90 POPULAR LECTURES AND ADDRESSES. 



circles are called by Sumner circles of equal 

 altitude. The portions of them shown on your 

 working chart are conveniently called Sumner 

 lines. Now simply by dead reckoning estimate 

 the course and distance made by the ship in the 

 interval between the two observations. Take a 

 length equal to this distance, and by aid of a 

 parallel ruler place it in proper direction, with one 

 end of it on one of the Sumner lines, and the other 

 on the other. The two ends of the line show the 

 places of the ship at the instants of the two 

 observations. 



The process of drawing on a globe which I put 

 before you is, you must understand, merely put 

 by way of illustration of the principle. It would 

 be practically impossible, or at all events so 

 difficult as to be impracticable, to carry out the 

 construction at sea by means of compasses on 

 a globe, or by ruler and compasses on a plane 

 chart, with sufficient exactness to give the ship's 

 place as accurately as it can be determined from 

 the observations. Calculations by what is called 

 spherical trigonometry, therefore, must take the 



