9 0.7 1.4 2.1 2.8 3.6 4.3 5.0 5.7 6.5 7.2

10′ 20′ 30′ 40′ 50′ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′ 10′ 20′ 30′ 40′ 50′ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′



SecondDiff.andCorr.


Diff.andCorr.



10′ 20′ 30′ 40′ 50′ ⇓ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′ 10′ 20′ 30′ 40′ 50′ ⇓ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′

44.0 7.3 14.6 22.0 29.3 36.6 .0 0.0 0.7 1.5 2.2 3.0 3.7 4.4 5.2 5.9 6.7

1.13.25.37.59.611.713.916.018.120.322.424.526.728.830.933.135.2

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.6

52.0 8.6 17.3 26.0 34.6 43.3 .0 0.0 0.9 1.7 2.6 3.5 4.4 5.2 6.1 7.0 7.9 1.85.59.1

12.816.520.123.827.431.134.7

0.10.20.30.40.50.60.70.80.9

44.1 7.3 14.7 22.0 29.4 36.7 .1 0.1 0.8 1.6 2.3 3.0 3.8 4.5 5.3 6.0 6.7 52.1 8.7 17.3 26.0 34.7 43.4 .1 0.1 1.0 1.8 2.7 3.6 4.5 5.3 6.2 7.1 8.044.2 7.3 14.7 22.1 29.4 36.8 .2 0.1 0.9 1.6 2.4 3.1 3.9 4.6 5.3 6.1 6.8 52.2 8.7 17.4 26.1 34.8 43.5 .2 0.2 1.0 1.9 2.8 3.7 4.5 5.4 6.3 7.2 8.044.3 7.4 14.8 22.1 29.5 36.9 .3 0.2 1.0 1.7 2.4 3.2 3.9 4.7 5.4 6.2 6.9 52.3 8.7 17.4 26.1 34.9 43.6 .3 0.3 1.1 2.0 2.9 3.8 4.6 5.5 6.4 7.3 8.144.4 7.4 14.8 22.2 29.6 37.0 .4 0.3 1.0 1.8 2.5 3.3 4.0 4.7 5.5 6.2 7.0 52.4 8.7 17.5 26.2 34.9 43.7 .4 0.3 1.2 2.1 3.0 3.8 4.7 5.6 6.5 7.3 8.2

44.5 7.4 14.8 22.3 29.7 37.1 .5 0.4 1.1 1.9 2.6 3.3 4.1 4.8 5.6 6.3 7.0 52.5 8.8 17.5 26.3 35.0 43.8 .5 0.4 1.3 2.2 3.1 3.9 4.8 5.7 6.6 7.4 8.344.6 7.4 14.9 22.3 29.7 37.2 .6 0.4 1.2 1.9 2.7 3.4 4.2 4.9 5.6 6.4 7.1 52.6 8.8 17.5 26.3 35.1 43.8 .6 0.5 1.4 2.3 3.1 4.0 4.9 5.8 6.6 7.5 8.444.7 7.5 14.9 22.4 29.8 37.3 .7 0.5 1.3 2.0 2.7 3.5 4.2 5.0 5.7 6.5 7.2 52.7 8.8 17.6 26.4 35.2 43.9 .7 0.6 1.5 2.4 3.2 4.1 5.0 5.9 6.7 7.6 8.544.8 7.5 15.0 22.4 29.9 37.4 .8 0.6 1.3 2.1 2.8 3.6 4.3 5.0 5.8 6.5 7.3 52.8 8.8 17.6 26.4 35.2 44.0 .8 0.7 1.6 2.4 3.3 4.2 5.1 5.9 6.8 7.7 8.644.9 7.5 15.0 22.5 30.0 37.5 .9 0.7 1.4 2.2 2.9 3.6 4.4 5.1 5.9 6.6 7.3 52.9 8.9 17.7 26.5 35.3 44.1 .9 0.8 1.7 2.5 3.4 4.3 5.2 6.0 6.9 7.8 8.7

45.0 7.5 15.0 22.5 30.0 37.5 .0 0.0 0.8 1.5 2.3 3.0 3.8 4.5 5.3 6.1 6.8 53.0 8.8 17.6 26.5 35.3 44.1 .0 0.0 0.9 1.8 2.7 3.6 4.5 5.3 6.2 7.1 8.02.16.2

10.414.518.622.826.931.135.2

0.10.20.30.40.50.60.70.8

45.1 7.5 15.0 22.5 30.0 37.6 .1 0.1 0.8 1.6 2.4 3.1 3.9 4.6 5.4 6.1 6.9 53.1 8.8 17.7 26.5 35.4 44.2 .1 0.1 1.0 1.9 2.8 3.7 4.5 5.4 6.3 7.2 8.145.2 7.5 15.0 22.6 30.1 37.6 .2 0.2 0.9 1.7 2.4 3.2 3.9 4.7 5.5 6.2 7.0 53.2 8.8 17.7 26.6 35.4 44.3 .2 0.2 1.1 2.0 2.9 3.7 4.6 5.5 6.4 7.3 8.245.3 7.5 15.1 22.6 30.2 37.7 .3 0.2 1.0 1.7 2.5 3.3 4.0 4.8 5.5 6.3 7.1 53.3 8.9 17.8 26.6 35.5 44.4 .3 0.3 1.2 2.1 2.9 3.8 4.7 5.6 6.5 7.4 8.345.4 7.6 15.1 22.7 30.3 37.8 .4 0.3 1.1 1.8 2.6 3.3 4.1 4.9 5.6 6.4 7.1 53.4 8.9 17.8 26.7 35.6 44.5 .4 0.4 1.2 2.1 3.0 3.9 4.8 5.7 6.6 7.5 8.4

