## Variation of the Compass Needle

Observation of the Sun

© 2004 by Robert N. Bergantino

Lewis took two observations for Magnetic Declination six minutes apart after taking the PM Equal Altitudes observation on June 5. The time of the observations can be determined either from 1) the chronometer error at noon on the 5th and 6th or 2) by calculating the observation times from a) the octant latitude, b) the sun's estimated declination and c) the sun's observed altitude. Both methods produce times within several seconds of each other—a good check on the data.

The circumferentor (a 6-inch-diameter surveying compass) used to measure the bearing of the sun during this observation could be read only to the nearest½ arc minute. In addition, it is difficult to aim the surveying compass's sighting vanes directly at the center of the sun, even if using smoked glass to block the sun's glare. These difficulties can either re-enforce each other and make the reading worse or compensate for one another and result in a "good" observation.

During the observations, the sun's bearings obtained from the surveying compass were S76°W and S77°W. These bearings can be converted to azimuths of 256° and 257°, respectively. Using the octant latitude, the sun's declination and the sun's hour angle,^{1} the true azimuth of the sun at that time can be calculated.^{2} For the first observation the Magnetic Declination turns out to be 17°10'50"E and for the second 17°22'45"E. Because most hand-held compasses can be read only to the nearest degree, the results of these observations could be reported simply as 17°E.

At first glance the magnetic declination here of 17°E is something of a surprise considering that the captains' observations in October 1805 at Clearwater Canoe Camp, less than 25 miles to the northwest, produced an average magnetic declination of 18½°E. The difference may have been caused by local magnetic anomalies, including the expedition's knives, rifles and other equipment, or even from iron-rich basaltic rocks, especially at Clearwater Canoe Camp.

1. Hour angle = the difference in time from noon in hours ◊ 15.

2. Sine½ azimuth = {√ [cosine½ (z + l + d) ◊ sine½ (z + l—d)] ˜ (sine z ◊ cosine l)} where z = zenith distance (90°—sun's true altitude), l = latitude and d = sun's declination.

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