WHEN using the formula, L = Z+d, for meridian altitude and reduction sights, the different precepts are not easy to remember, so much so, that often a projection on the plane of the meridian is drawn to show how the various elements should be combined. In addition, an approximate altitude must be calculated in order to find the height of eye correction in preparing a constant.
The following method, using the haversine-cosine formula, gets away from the usual precepts; all sights being worked alike in the case of the upper transit of any body. There is no separate operation required to calculate an approximate altitude. The work is extremely short and simple. The haversine-cosine formula for the calculation of the line of position is as follows:
hav z = (hav t cos L cos d) + hav(L~d)- When the body is on the meridian, t, the angle of the body from the meridian, becomes zero, the body bears north or south and the value, (hav t cos L cos d), drops out leaving:
hav z= hav (L~d) z= (L~d)