45.5 7.6 15.2 22.8 30.3 37.9 .5 0.4 1.1 1.9 2.7 3.4 4.2 4.9 5.7 6.4 7.2 53.5 8.9 17.8 26.8 35.7 44.6 .5 0.4 1.3 2.2 3.1 4.0 4.9 5.8 6.7 7.6 8.545.6 7.6 15.2 22.8 30.4 38.0 .6 0.5 1.2 2.0 2.7 3.5 4.2 5.0 5.8 6.5 7.3 53.6 8.9 17.9 26.8 35.7 44.7 .6 0.5 1.4 2.3 3.2 4.1 5.0 5.9 6.8 7.7 8.645.7 7.6 15.3 22.9 30.5 38.1 .7 0.5 1.3 2.0 2.8 3.6 4.3 5.1 5.8 6.6 7.4 53.7 9.0 17.9 26.9 35.8 44.8 .7 0.6 1.5 2.4 3.3 4.2 5.1 6.0 6.9 7.8 8.645.8 7.7 15.3 22.9 30.6 38.2 .8 0.6 1.4 2.1 2.9 3.6 4.4 5.2 5.9 6.7 7.4 53.8 9.0 18.0 26.9 35.9 44.9 .8 0.7 1.6 2.5 3.4 4.3 5.2 6.1 7.0 7.8 8.745.9 7.7 15.3 23.0 30.6 38.3 .9 0.7 1.4 2.2 3.0 3.7 4.5 5.2 6.0 6.7 7.5 53.9 9.0 18.0 27.0 36.0 45.0 .9 0.8 1.7 2.6 3.5 4.4 5.3 6.2 7.0 7.9 8.8

46.0 7.6 15.3 23.0 30.6 38.3 .0 0.0 0.8 1.5 2.3 3.1 3.9 4.6 5.4 6.2 7.0 1.23.55.88.110.512.815.117.419.822.124.426.729.131.433.736.0

0.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5

54.0 9.0 18.0 27.0 36.0 45.0 .0 0.0 0.9 1.8 2.7 3.6 4.5 5.4 6.4 7.3 8.2

2.47.2

12.016.821.626.431.236.0

0.10.20.30.40.50.60.7

46.1 7.7 15.3 23.0 30.7 38.4 .1 0.1 0.9 1.6 2.4 3.2 4.0 4.7 5.5 6.3 7.1 54.1 9.0 18.0 27.0 36.0 45.1 .1 0.1 1.0 1.9 2.8 3.7 4.6 5.5 6.4 7.4 8.346.2 7.7 15.4 23.1 30.8 38.5 .2 0.2 0.9 1.7 2.5 3.3 4.0 4.8 5.6 6.4 7.1 54.2 9.0 18.0 27.1 36.1 45.1 .2 0.2 1.1 2.0 2.9 3.8 4.7 5.6 6.5 7.4 8.446.3 7.7 15.4 23.1 30.9 38.6 .3 0.2 1.0 1.8 2.6 3.3 4.1 4.9 5.7 6.4 7.2 54.3 9.0 18.1 27.1 36.2 45.2 .3 0.3 1.2 2.1 3.0 3.9 4.8 5.7 6.6 7.5 8.446.4 7.7 15.5 23.2 30.9 38.7 .4 0.3 1.1 1.9 2.6 3.4 4.2 5.0 5.7 6.5 7.3 54.4 9.1 18.1 27.2 36.3 45.3 .4 0.4 1.3 2.2 3.1 4.0 4.9 5.8 6.7 7.6 8.5

46.5 7.8 15.5 23.3 31.0 38.8 .5 0.4 1.2 1.9 2.7 3.5 4.3 5.0 5.8 6.6 7.4 54.5 9.1 18.2 27.3 36.3 45.4 .5 0.5 1.4 2.3 3.2 4.1 5.0 5.9 6.8 7.7 8.646.6 7.8 15.5 23.3 31.1 38.8 .6 0.5 1.2 2.0 2.8 3.6 4.3 5.1 5.9 6.7 7.4 54.6 9.1 18.2 27.3 36.4 45.5 .6 0.5 1.5 2.4 3.3 4.2 5.1 6.0 6.9 7.8 8.746.7 7.8 15.6 23.4 31.2 38.9 .7 0.5 1.3 2.1 2.9 3.6 4.4 5.2 6.0 6.7 7.5 54.7 9.1 18.3 27.4 36.5 45.6 .7 0.6 1.5 2.5 3.4 4.3 5.2 6.1 7.0 7.9 8.846.8 7.8 15.6 23.4 31.2 39.0 .8 0.6 1.4 2.2 2.9 3.7 4.5 5.3 6.0 6.8 7.6 54.8 9.2 18.3 27.4 36.6 45.7 .8 0.7 1.6 2.5 3.5 4.4 5.3 6.2 7.1 8.0 8.946.9 7.9 15.7 23.5 31.3 39.1 .9 0.7 1.5 2.2 3.0 3.8 4.6 5.3 6.1 6.9 7.7 54.9 9.2 18.3 27.5 36.6 45.8 .9 0.8 1.7 2.6 3.5 4.5 5.4 6.3 7.2 8.1 9.0

47.0 7.8 15.6 23.5 31.3 39.1 .0 0.0 0.8 1.6 2.4 3.2 4.0 4.7 5.5 6.3 7.1 55.0 9.1 18.3 27.5 36.6 45.8 .0 0.0 0.9 1.8 2.8 3.7 4.6 5.5 6.5 7.4 8.3

2.98.6

14.420.225.931.737.5

0.10.20.30.40.50.6

47.1 7.8 15.7 23.5 31.4 39.2 .1 0.1 0.9 1.7 2.5 3.2 4.0 4.8 5.6 6.4 7.2 55.1 9.2 18.3 27.5 36.7 45.9 .1 0.1 1.0 1.9 2.9 3.8 4.7 5.6 6.6 7.5 8.447.2 7.8 15.7 23.6 31.4 39.3 .2 0.2 0.9 1.7 2.5 3.3 4.1 4.9 5.7 6.5 7.3 55.2 9.2 18.4 27.6 36.8 46.0 .2 0.2 1.1 2.0 3.0 3.9 4.8 5.7 6.7 7.6 8.547.3 7.9 15.8 23.6 31.5 39.4 .3 0.2 1.0 1.8 2.6 3.4 4.2 5.0 5.8 6.6 7.4 55.3 9.2 18.4 27.6 36.9 46.1 .3 0.3 1.2 2.1 3.1 4.0 4.9 5.8 6.8 7.7 8.647.4 7.9 15.8 23.7 31.6 39.5 .4 0.3 1.1 1.9 2.7 3.5 4.3 5.1 5.9 6.6 7.4 55.4 9.2 18.5 27.7 36.9 46.2 .4 0.4 1.3 2.2 3.1 4.1 5.0 5.9 6.8 7.8 8.7

