The original number in table 2-1 is also called an antilog. Notice that a number greater than one is a positive log. Any number less than 1, but greater than zero, is a negative log. Logs are also required between the numbers 1 and 10. Since the log of 1 is 0 and the log of 10 is 1, the numbers 1 through 9 are decimals. (See table 2-2.) Notice the relationships between numbers and their logs as follows: When numbers are multiplied, their logs are added. Example: 8 = 2 ´   4. The sum of log 2 and log 4 equals log 8: 0.30 + 0.60 = 0.90. When  numbers  are  divided,  their  logs  are subtracted.  Example:  3  =  6 ¸ 2.  Log  3  is  the difference between log 6 and log 2: 0.78 - 0.30 = 0.48. The previous discussion is provided to give you a general idea on how logarithms are derived. It is not necessary for you to memorize logarithms, or refer to the log tables. All scientific calculators have a "log" key that converts numbers to logarithmic form. You should become familiar with the functions of your calculator  before  proceeding  with  the  study  of photographic quality assurance. For more information on using logarithms, refer to the chapter on logarithms in  Mathematics,  Volume  1,  NAVEDTRA  10069. One    of    the    main    uses    of    logarithms    in photographic quality assurance is to take the numbers used to indicate exposure in characteristic curves and reduce them to a manageable form. For example, the sensitometer in your imaging facility is set on an exposure  time  of  1/100  second  and  provides  an illuminance of 80,000 lux (or meter-candles). The log exposure can be calculated easily as follows: E ´ T = H 80,000 (lux) ´ 1/100 (set) = 800 lux seconds The log exposure = the log of 800 or 2.90 When you convert exposure to logarithmic form, both density and exposure are on the same scale. A characteristic  curve  indicates  how  exposure  and processing  differences  affect  photographic  emulsions by comparing density and the log of exposure. To  describe  sensitometry,  you  must  become acquainted with several new terms and formulas. As a starting point, you should become familiar with the terms transmission, opacity, and density, or T, O, and D. TRANSMISSION Most photographic material, even clear film, does not transmit all of the incident light that is relevant to it. Transmission is a measure of the light-passing ability of a film or other medium. The transmission of  a  processed  film  refers  to  the  fraction,  or percentage, of incident light that passes through the film. In a formula, transmission is represented by a capital  letter  T.  The  formula  for  determining transmission is as follows: Table  2-2.—Common  Logarithms  Between  1  and  10 T =  Amount  of  transmitted  light Amount  of  incident  light The result is never more than 1/1, or 1.00. For example, when 10 meter-candles (mc) of light are incident (or falling) to a film and 5 mc is passing through it, the transmission is as follows: T = 5/10 or T = 0.50, or 50 percent. When 2 mc is transmitted, the formula reads T = 2/10 or 0.20, or T = 20 percent. OPACITY Opacity is the ability of a medium to absorb light. The  two terms,  transmission  and  opacity,  are  directly opposite  in  meaning.  Opacity  is  indicated  in  a 2-4