The course to be steered to allow for a set due to current or wind may be obtained by a graphical solution on the chart, though it will be preferable to do this on other paper, using a larger scale. (Fig. 38.) The direction and velocity of the set and the course and speed of the ship may be considered as two sides of a parallelogram of forces, of which the diagonal is the distance and course made good. To obtain the course to steer to reach a given point with a given current and speed of vessel, lay down the direction of the destination; from the starting point lay off the direction of set and the amount in one hour; from the extremity of this describe an arc with radius equal to the speed of the vessel in one hour. A line drawn from the extremity of the direction of set to the point of intersection of the arc and the course to be made good will give the direction of the course to be steered, and the point of intersection will also be the estimated position of the vessel at the end of the hour's run. #Methods of locating a vessel.# The principal methods used for locating the position of a vessel are by astronomical observations, by dead reckoning, by compass bearings, by ranges, by horizontal angles, by soundings, by vertical angles, and by sound. The full discussion of these methods pertains to navigation and pilotage, and they will be only briefly referred to here as to their graphical application to charts. #Astronomical methods.# There are a number of methods of obtaining the position of a vessel by astronomical observations. When the position is computed the chart enters into these only in the plotting of the final result, so that with one exception these methods will not be referred to further here. The elegant method discovered by an American seaman, Captain Sumner, in 1843, is in part graphical, to be worked out upon the chart. This method is based on the obvious fact that at any instant there is a point on the earth having the sun in its zenith and which is the center of circles on the earth's surface along the circumference of any one of which the sun's altitude is the same at all points. A short portion of such a circle may be considered as a straight line and can be determined by locating one point and its direction, or two points in it. This is known as a Sumner line. (Fig. 39.)