47.5 7.9 15.8 23.8 31.7 39.6 .5 0.4 1.2 2.0 2.8 3.6 4.4 5.1 5.9 6.7 7.5

1.33.86.38.911.414.016.519.021.624.126.729.231.734.3

0.10.20.30.40.50.60.70.80.91.01.11.21.3

55.5 9.3 18.5 27.8 37.0 46.3 .5 0.5 1.4 2.3 3.2 4.2 5.1 6.0 6.9 7.9 8.847.6 7.9 15.9 23.8 31.7 39.7 .6 0.5 1.3 2.1 2.8 3.6 4.4 5.2 6.0 6.8 7.6 55.6 9.3 18.5 27.8 37.1 46.3 .6 0.6 1.5 2.4 3.3 4.3 5.2 6.1 7.0 8.0 8.947.7 8.0 15.9 23.9 31.8 39.8 .7 0.6 1.3 2.1 2.9 3.7 4.5 5.3 6.1 6.9 7.7 55.7 9.3 18.6 27.9 37.2 46.4 .7 0.6 1.6 2.5 3.4 4.3 5.3 6.2 7.1 8.0 9.047.8 8.0 16.0 23.9 31.9 39.9 .8 0.6 1.4 2.2 3.0 3.8 4.6 5.4 6.2 7.0 7.8 55.8 9.3 18.6 27.9 37.2 46.5 .8 0.7 1.7 2.6 3.5 4.4 5.4 6.3 7.2 8.1 9.147.9 8.0 16.0 24.0 32.0 40.0 .9 0.7 1.5 2.3 3.1 3.9 4.7 5.5 6.3 7.0 7.8 55.9 9.4 18.7 28.0 37.3 46.6 .9 0.8 1.8 2.7 3.6 4.5 5.5 6.4 7.3 8.2 9.2

48.0 8.0 16.0 24.0 32.0 40.0 .0 0.0 0.8 1.6 2.4 3.2 4.0 4.8 5.7 6.5 7.3 56.0 9.3 18.6 28.0 37.3 46.6 .0 0.0 0.9 1.9 2.8 3.8 4.7 5.6 6.6 7.5 8.5

3.610.918.225.532.840.1

0.10.20.30.40.5

48.1 8.0 16.0 24.0 32.0 40.1 .1 0.1 0.9 1.7 2.5 3.3 4.1 4.9 5.7 6.5 7.4 56.1 9.3 18.7 28.0 37.4 46.7 .1 0.1 1.0 2.0 2.9 3.9 4.8 5.7 6.7 7.6 8.648.2 8.0 16.0 24.1 32.1 40.1 .2 0.2 1.0 1.8 2.6 3.4 4.2 5.0 5.8 6.6 7.4 56.2 9.3 18.7 28.1 37.4 46.8 .2 0.2 1.1 2.1 3.0 4.0 4.9 5.8 6.8 7.7 8.748.3 8.0 16.1 24.1 32.2 40.2 .3 0.2 1.1 1.9 2.7 3.5 4.3 5.1 5.9 6.7 7.5 56.3 9.4 18.8 28.1 37.5 46.9 .3 0.3 1.2 2.2 3.1 4.0 5.0 5.9 6.9 7.8 8.848.4 8.1 16.1 24.2 32.3 40.3 .4 0.3 1.1 1.9 2.7 3.6 4.4 5.2 6.0 6.8 7.6 56.4 9.4 18.8 28.2 37.6 47.0 .4 0.4 1.3 2.3 3.2 4.1 5.1 6.0 7.0 7.9 8.9

48.5 8.1 16.2 24.3 32.3 40.4 .5 0.4 1.2 2.0 2.8 3.6 4.4 5.3 6.1 6.9 7.7 56.5 9.4 18.8 28.3 37.7 47.1 .5 0.5 1.4 2.4 3.3 4.2 5.2 6.1 7.1 8.0 8.948.6 8.1 16.2 24.3 32.4 40.5 .6 0.5 1.3 2.1 2.9 3.7 4.5 5.3 6.1 7.0 7.8 56.6 9.4 18.9 28.3 37.7 47.2 .6 0.6 1.5 2.4 3.4 4.3 5.3 6.2 7.2 8.1 9.048.7 8.1 16.3 24.4 32.5 40.6 .7 0.6 1.4 2.2 3.0 3.8 4.6 5.4 6.2 7.0 7.8 56.7 9.5 18.9 28.4 37.8 47.3 .7 0.7 1.6 2.5 3.5 4.4 5.4 6.3 7.3 8.2 9.148.8 8.2 16.3 24.4 32.6 40.7 .8 0.6 1.5 2.3 3.1 3.9 4.7 5.5 6.3 7.1 7.9 56.8 9.5 19.0 28.4 37.9 47.4 .8 0.8 1.7 2.6 3.6 4.5 5.5 6.4 7.3 8.3 9.248.9 8.2 16.3 24.5 32.6 40.8 .9 0.7 1.5 2.3 3.2 4.0 4.8 5.6 6.4 7.2 8.0 56.9 9.5 19.0 28.5 38.0 47.5 .9 0.8 1.8 2.7 3.7 4.6 5.6 6.5 7.4 8.4 9.3

