**Navigational Mathematics: Harrison and Bowditch**

John Harrison 1693 - 1776, England

Nathaniel Bowditch, 1773 - 1838, Massachusetts USA

"I never came across one of Laplace's *Thus it plainly appears* without feeling sure that I have hours of hard work before me to fill up the chasm and find out and show *how* in plainly appears."

### -Bowditch Quoted in F Cajori, *The Teaching and History of Mathematics in the United States*

**John Harrison** solved the "greatest scientific problem of his time" - that of keeping accurate time on the seas in order to be able to determine the longitude of a vessel. Prior to this invention and discovery, many people died on the seas, as they could not determine where they were located. Wikipedia has some nice pictures of artifacts.

**Nathaniel Bowditch** is known for undertaking a huge project to correct the mathematical errors contained in the Navigation Guides published up to his time, thereby saving many lives lost to published misinformation. His *New American Practical Navigator* (1802) began as a project to correct and extend the work of John Hamilton Moore, but in the end he made so many corrections and original contributions it became his own work. It is still in use today, and the text can be viewed online from links at the bottom of this Wikipedia article.

## Biographical Info

John Harrison biography sites:

http://www.royalnavalmuseum.org/info_sheets_john_harrison.htm

http://www.madehow.com/inventorbios/73/John-Harrison.html

http://www.pbs.org/wgbh/nova/longitude/

http://www.nahste.ac.uk/isaar/GB_0237_NAHSTE_P0354.html

Nathaniel Bowditch biography sites:

http://www-history.mcs.st-andrews.ac.uk/Biographies/Bowditch.html

A more readable bio, less technical: http://library.thinkquest.org/6169/nat.htm

## Activities and Links

The PBS site for the series "Longitude" based on the Dava Sobel novel is rich with activities related to Harrison's invention and navigational science / mathematics:

http://www.pbs.org/wgbh/nova/longitude/

There is a teacher's guide , an activity that includes quite a bit of math, and an interactive game to play "Find Your Longitude" and "Find Your Latitude."

Secrets of Ancient Navigation is written about here.

More extension activities are found here.

Ever wonder how the Global Positioning System (GPS) works? This extraordinarily complex system is actually based on some simple concepts.Play the GPS Game

Navigational math worksheets http://www.randommasters.com.au/navigation.php

Where Are We? Activities. High school site, but some is accessible to younger students http://pulse.pharmacy.arizona.edu/math/where_arewe.html

Navigational Math Activity for 6th-8th grades http://www.ion.org/satdiv/education/lesson4.pdf