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Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. This book is intended for the use of young men of limited mathematical training who hope to qualify as Ensigns in the United States Navy, or for officers in the Naval Reserve, or Merchant Marine. The text is clari fied by a far fuller use Of diagrams than in other works Of similar scope, for the author believes in graphic ex planations whenever these are possible. The work is Of a practical character and deals with the subject from the modern standpoint, leading up to an understanding of the value of Sumner lines and St. Hilaire's method. The endeavor has been made to use simple language and to avoid mathematical abstractions and exercises that are of little practical value to the navigator.