49.0 8.1 16.3 24.5 32.6 40.8 .0 0.0 0.8 1.6 2.5 3.3 4.1 4.9 5.8 6.6 7.4

1.44.27.19.912.715.518.421.224.026.829.732.535.3

0.10.20.30.40.50.60.70.80.91.01.11.2

57.0 9.5 19.0 28.5 38.0 47.5 .0 0.0 1.0 1.9 2.9 3.8 4.8 5.7 6.7 7.7 8.6

5.015.025.035.1

0.10.20.3

49.1 8.2 16.3 24.5 32.7 40.9 .1 0.1 0.9 1.7 2.6 3.4 4.2 5.0 5.9 6.7 7.5 57.1 9.5 19.0 28.5 38.0 47.6 .1 0.1 1.1 2.0 3.0 3.9 4.9 5.8 6.8 7.8 8.749.2 8.2 16.4 24.6 32.8 41.0 .2 0.2 1.0 1.8 2.6 3.5 4.3 5.1 5.9 6.8 7.6 57.2 9.5 19.0 28.6 38.1 47.6 .2 0.2 1.1 2.1 3.1 4.0 5.0 5.9 6.9 7.9 8.849.3 8.2 16.4 24.6 32.9 41.1 .3 0.2 1.1 1.9 2.7 3.5 4.4 5.2 6.0 6.8 7.7 57.3 9.5 19.1 28.6 38.2 47.7 .3 0.3 1.2 2.2 3.2 4.1 5.1 6.0 7.0 8.0 8.949.4 8.2 16.5 24.7 32.9 41.2 .4 0.3 1.2 2.0 2.8 3.6 4.5 5.3 6.1 6.9 7.8 57.4 9.6 19.1 28.7 38.3 47.8 .4 0.4 1.3 2.3 3.3 4.2 5.2 6.1 7.1 8.0 9.0

49.5 8.3 16.5 24.8 33.0 41.3 .5 0.4 1.2 2.1 2.9 3.7 4.5 5.4 6.2 7.0 7.8 57.5 9.6 19.2 28.8 38.3 47.9 .5 0.5 1.4 2.4 3.4 4.3 5.3 6.2 7.2 8.1 9.149.6 8.3 16.5 24.8 33.1 41.3 .6 0.5 1.3 2.1 3.0 3.8 4.6 5.4 6.3 7.1 7.9 57.6 9.6 19.2 28.8 38.4 48.0 .6 0.6 1.5 2.5 3.4 4.4 5.4 6.3 7.3 8.2 9.249.7 8.3 16.6 24.9 33.2 41.4 .7 0.6 1.4 2.2 3.1 3.9 4.7 5.5 6.4 7.2 8.0 57.7 9.6 19.3 28.9 38.5 48.1 .7 0.7 1.6 2.6 3.5 4.5 5.5 6.4 7.4 8.3 9.349.8 8.3 16.6 24.9 33.2 41.5 .8 0.7 1.5 2.3 3.1 4.0 4.8 5.6 6.4 7.3 8.1 57.8 9.7 19.3 28.9 38.6 48.2 .8 0.8 1.7 2.7 3.6 4.6 5.6 6.5 7.5 8.4 9.449.9 8.4 16.7 25.0 33.3 41.6 .9 0.7 1.6 2.4 3.2 4.0 4.9 5.7 6.5 7.3 8.2 57.9 9.7 19.3 29.0 38.6 48.3 .9 0.9 1.8 2.8 3.7 4.7 5.7 6.6 7.6 8.5 9.5

50.0 8.3 16.6 25.0 33.3 41.6 .0 0.0 0.8 1.7 2.5 3.4 4.2 5.0 5.9 6.7 7.6 58.0 9.6 19.3 29.0 38.6 48.3 .0 0.0 1.0 1.9 2.9 3.9 4.9 5.8 6.8 7.8 8.8

8.224.641.0

0.10.2

50.1 8.3 16.7 25.0 33.4 41.7 .1 0.1 0.9 1.8 2.6 3.5 4.3 5.1 6.0 6.8 7.7 58.1 9.7 19.3 29.0 38.7 48.4 .1 0.1 1.1 2.0 3.0 4.0 5.0 5.9 6.9 7.9 8.950.2 8.3 16.7 25.1 33.4 41.8 .2 0.2 1.0 1.9 2.7 3.5 4.4 5.2 6.1 6.9 7.7 58.2 9.7 19.4 29.1 38.8 48.5 .2 0.2 1.2 2.1 3.1 4.1 5.1 6.0 7.0 8.0 9.050.3 8.4 16.8 25.1 33.5 41.9 .3 0.3 1.1 1.9 2.8 3.6 4.5 5.3 6.1 7.0 7.8 58.3 9.7 19.4 29.1 38.9 48.6 .3 0.3 1.3 2.2 3.2 4.2 5.2 6.1 7.1 8.1 9.150.4 8.4 16.8 25.2 33.6 42.0 .4 0.3 1.2 2.0 2.9 3.7 4.5 5.4 6.2 7.1 7.9 58.4 9.7 19.5 29.2 38.9 48.7 .4 0.4 1.4 2.3 3.3 4.3 5.3 6.2 7.2 8.2 9.2

50.5 8.4 16.8 25.3 33.7 42.1 .5 0.4 1.3 2.1 2.9 3.8 4.6 5.5 6.3 7.2 8.0

1.64.88.011.214.517.720.924.127.330.533.736.9

0.10.20.30.40.50.60.70.80.91.01.1

58.5 9.8 19.5 29.3 39.0 48.8 .5 0.5 1.5 2.4 3.4 4.4 5.4 6.3 7.3 8.3 9.350.6 8.4 16.9 25.3 33.7 42.2 .6 0.5 1.3 2.2 3.0 3.9 4.7 5.6 6.4 7.2 8.1 58.6 9.8 19.5 29.3 39.1 48.8 .6 0.6 1.6 2.5 3.5 4.5 5.5 6.4 7.4 8.4 9.450.7 8.5 16.9 25.4 33.8 42.3 .7 0.6 1.4 2.3 3.1 4.0 4.8 5.6 6.5 7.3 8.2 58.7 9.8 19.6 29.4 39.2 48.9 .7 0.7 1.7 2.6 3.6 4.6 5.6 6.5 7.5 8.5 9.550.8 8.5 17.0 25.4 33.9 42.4 .8 0.7 1.5 2.4 3.2 4.0 4.9 5.7 6.6 7.4 8.2 58.8 9.8 19.6 29.4 39.2 49.0 .8 0.8 1.8 2.7 3.7 4.7 5.7 6.6 7.6 8.6 9.650.9 8.5 17.0 25.5 34.0 42.5 .9 0.8 1.6 2.4 3.3 4.1 5.0 5.8 6.6 7.5 8.3 58.9 9.9 19.7 29.5 39.3 49.1 .9 0.9 1.9 2.8 3.8 4.8 5.8 6.7 7.7 8.7 9.7

