HOW COULD AN EXPLORER FIND THE POLE 93 



plorer must fall back on the method of Sumner's lines, and fortunately 

 they can be applied with special facility in the neighborhood of the 

 pole. 



Let us suppose then that an explorer is approaching the north pole 

 in the neighborhood of meridian 120 degrees. (See Fig. 2, where the 

 outer circle represents a circle one degree from the pole, and the 

 radiating lines are the meridians, degree being that of Greenwich.) 

 He determines the altitude of the sun when by his chronometer, let us 

 say, it is in longitude 30 degrees. He now works out his latitude on 

 the supposition that he also is in longitude 30 degrees; suppose his 

 results give an apparent altitude of 89 degrees 50 minutes. He lays 

 off that latitude on the 30th meridian at A, and draws a straight line 



270 



A A' at right angles to the latter; this line will practically coincide 

 with a part of the circle at all of whose points the sun has the ob- 

 served altitude at the time the observations were made; his position 

 is therefore somewhere on this straight line, and, guessing about how 

 far he has traveled from his last determined position, he can estimate 

 roughly where he is; but if bad weather has prevented observations for 

 several days, or the unknown drift of the ice has been strong, he might 

 be many miles wrong. 



If he should wait for six hours and make another similar observa- 

 tion of the sun's altitude when it is on the 120th meridian, he would 

 determine a second line on which he would be ; his true position would 

 then be at the intersection of these two lines. If the second observa- 

 tion determined an apparent latitude of 89 degrees 40 minutes, he 

 would lay off this latitude on the 120th meridian, draw a straight line, 

 BB', at right angles to the latter, and his true position would be at B; 



