Similarly, Pub 229 provides a very large table of Hc and Zn for given LHAs and latitudes. In order to keep Pub 229 to only six volumes, the tables must be entered using only whole degrees of LHA and whole degrees of latitude.
We therefore select our Assumed Position, AP, to make this true. Remember that our AP just needs to be close to our actual position, maybe within a hundred miles or so. In this module we chose our Dead Reckoning position (DR) as our AP. However, if using Pub 229, you will need to select a different AP, because it is very, very rare that at the time of your sextant reading, your DR longitude and latitude would be at one of Pub 229's tabulated entry points. Therefore, we carefully select an AP to make this true. That is, we select a new longitude—near our DR longitude—so the LHA of the object is a whole degree. And we select a new latitude—near our DR latitude—so it is a whole degree. The resulting position is our Assumed Position, and it will differ from our DR. With this carefully selected AP, we can then use Pub 229 to look up the object's Hc and Zn.
Two tricky points. First, the Hc and Zn from Pub 229 are valid at the Assumed Position, not the Dead Reckoning position. So the azimuth line, intercept, and LOP are drawn from the AP, not the DR.
The second tricky point is that the AP is valid only for one object observed. If you observe three objects as you would do in a three-star fix, you will have three different APs. The reason is that our AP longitude is computed to make the LHA of the object a whole degree. Each object will have its own LHA, therefore we compute a new AP for each object.
One point of emphasis. The only reason you might use an Assumed Position that is different from your DR position is if you are using a book like Pub 229 to look up tabular values of Hc, Zn. In the examples in this module, we used the USNO web site, therefore everything was determined and plotted at our DR position.
The use of an Assumed Position that differs from a DR position is one of the trickier concepts in celestial navigation. If it seems unclear right now, do not worry about it. However, you will want to become familiar with it should you need to navigate using the publications such as Pub 229.