51.0 8.5 17.0 25.5 34.0 42.5 .0 0.0 0.9 1.7 2.6 3.4 4.3 5.1 6.0 6.9 7.7 59.0 9.8 19.6 29.5 39.3 49.1 .0 0.0 1.0 2.0 3.0 4.0 5.0 5.9 6.9 7.9 8.9

16.248.6 0.1

51.1 8.5 17.0 25.5 34.0 42.6 .1 0.1 0.9 1.8 2.7 3.5 4.4 5.2 6.1 7.0 7.8 59.1 9.8 19.7 29.5 39.4 49.2 .1 0.1 1.1 2.1 3.1 4.1 5.1 6.0 7.0 8.0 9.051.2 8.5 17.0 25.6 34.1 42.6 .2 0.2 1.0 1.9 2.7 3.6 4.5 5.3 6.2 7.0 7.9 59.2 9.8 19.7 29.6 39.4 49.3 .2 0.2 1.2 2.2 3.2 4.2 5.2 6.1 7.1 8.1 9.151.3 8.5 17.1 25.6 34.2 42.7 .3 0.3 1.1 2.0 2.8 3.7 4.5 5.4 6.3 7.1 8.0 59.3 9.9 19.8 29.6 39.5 49.4 .3 0.3 1.3 2.3 3.3 4.3 5.3 6.2 7.2 8.2 9.251.4 8.6 17.1 25.7 34.3 42.8 .4 0.3 1.2 2.1 2.9 3.8 4.6 5.5 6.4 7.2 8.1 59.4 9.9 19.8 29.7 39.6 49.5 .4 0.4 1.4 2.4 3.4 4.4 5.4 6.3 7.3 8.3 9.3

51.5 8.6 17.2 25.8 34.3 42.9 .5 0.4 1.3 2.1 3.0 3.9 4.7 5.6 6.4 7.3 8.2 59.5 9.9 19.8 29.8 39.7 49.6 .5 0.5 1.5 2.5 3.5 4.5 5.5 6.4 7.4 8.4 9.4

0.048.2 0.0

51.6 8.6 17.2 25.8 34.4 43.0 .6 0.5 1.4 2.2 3.1 3.9 4.8 5.7 6.5 7.4 8.2 59.6 9.9 19.9 29.8 39.7 49.7 .6 0.6 1.6 2.6 3.6 4.6 5.6 6.5 7.5 8.5 9.551.7 8.6 17.3 25.9 34.5 43.1 .7 0.6 1.5 2.3 3.2 4.0 4.9 5.8 6.6 7.5 8.3 59.7 10.0 19.9 29.9 39.8 49.8 .7 0.7 1.7 2.7 3.7 4.7 5.7 6.6 7.6 8.6 9.651.8 8.7 17.3 25.9 34.6 43.2 .8 0.7 1.5 2.4 3.3 4.1 5.0 5.8 6.7 7.6 8.4 59.8 10.0 20.0 29.9 39.9 49.9 .8 0.8 1.8 2.8 3.8 4.8 5.8 6.7 7.7 8.7 9.751.9 8.7 17.3 26.0 34.6 43.3 .9 0.8 1.6 2.5 3.3 4.2 5.1 5.9 6.8 7.6 8.5 59.9 10.0 20.0 30.0 40.0 50.0 .9 0.9 1.9 2.9 3.9 4.9 5.9 6.8 7.8 8.8 9.8

10′ 20′ 30′ 40′ 50′ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′ 10′ 20′ 30′ 40′ 50′ 0′ 1′ 2′ 3′ 4′ 5′ 6′ 7′ 8′ 9′


III

PREFACE

This six-volume series ofSight Reduction Tables for Marine Navigationis designed to facilitate thepractice of celestial navigation at sea by the Marcq Saint Hilaire or intercept method.

The tabular data are the solutions of the navigational triangle of which two sides and the included angleare known and it is necessary to find the values of the third side and adjacent angle.

The tables, intended for use withThe Nautical Almanac, are designed for precise interpolation ofaltitude for declination by means of interpolation tables which facilitate linear interpolation and provideadditionally for the effect of second differences when required.

The diagrams for additional interpolation of the altitude for latitude and local hour angle increments,which were in each volume of the first printing of the tables, have been omitted from the reprint of thisvolume.

The concept, design, development, and preparation of these tables are the results of the collaborativeefforts and joint accomplishments of the National Imagery and Mapping Agency, the U.S. NavalObservatory, and Her Majesty’s Nautical Almanac Office, Royal Greenwich Observatory. The tabularmaterial in identical format has been published in the United Kingdom by the Hydrographic Department,Ministry of Defence (Navy), as N.P. 401.

This reprint was compiled on a Hewlett Packard K420 server with an HP C180 client workstation, and wascomposed in its entirety as a digital document.

Users should refer corrections, additions, and comments for improving this product to:

MARITIME SAFETY INFORMATION CENTERST D 44NATIONAL IMAGERY AND MAPPING AGENCY4600 SANGAMORE ROADBETHESDA MD 20816-5003

IV

CONTENTS

PagePREFACE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .IIIINTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .V

A. DESCRIPTION OF TABLES1. Purpose and Scope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .V2. Arrangement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .V

B. INTERPOLATION1. Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .X2. First and Second Differences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .X3. Linear Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .X4. The Interpolation Table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XI5. Interpolation when Second Differences are Required. . . . . . . . . . . . . . . . . . . . . . . . .XIII

C. SPECIAL TECHNIQUES1. Adjustment of Straight Line of Position. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XV2. Interpolation for Latitude and Local Hour Angle . . . . . . . . . . . . . . . . . . . . . . . . . . .XVII3. Interpolation near the Horizon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XVII4. Negative Altitudes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XVIII5. Interpolation near the Zenith. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XVIII

D. OTHER APPLICATIONS1. Star Identification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XIX2. Great-Circle Sailing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XX3. Points along Great Circle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XXIII4. General Spherical Triangle Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XXIII5. Compass Error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XXIV

