NAVIGATION" CURTISS. 137 



that the knowledge of the latitude was not sufficiently reliable to 

 afford a determination of longitude. Nevertheless Sumner computed 

 his longitude, using the latitude by dead reckoning, and got a po- 

 sition 15 minutes east of that by dead reckoning. Then in order to 

 determine how far errors in his assumed latitude would affect the 

 computed longitude he assumed a second latitude 10 minutes farther 

 north and got a position 27 miles east northeast of the former posi- 

 tion and toward the danger. A third assumed latitude still farther 

 north gave a third point 27 miles still farther east northeast of the 

 first point. Upon plotting these positions on a chart they were seen 

 to be on a straight line and this line passed through Small's light 

 off the coast of Wales. Credit is due Sumner because he realized 

 then that anywhere on the line he had determined the altitude of 

 the sun at the time of observation would have had the value he 

 measured, and that such would be the case only on that line. He 

 therefore assumed that he was on that line and, keeping his course 

 east northeast along it, made Small's light in less than an hour. 

 After hours of uncertainty off a rocky lee shore in the midst of a 

 winter gale what must have been Captain Sumner's relief when the 

 lighthouse appeared ahead. Later it developed that at the time of 

 his uncertainty his latitude by dead reckoning was 8 miles too far 

 south and his longitude 45 miles too far west. The result to the 

 ship might have been disastrous had this wrong position been 

 adopted. 



In using Sumner's method in its simplest form, altitudes are 

 measured of two suitable objects in quick succession or of the same 

 object at two suitable times. Each observation gives a line upon 

 which the ship must be situated. The intersection of these two lines 

 of position gives the position of the ship. If the two observations 

 are separated in time and the ship is moving, dead reckoning must 

 be used to allow for the ship's change in position between obser- 

 vations. 



Important advantages of the line of position methods are not hard 

 to find. Every observation for position is treated in the same way. 

 The method makes clear to the navigator how much information 

 his observation actually yields. With available tables, including 

 Lord Kelvin's Sumner Line Table, the calculations may be com- 

 pleted entirely without logarithms and with a minimum amount of 

 work. When the value of the newer methods is realized by navi- 

 gators it is not to be doubted that calculations for position will be 

 based universally on the Sumner line. 



In considering the foregoing methods of fixing astronomically the 

 position of a ship it is evident that, always when the two elements 

 of latitude and longitude are determined at different times and fre- 

 quently when they are determined by Sumner's method, the navi- 



