6. An evening twilight sight of three or four stars, preferably one in each quadrant. If these altitudes are taken correctly your position can be found to the dot.
7. A morning twilight sight for a fix or, at least, for latitude by Polaris.
8. The dead reckoning from noon to noon.
9. Distance run during the last 24 hours, from noon to noon
10. Distance to destination.
11. Set and drift of the current.
1. The A.M. Sun Sight
In order to make this a valuable sight for longitude it should be taken when the sun is on or as near as possible to the prime vertical. As the sun, in North latitudes, passes the prime vertical before sunrise in the winter, the following remarks do not hold for that season. In winter the only rule to follow is to observe the sun as soon as it is 10° or more above the horizon. In summer find out from the Azimuth Tables the local apparent time when the sun will bear 90°. Estimate, as closely as possible, the longitude you will be in the next morning when the local apparent time is as just found in the Azimuth Tables. This can be done by calculating the dead reckoning from the previous sight, or, what is even simpler, laying the distance off on the plotting chart. With this information find the W.T. corresponding to the L.A.T. mentioned above by some such formula as this: L.A.T. ± Lo. = G.A.T. ± Eq. T. (sign reversed) = G.M.T. ± C.C.(sign reversed) = C.T. - (C-W) = W.T. This will not be absolutely accurate, for the longitude you are in is only approximate, but it will be close enough for good results. This resulting W.T. will be the time to take the A.M. sight. About fifteen minutes before that time compare your watch with your chronometer to get the C-W. Also bring up the C.C. to date and make a note of it so that as much as possible of this detail work is accomplished before the sight is taken. Next, take your sextant and test it for index error. This should be done regularly before each series of sights as it is impossible to tell what may have happened when the sextant is lying idle, except by the above test. Now, with your sextant, watch and notebook, go to the place from which you have decided to take your observations and, at the proper watch time, start taking your altitudes. It is always advisable to take a number of sights, closely following each other, so that an error in one may be corrected somewhat by the others. Take at least three sights in close succession. At the same time have the log read and enter it in your notebook. An equally good method in fair weather is to secure the distance run from the revolutions of the propeller.
Having taken your sights, go to the standard compass and get a bearing of the sun, at the same time noting in your book the W.T. of the bearing and the compass heading of the ship. You are now ready to go below into the chart room and work out your position. What method shall you use? That depends upon your preference. You have missed the point of the previous lectures, however, if you forget that the New Navigation is based upon the Marc St. Hilaire Method, and this is undoubtedly the method your captain will prefer you to use if he is an Annapolis graduate. In this connection let me remind you again of the one fact, the oversight of which discourages so many beginners with the Marc St. Hilaire Method. The most probable fix, which you get by one sight only, is not actually a fix at all. Nor does any other method give you an accurate fix under like conditions. What the most probable fix is, and all it claims to be, is a point through which the required Sumner line is to be drawn. If your D.R. position happens to be only one mile away from the most probable fix, that is no assurance that the most probable fix is near the actual position of the ship. You may be 25 miles away from it. But the important information gained is that, though you may be 25 miles away, you know on what line you are, and when this line is later crossed with another line of position that fix will be accurate. "Two sights make a fix" is the whole matter in a nutshell.
2. The Compass Error