E. BACKGROUND1. Accuracy of Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XXV2. Computation Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XXV

F. GLOSSARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XXVIG. EXAMPLE SIGHT REDUCTIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XXIX

TABLE OF OFFSETS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XVISIGHT REDUCTION TABLES

Latitudes 45° to 52° . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-183Latitudes 53° to 60° . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184-365

INTERPOLATION TABLEDeclination Increment0.0′ to 31.9′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inside front coverDeclination Increment28.0′ to 59.9′. . . . . . . . . . . . . . . . . . . . . . . . . . . . .Inside back cover

V

INTRODUCTION

A. DESCRIPTION OF TABLES

1. Purpose and Scope.The main purpose of these tables is to facilitate the practice of celestialnavigation at sea. A secondary purpose is to provide, within the limitations of the tabular precision andinterval, a table of the solutions of a spherical triangle of which two sides and the included angle are knownand it is necessary to find the values of the third side and adjacent angle.

The tables have been designed primarily for use with the Marcq Saint Hilaire or intercept method ofsight reduction, utilizing a position assumed or chosen so that interpolation for latitude and local hour angleis not required.

For entering arguments of integral degrees of latitude, declination, and local hour angle, altitudes andtheir differences are tabulated to the nearest tenth of a minute, azimuth angles to the nearest tenth of adegree. But the tables are designed for precise interpolation of altitude for declination only by means ofinterpolation tables which facilitate linear interpolation and provide additionally for the effect of seconddifferences.

The data are applicable to the solutions of sights of all celestial bodies; there are no limiting values ofaltitude, latitude, hour angle, or declination.

2. Arrangement. The tables are divided into six volumes, each of which includes two eight-degreezones of latitude. An overlap of 1° occurs between volumes. The six volumes cover latitude bands 0° to15°, 15° to 30°, 30° to 45°, 45° to 60°, 60° to 75°, and 75° to 90°.

Each consecutive opening of the pages of a latitude zone differs from the preceding one by 1° of localhour angle (LHA). As shown in figures 1 and 2, the values of LHA are prominently displayed at the top andbottom of each page; the horizontal argument heading each column is latitude, and the vertical argument isdeclination.

For each combination of arguments, the tabulations are: the tabular altitude (ht or Tab. Hc), the altitudedifference (d) with its sign, and the azimuth angle (Z).

Within each opening, the data on the left-hand page are the altitudes, altitude differences, and azimuthangles of celestial bodies when the latitude of the observer has the same name as the declinations of thebodies. For any LHA tabulated on a left-hand page and any combination of the tabular latitude anddeclination arguments, the tabular altitude and associated azimuth angle respondents on the left-hand pageare those of a body above the celestial horizon of the observer.

The LHA’s tabulated on the left-hand pages are limited to the following ranges: 0° increasing to 90°and 360° decreasing to 270°. On any left-hand page there are two tabulated LHA’s, one LHA in the range0° increasing to 90° and the second in the range 360° decreasing to 270°.

On the right-hand page of each opening, the data above the horizontal rules are the tabular altitudes,altitude differences, and azimuth angles of celestial bodies above the celestial horizon when the latitude ofthe observer has a name contrary to the name of the declinations of the bodies and the LHA’s of the bodiesare those tabulated at the top of the page. The data below the horizontal rules are the tabular altitudes,altitude differences, and azimuth angles of celestial bodies above the celestial horizon when the latitude ofthe observer has the same name as the declinations of the bodies and the LHA’s of the bodies are thosetabulated at the bottom of the page.

The LHA’s tabulated at the top of a right-hand page are the same as those tabulated on the left-handpage of the opening. The LHA’s tabulated at the bottom of the right-hand page are limited to the range 90°increasing to 270°; one of the two LHA’s at the bottom of the page is in the range 90° increasing to 180°;the other LHA is in the range 180° increasing to 270°; the LHA in the range 90° increasing to 180° is thesupplement of the LHA at the top of the page in the range 0° increasing to 90°. When the LHA is 90°, theleft and right-hand pages are identical.

The horizontal rules, known as the Contrary-Same Line or C-S Line, indicate the degree of declinationin which the celestial horizon occurs.

60°, 300° L.H.A.

FIGURE1VI

60°, 300° L.H.A. LATITUDE SAME NAME AS DECLINATION

L.H.A. greater than 180° .....Zn=ZL.H.A. less than 180°.............Zn=360°–ZLATITUDE SAME NAME AS DECLINATION N. Lat. {

