Solution to: ‘Round Cape Horn by way of the moon and sun’

The lower-limb sun sight should be relatively benign, but we will review the process nevertheless, so we can reinforce our understanding.

Hs 19 degrees 53.5 minutes

Dip (-) 4.3 minutes

App alt 19 degrees 49.2 minutes

3rd corr (+) 13.6 minutes

Ho 20 degrees 2.8 minutes

GHA 71 degrees 56.2 minutes

Inc and corr (+) 7 degrees 2.5 minutes

GHA 78 degrees 58.7 minutes

(-) Assumed longitude 29 degrees 58.7 minutes

LHA 49 degrees

I chose an assumed longitude of 29 degrees 58.7 minutes because it is closest to the DR longitude of 30 degrees W.

Declination is S 19 degrees 0.2 minutes, and the d correction is (-) 0.6 minutes

Dec. S 19 degrees 0.2 minutes

-0.3 minutes

Dec. S 18 degrees 59.9 minutes

Enter H.O. 249 Vol. 2, page 203:

Hc 20 degrees 3 minutes d Z 131 degrees

There is no d correction, as I rounded off the declination to 19 degrees.

Hc 20 degrees 3 minutes

Ho 20 degrees 2.8 minutes

Intercept is 0.2 minutes Away, as Hc is greater than the Ho.

Moon Sight

The reduction of a moon sight is not all that difficult — just cumbersome to those who are more accustomed to reducing a sun sight. The key to remember — and the directions are written in the Nautical Almanac — is to add the V correction to the GHA and either subtract or add the d correction for the declination, depending on whether the declination is increasing or decreasing. The time of the upper limb sight is 17:24:35. Height of eye is 20 feet, and there is no index error.

GHA 22 degrees 47.5 minutes V +14.0 Dec. S 5 degrees 50.1 minutes d 14.7 minutes
HP 57.0

Inc 5 degrees 52 minutes

+V (from Increments and corrections page xiv of the Nautical Almanac) +5.7

GHA 28 degrees 45.2 minutes

+360 degrees

-Assumed longitude 30 degrees 45.2 minutes

LHA 358 degrees

I add 360 degrees to the GHA when I subtract the assumed longitude to get a positive number. (You can see that the assumed longitude is greater than the GHA; therefore, we add another whole circle, 360 degrees, to the GHA so that we can get our LHA.)

We have now an assumed position of 33 degrees N by 30 degrees 45.2 minutes W.

The declination of the moon is listed as S 5 degrees 50.1 minutes. The d correction is subtracted, as the declination is decreasing as we can see by inspection. The d correction is -6 minutes, so the final declination is S 5 degrees 44.1 minutes.

The HP is the Horizontal Parallax and is used for the 3rd correction for the moon, which includes parallax, semidiameter and refraction.

To reduce the Hs to Ho, we do the following:

Hs 50 degrees 57.8 minutes

-dip 4.3 minutes

App alt 50 degrees 53.5 minutes

3rd corr + 46.3 minutes

+ 3.4 minutes for upper limb

51 degrees 43.2 minutes

30 minutes (for upper limb sight always subtract 30 minutes as per directions)

Ho 51 degrees 13.2 minutes Declination S 5 degrees 44.1 minutes

Now we can enter H.O. 249 Vol. 2, page 200. My assumed latitude is 33 degrees N and assumed longitude is 30 degrees 45.2 minutes

Hc 51 degrees 57 minutes d -60 Z 177 degrees

Go to Table 5 for 44 minutes of declination, which equals 44 minutes. This is subtracted from the HC as noted by inspection. The final Hc is 51 degrees 13 minutes.

Ho 51 degrees 13.2 minutes

Hc 51 degrees 13 minutes

Intercept is 0.2 Toward, as Ho is greater than the HC.

Whew! Look over what I have done and see if you can follow it. If you are unfamiliar with moon sights, go to Mixter�s or Bowditch and review the process. The final step in this process is to plot the position using the assumed positions of the sun and moon. The fix is right on the DR. Capt. McMillan was a good shot.

As always, contact me with any questions.

D: 0.02′ Toward

E: 33 degrees 01′ N by 29 56′ W