NavList:

" A Guide Book to the Local Marine Board Exmination - Ordinary Examination" published in 1856 has a lengthy chapter called Simple Rules of  Arithmetic. It is very basic stuff. The "-" operand is introduced as a subtraction operation. It is not (as far as I can tell - I scanned the pages quickly) used  to define negative numbers.

However...... the chapter on logarithms states that numbers less than zero are negative numbers. The negative sign "-" is defined.  Bar notation is introduced and the difference between  bar2.678 and -2.678 is clearly explained - I understand it!  Tabular notation is introduced to avoid the "confusion that might arise in the additon and subtraction of  negative numbers."

A second mate  had to be 17 years of age (went to sea at 13?), have been at sea for four years, understand the  first five rules of arithmetic and understand the use of logarithms.  In 1856  it is probable that second mates had heard of negative numbers but if they undertood them or used them is another matter. When using "simple arithmetic"  he did not need negative numbers because N, S, E, W, Same, Different could be used instead.

Rule 1  To write in figures a number expressed in words.

Rule II To expressin words the number denoteed by a line of figures.

Rule III Addition

Rule lV Subtraction

Rule V Multiplication multiplier < 12   why????

Rule Vl  multiplication multiplier > 12

David C