INTRODUCTION

45° 46° 47° 48° 49° 50° 51° 52° Dec. 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22.3 – 9.1 28.2 54 15.0 – 8.3 28.9 55 07.4 – 7.5 29.5 55 59.4 – 6.6 30.3 56 51.0 – 5.6 31.0 57 42.2 – 4.7 31.9 71 72 51 25.3 – 12.0 25.4 52 19.3 – 11.2 26.0 53 13.2 – 10.6 26.5 54 06.7 – 9.8 27.2 54 59.9 – 9.0 27.8 55 52.8 – 8.1 28.5 56 45.4 – 7.3 29.2 57 37.5 – 6.3 30.0 72 73 51 13.3 – 13.2 23.8 52 08.1 – 12.6 24.4 53 02.6 – 11.8 24.9 53 56.9 – 11.1 25.5 54 50.9 – 10.4 26.1 55 44.7 – 9.7 26.7 56 38.1 – 8.8 27.4 57 31.2 – 8.0 28.1 73 74 51 00.1 – 14.4 22.3 51 55.5 – 13.8 22.8 52 50.8 – 13.2 23.3 53 45.8 – 12.6 23.8 54 40.5 – 11.8 24.4 55 35.0 – 11.1 25.0 56 29.3 – 10.4 25.6 57 23.2 – 9.5 26.3 74 75 50 45.7 – 15.6 20.8 51 41.7 – 15.1 21.2 52 37.6 – 14.5 21.7 53 33.2 – 13.9 22.2 54 28.7 – 13.3 22.7 55 23.9 – 12.5 23.2 56 18.9 – 11.8 23.8 57 13.7 – 11.1 24.5 75 76 50 30.1 – 16.9 19.2 51 26.6 – 16.3 19.6 52 23.1 – 15.8 20.1 53 19.3 – 15.2 20.5 54 15.4 – 14.6 21.0 55 11.4 – 14.1 21.5 56 07.1 – 13.4 22.1 57 02.6 – 12.7 22.7 76 77 50 13.2 – 17.9 17.7 51 10.3 – 17.5 18.1 52 07.3 – 17.0 18.5 53 04.1 – 16.5 18.9 54 00.8 – 16.0 19.4 54 57.3 – 15.4 19.8 55 53.7 – 14.8 20.3 56 49.9 – 14.2 20.9 77 78 49 55.3 – 19.1 16.2 50 52.8 – 18.6 16.6 51 50.3 – 18.2 16.9 52 47.6 – 17.7 17.3 53 44.8 – 17.2 17.7 54 41.9 – 16.8 18.2 55 38.9 – 16.3 18.6 56 35.7 – 15.7 19.1 78 79 49 36.2 – 20.2 14.8 50 34.2 – 19.8 15.1 51 32.1 – 19.4 15.4 52 29.9 – 19.0 15.7 53 27.6 – 18.6 16.1 54 25.1 – 18.1 16.5 55 22.6 – 17.6 16.9 56 20.0 – 17.2 17.3 79 80 49 16.0 – 21.2 13.3 50 14.4 – 21.0 13.6 51 12.7 – 20.6 13.9 52 10.9 – 20.3 14.2 53 09.0 – 19.8 14.5 54 07.0 – 19.4 14.9 55 05.0 – 19.0 15.2 56 02.8 – 18.6 15.6 80 81 48 54.8 – 22.3 11.9 49 53.4 – 22.0 12.1 50 52.1 – 21.7 12.4 51 50.6 – 21.3 12.7 52 49.2 – 21.1 13.0 53 47.6 – 20.7 13.3 54 46.0 – 20.4 13.6 55 44.2 – 19.9 13.9 81 82 48 32.5 – 23.3 10.5 49 31.4 – 23.0 10.7 50 30.4 – 22.8 10.9 51 29.3 – 22.6 11.2 52 28.1 – 22.2 11.4 53 26.9 – 21.9 11.7 54 25.6 – 21.6 12.0 55 24.3 – 21.3 12.3 82 83 48 09.2 – 24.3 9.1 49 08.4 – 24.1 9.3 50 07.6 – 23.9 9.5 51 06.7 – 23.6 9.7 52 05.9 – 23.4 9.9 53 05.0 – 23.2 10.1 54 04.0 – 22.9 10.4 55 03.0 – 22.6 10.6 83 84 47 44.9 – 25.3 7.7 48 44.3 – 25.1 7.9 49 43.7 – 24.9 8.1 50 43.1 – 24.7 8.2 51 42.5 – 24.5 8.4 52 41.8 – 24.3 8.6 53 41.1 – 24.0 8.8 54 40.4 – 23.8 9.0 84 85 47 19.6 – 26.2 6.4 48 19.2 – 26.0 6.5 49 18.8 – 25.9 6.6 50 18.4 – 25.7 6.8 51 18.0 – 25.6 6.9 52 17.5 – 25.4 7.1 53 17.1 – 25.3 7.3 54 16.6 – 25.1 7.4 85 86 46 53.4 – 27.1 5.1 47 53.2 – 27.0 5.2 48 52.9 – 26.8 5.3 49 52.7 – 26.8 5.4 50 52.4 – 26.6 5.5 51 52.1 – 26.5 5.6 52 51.8 – 26.3 5.7 53 51.5 – 26.2 5.9 86 87 46 26.3 – 27.9 3.8 47 26.2 – 27.9 3.8 48 26.1 – 27.8 3.9 49 25.9 – 27.7 4.0 50 25.8 – 27.7 4.1 51 25.6 – 27.5 4.2 52 25.5 – 27.5 4.3 53 25.3 – 27.4 4.4 87 88 45 58.4 – 28.8 2.5 46 58.3 – 28.7 2.5 47 58.3 – 28.7 2.6 48 58.2 – 28.6 2.6 49 58.1 – 28.6 2.7 50 58.1 – 28.6 2.8 51 58.0 – 28.5 2.8 52 57.9 – 28.4 2.9 88 89 45 29.6 – 29.6 1.2 46 29.6 – 29.6 1.3 47 29.6 – 29.6 1.3 48 29.6 – 29.6 1.3 49 29.5 – 29.5 1.3 50 29.5 – 29.5 1.4 51 29.5 – 29.5 1.4 52 29.5 – 29.5 1.4 89

90 45 00.0 – 30.4 0.0 46 00.0 – 30.4 0.0 47 00.0 – 30.4 0.0 48 00.0 – 30.4 0.0 49 00.0 – 30.4 0.0 50 00.0 – 30.5 0.0 51 00.0 – 30.5 0.0 52 00.0 – 30.5 0.0 90

45° 46° 47° 48° 49° 50° 51° 52°

L.H.A. 60°, 300°

L.H.A. 120°, 240°LATITUDE SAME NAME AS DECLINATIONL.H.A. greater than 180° ....Zn=180°–ZL.H.A. less than 180°............Zn=180°+Z

