# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Plotting charts**

**From:**Frank Reed

**Date:**2009 Nov 13, 21:56 -0800

Here's the instructions on plotting and using charts for Sumner Lines from the 1906 Bowditch (available on Google Books here: http://books.google.com/books?id=4GcDAAAAYAAJ). This is just about the time period when Sumner Lines were becoming standard navigation procedure in the US Navy. Contrary to the popular legend, they did not catch on soon after Sumner's original paper was published. "FINDING THE INTERSECTION OF SUMNER LINES. 381. The intersection of Sumner lines may be found either graphically or by computation. 382. Graphic Methods.-Each line may be plotted upon the chart of the locality in which the ship is being navigated and the intersection thus found. The details of the plotting will be obvious, whether the line is defined by two of its points, or by one point and its direction. This plan will commend itself especially when the vessel is near shore, as the chart in use will then probably be one of conveniently large scale, and it will be an advantage to see where the position falls with reference to soundings and landmarks. 383. When clear of the land it is often inconvenient to follow this plan; a large scale chart may not be at hand, it may not be desired to deface the chart with numerous lines, or the necessary space for chart work may not be available. In such a case, the following method is recommended, as it obviates the disadvantages of the other. To understand the principle of this method, suppose that the lines are defined by the latitude and longitude of two points of each, and consider that they are plotted on a chart which is constructed upon a sheet of elastic rubber. It is evident that if, while holding it fast in the direction of the meridians, we stretch this rubber along the lines of the parallels in a uniform manner until the length of each minute of longitude is made to equal a minute of latitude, the chart, while losing its accuracy as portraying actual conditions on the earth's surface, still correctly represents the positions of the various points in terms of the new coordinates which have been created, namely, those in which a minute of latitude is equal to a minute of longitude. Thus, if on the true chart a point is m minutes north and n minutes east of another, on the stretched one it will still be m minutes north and n minutes east, the only difference being that the minutes of longitude will now be of a different length; and if on the original chart the two Summer lines intersect at a point m minutes north and n minutes east (on the original scale) of some definite point of one of the lines, the intersection on the stretched chart will lie m minutes north and n minutes (of the new scale) to the east of the same point. A stricter mathematical conception of the stretched chart and its properties may perhaps be obtained by considering the chart of the locality to be projected (with the eye at the zenith) upon a plane which passes through one of the meridians and makes an angle with the plane of the horizon which is equal to the latitude; each minute of longitude will then be increased by multiplying it by the secant of the latitude, and thus becomes equal to a minute of latitude. From a consideration of the properties of this hypothetical chart it may be seen that the following rule may be laid down: If two or more Sumner lines be plotted by their latitude and longitude upon any sheet of paper, using a scale whereon latitude and longitude are equal regardless of the latitude of the locality, the intersection of those lines, measured by coordinates on the scale employed, correctly represents the intersection of the lines as it would be measured upon a true chart. It follows from this that we may plot Sumner lines upon any piece of paper, measuring the coordinates with an ordinary scale ruler, and assigning any convenient length for the mile; the larger the scale the more accurate will be the determination. Or, what is even more convenient, we may employ "profile paper," whereon lines are ruled at right angles to each other and at equal distances apart, in which case no scale ruler is needed. One caution must be observed in using this method; all longitudes employed on the paper for any purpose must be those of the scale, namely, one minute of longitude equals one minute of latitude. For instance, if the two Sumner lines be taken at different times, in bringing the first up to the position of the second by the intermediate run, that run must be laid down to scale; that is, the easting or westing must appear as so many minutes of longitude, not so many miles. To do this enter the traverse table with course and distance run, and pick out latitude and departure; then, by means of the middle latitude, convert departure into minutes of longitude and bring the first line to the second by laying off so many minutes of latitude north or south, and so many of longitude east or west. In the ease where the Sumner is defined by one position and its line of direction, it is not correct to lay down the angle to the meridian on the hypothetical chart, for all angles are distorted thereon. The best way is to find another position on the line by assuming a second latitude ten or twenty miles removed from that of the point given, entering the traverse table with the angle that the line makes with the meridian as a course, and abreast the latitude taking out the departure; convert departure into difference of longitude, and plot the second point by its coordinates from the first." -FER --~--~---------~--~----~------------~-------~--~----~ NavList message boards: www.fer3.com/arc Or post by email to: NavList@googlegroups.com To unsubscribe, email NavList+unsubscribe@googlegroups.com -~----------~----~----~----~------~----~------~--~---