24. The altitude at the second sight is now calculated by using the assumed latitude and longitude corrected for run between sights which is obtained as follows: Entering the Traverse Tables with course S 50° W and the distance 54 miles, the corresponding difference of latitude and departure are, respectively, 34.7' S and 41.4' W. The difference of longitude corresponding to a departure of 41.4 and a middle latitude of 33° 30' is 49.7' W. Lat. in 33° 18.3' N Long. in = 136° 13.3′ E Computation for Altitude at Second Sight G. M. T., Sept. 16-19h 37m 88 Eq. of T. + 5m 138 G. App. T., Sept. 16-19h 42m 218 Long. (136° 13′ 18′′ E) in time = 9h 4m 53" L. App. T., Sept. 16-28h 47m 14s Or, Sept. 17 4h 47m 148 P. M. cos H. A. 71° 48′ 30′′-9.49443 NOTE. In determining the numbers corresponding to log A and log B the student must keep in mind the fact that 10 is understood to follow the values of log A and log B. Thus, log A 8.38919-10, or 2.38919, and log B=9.41607-10, or 1.41607. The student must remember this in order to avoid confusion regarding the position of the decimal point in A and B. 25. The first line of position by Sumner's method is now plotted on the chart, a representation of which is shown in Fig. 11. The sun's true azimuth S 40° W at first sight is projected from the point a in latitude 33° 53′ N and longitude 136° 44' 15" E, which is the first position obtained by Sumner's method. A line drawn perpendicular to the azimuth will be the first Sumner line. In the same manner the second Sumner line is plotted in latitude 33° 18.3' N and longitude 136° 14′ E, which is the second position obtained by Sumner's method. Then the first line is transferred parallel with itself in the direction of the run made between sights, S 50° W, 54 miles. The intersection of this line with the second Sumner line will give the true position of the ship by Sumner's method at the time the second observation was made. 26. To plot the lines calculated by St. Hilaire's method, the assumed, or dead-reckoning, position is used as a base. From this point b in latitude 33° 53′ N and longitude 137° 3′ E the first azimuth S 40° W is laid off as shown in Fig. 11. Since the observed altitude in this case is greater than the calculated altitude, the difference between the altitudes, 10 miles (also known as intercept) is laid off toward the observed body, and through the point c thus established, and perpendicular to the azimuth, is drawn the first line of position found by St. Hilaire's method. For the sake of convenience, this line may be named the first Hilaire line to distinguish it from the Sumner line. The second line of position by St. Hilaire's method is plotted in a like manner from the position e which is found by applying to the assumed position the difference of latitude and the difference of longitude due to the run between sights, as already shown in calculation for altitude at second sight. From this point e, along the azimuth line S 82° W, but in opposite direction, or away from the observed body, is laid off the altitude difference of 1 mile, since in this case the observed altitude is less than the calculated altitude. 27. The first Hilaire line is now transferred parallel with itself, a distance and in a direction equal to the course and distance run, and its point of intersection with the second Hilaire line will give the true position of the ship. It will be noticed that the true positions obtained, respectively, by Sumner's and St. Hilaire's methods differ slightly in longitude. This difference is due to logarithms and to the plotting of lines made purposely to separate the two sets of lines. By more rigorous computation and plotting, the lines of position by both methods will coincide. 28. Locating Second Plotting Point.-Advocates of the St. Hilaire method in some cases suggest the use of the first point of position for use as a base in the calculation of the second altitude as a substitute for the assumed latitude and longitude corrected for run between sights. Thus, if a, Fig. 12, is the assumed, or dead-reckoning, position when the first observation is made, a c the altitude difference, and c the first position point on the line m n, it is proposed to use c as the point from which to locate the second plotting point x, assuming a b to be the run between observations. In other words, instead of using the latitude and longitude of a, corrected for the run |