## Latitude from Sun's Altitude, Declination and Hour Angle

Equal Altitudes

Robert Bergantino

Although the captains did not provide the sun's altitude for the meridian observations they took, they did record data from seven other observations from which the latitude of Clearwater Canoe Camp can be calculated. The data to calculate these latitudes come from the three Equal Altitudes observations (one each, morning and afternoon) and one observation for magnetic declination of the compass (variation of the needle). Unlike a Meridian Altitude observation of the sun–for which the observer does not need a chronometer or precise timepiece–to make a calculation for latitude from the sun's altitude, declination and hour angle, it is necessary to have the correct Local Apparent Time.^{1} This correct time generally comes from two Equal Altitudes observations taken a day apart, which give the chronometer's error at local apparent noon on each day and, from that, the chronometer's daily rate of loss or gain. Another element that is needed in these calculations is that the sun's declination for the time of the observation must be determined from the Greenwich Time of the observation. This requires making an estimate of one's longitude. Additionally, the sun's altitude must be for its true center, and this requires making corrections to the observed altitude for index error, refraction, parallax and, usually, the sun's semidiameter.

Because the latitude calculated from the forenoon and afternoon Equal Altitudes observations on a given day usually were nearly the same, they were averaged for that day in the following table. The latitudes are rounded to the nearest second.

In this table the latitude of 46° 30' 26" would place the camp at the base of the mountain on the north side of the river.

1. Local Apparent Time: This is the time that is shown by the sun (sun dial time) at the place where you are. It is not the time shown at a standard meridian such as Mountain Standard Time (unless you happen to be at 105° west longitude). Nor is it the time shown by a clock, because clocks keep mean or average time, which can differ from Apparent Time by more than 16 minutes.

Funded in part by the Idaho Governor's Lewis and Clark Trail Committee