LATITUDE CONTRARY NAME TO DECLINATION

S. Lat. {

A. DESCRIPTION OF TABLES

FIGURE2VII

45° 46° 47° 48° 49° 50° 51° 52° Dec. Hc d Z Hc d Z Hc d Z Hc d Z Hc d Z Hc d Z Hc d Z Hc d Z Dec. ° ° ′ ′ ° ° ′ ′ ° ° ′ ′ ° ° ′ ′ ° ° ′ ′ ° ° ′ ′ ° ° ′ ′ ° ° ′ ′ ° ° 0 20 42.3 – 45.5 112.2 20 19.4 – 46.1 112.6 19 56.3 – 46.8 112.9 19 32.8 – 47.4 113.2 19 09.0 – 48.0 113.5 18 44.8 – 48.6 113.9 18 20.4 – 49.2 114.2 17 55.7 – 49.7 114.5 0 1 19 56.8 – 45.6 112.9 19 33.3 – 46.2 113.2 19 09.5 – 46.9 113.6 18 45.4 – 47.5 113.9 18 21.0 – 48.2 114.2 17 56.2 – 48.7 114.5 17 31.2 – 49.3 114.8 17 06.0 – 49.9 115.0 1 2 19 11.2 – 45.7 113.6 18 47.1 – 46.4 113.9 18 22.6 – 47.0 114.2 17 57.9 – 47.7 114.5 17 32.8 – 48.2 114.8 17 07.5 – 48.8 115.1 16 41.9 – 49.3 115.4 16 16.1 – 49.9 115.6 2 3 18 25.5 – 45.9 114.3 18 00.7 – 46.6 114.6 17 35.6 – 47.2 114.9 17 10.2 – 47.7 115.2 16 44.6 – 48.4 115.4 16 18.7 – 48.9 115.7 15 52.6 – 49.5 116.0 15 26.2 – 50.0 116.2 3 4 17 39.6 – 46.0 115.0 17 14.1 – 46.6 115.2 16 48.4 – 47.2 115.5 16 22.5 – 47.9 115.8 15 56.2 – 48.4 116.0 15 29.8 – 49.1 116.3 15 03.1 – 49.6 116.5 14 36.2 – 50.2 116.8 4 5 16 53.6 – 46.2 115.6 16 27.5 – 46.8 115.9 16 01.2 – 47.4 116.2 15 34.6 – 48.0 116.4 15 07.8 – 48.6 116.7 14 40.7 – 49.1 116.9 14 13.5 – 49.7 117.1 13 46.0 – 50.1 117.3 5 6 16 07.4 – 46.3 116.3 15 40.7 – 46.9 116.5 15 13.8 – 47.5 116.8 14 46.6 – 48.1 117.0 14 19.2 – 48.6 117.3 13 51.6 – 49.2 117.5 13 23.8 – 49.7 117.7 12 55.9 – 50.3 117.9 6 7 15 21.1 – 46.4 117.0 14 53.8 – 47.0 117.2 14 26.3 – 47.6 117.4 13 58.5 – 48.1 117.7 13 30.6 – 48.8 117.9 13 02.4 – 49.2 118.1 12 34.1 – 49.8 118.3 12 05.6 – 50.3 118.5 7 8 14 34.7 – 46.5 117.6 14 06.8 – 47.1 117.8 13 38.7 – 47.7 118.1 13 10.4 – 48.3 118.3 12 41.8 – 48.8 118.5 12 13.2 – 49.4 118.7 11 44.3 – 49.9 118.8 11 15.3 – 50.4 119.0 8 9 13 48.2 – 46.6 118.3 13 19.7 – 47.2 118.5 12 51.0 – 47.8 118.7 12 22.1 – 48.3 118.9 11 53.0 – 48.9 119.1 11 23.8 – 49.4 119.2 10 54.4 – 49.9 119.4 10 24.9 – 50.5 119.6 9 10 13 01.6 – 46.7 118.9 12 32.5 – 47.3 119.1 12 03.2 – 47.9 119.3 11 33.8 – 48.5 119.5 11 04.1 – 48.9 119.7 10 34.4 – 49.5 119.8 10 04.5 – 50.0 120.0 9 34.4 – 50.5 120.1 10 11 12 14.9 – 46.9 119.6 11 45.2 – 47.4 119.7 11 15.3 – 47.9 119.9 10 45.3 – 48.4 120.1 10 15.2 – 49.0 120.2 9 44.9 – 49.5 120.4 9 14.5 – 50.1 120.5 8 43.9 – 50.5 120.7 11 12 11 28.0 – 46.8 120.2 10 57.8 – 47.5 120.4 10 27.4 – 48.0 120.5 9 56.9 – 48.6 120.7 9 26.2 – 49.1 120.8 8 55.4 – 49.6 121.0 8 24.4 – 50.1 121.1 7 53.4 – 50.6 121.2 12 13 10 41.2 – 47.0 120.8 10 10.3 – 47.5 121.0 9 39.4 – 48.1 121.1 9 08.3 – 48.6 121.3 8 37.1 – 49.1 121.4 8 05.8 – 49.7 121.5 7 34.3 – 50.1 121.7 7 02.8 – 50.6 121.8 13 14 9 54.2 – 47.0 121.5 9 22.8 – 47.6 121.6 8 51.3 – 48.1 121.7 8 19.7 – 48.7 121.9 7 48.0 – 49.2 122.0 7 16.1 – 49.7 122.1 6 44.2 – 50.2 122.2 6 12.2 – 50.7 122.3 14 15 9 07.2 – 47.1 122.1 8 35.2 – 47.6 122.2 8 03.2 – 48.2 122.3 7 31.0 – 48.7 122.5 6 58.8 – 49.2 122.6 6 26.4 – 49.7 122.7 5 54.0 – 50.2 122.8 5 21.5 – 50.7 122.8 15 16 8 20.1 – 47.2 122.7 7 47.6 – 47.7 122.8 7 15.0 – 48.2 122.9 6 42.3 – 48.7 123.0 6 09.6 – 49.3 123.1 5 36.7 – 49.7 123.2 5 03.8 – 50.2 123.3 4 30.8 – 50.7 123.4 16 17 7 32.9 – 47.2 123.3 6 59.9 – 47.8 123.4 6 26.8 – 48.3 123.5 5 53.6 – 48.8 123.6 5 20.3 – 49.3 123.7 4 47.0 – 49.8 123.8 4 13.6 – 50.3 123.9 3 40.1 – 50.7 123.9 17 18 6 45.7 – 47.3 124.0 6 12.1 – 47.7 124.1 5 38.5 – 48.3 124.1 5 04.8 – 48.8 124.2 4 31.0 – 49.3 124.3 3 57.2 – 49.8 124.4 3 23.3 – 50.3 124.4 2 49.4 – 50.7 124.4 18 19 5 58.4 – 47.2 124.6 5 24.4 – 47.9 124.7 4 50.2 – 48

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