# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Logarithms: adding ten**

**From:**Ed Popko

**Date:**2019 May 11, 03:44 -0700

Logarithms were used extensively in navigation computations in the 19th century.

The logarithm, base 10 for example, of the Sine of 45 degrees is a decimal and it's logarithm is a negative decimal:

SIN(45) = .707107 and its log is -0.150515.

Logarithms eliminated the multiplication and division, operations now acomplished with addition and subtraction. However, in the 19th century, there was a 'distaste' for doing calculations with negative numbers. A common practice was to add 10 to the log and use that form for computation, thus:

Sin(45) .707107

Log -0.150515

Log+10 9.849485 (adding 10 to a log is adding 10^10 or 10,000,000,000 to the common number)

To be consistent, all logs in the algorithm had to be treated the same way. At the conclusion of the sum of a number of such logs, the 10's were rejected and the log+10 looked up in a table to find the anti-log angle in standard notation form.

What is the Log+10 form of a logarithm called?

Ed