NAVIGATION 91 



place of drawing by ruler and compasses ; and it 

 is by calculation that the ship's place is found every 

 day at sea from the observations of altitude. The 

 ordinary mode of calculation is given in full in 

 every book on navigation and need not be repeated 

 to you by me. 



52. The clear and obvious mode of interpreting 

 the information derivable from a single altitude of 

 the sun or stars which I have put before you, 

 is due to Captain Thomas B. Sumner of Boston, 

 Massachusetts. It is not only valuable as giving 

 us a clear view of the geometrical process under- 

 lying the piece of calculation by logarithmic tables 

 which is performed morning and evening by the 

 practical navigator at sea, but it actually gives 

 him a much more useful practical way of working 

 out the results of his observations than that which 

 is ordinarily taught in schools and books of 

 navigation, and ordinarily practised on board ship. 

 It is too usual to wait for the noon observation 

 before working out the result of the morning 

 altitude. Instead of this, the Sumner line ought to 

 be calculated for each observation independently, 



