The 'Addison Scale' is an extension of the existing International Scale of River Difficulty.  It's purpose is to add precision to the International scale.

The International Scale serves to compare the difficulty of rapids in a general sense, and provides a more or less agreed-upon standard for reducing the variables of difficulty, danger, and consequences down to a single datum, expressed as a number.  The limitation of this system is that it leaves some ambiguity in the rating- a rapid may require the paddler only to execute moves that are class 3 in difficulty, but if the consequences of a mistake are severe, the rating may be bumped up a bit- meaning that some rapids' values are inflated, which in turn can lead to confusion about just what a given 'class' designation means.

By comparison, the Addison Scale uses 3 data to describe any given rapid-  The first represents the difficulty of the rapid, the second represents the consequences of the rapid, and the third represents the availability of rescue.

Difficulty: The first data is simply 'how difficult is the rapid to run', and the scale used goes from I to VI using the same criteria as the International Scale.  This data does not take into account the consequences of a mistake- it merely measures the skill level that is required to run the rapid.

Consequences:  The second data reflects the consequences, rather than the difficulty, of a given rapid or feature.  The Scale used goes from I to VI using the same criteria as the International Scale.

Remoteness: The third data reflects the availability of rescue, expressed in terms of how much time it would take for rescue to arrive.  The scale is as follows:

a) Rescue/Medical support is within 6 hours
b) Rescue/Medical support is between 6 and 24 hours away.
c) Rescue/Medical support is more than 24 hours away.

Putting it all together:  With these three data points we can describe a feature more precisely than we can with one data point- for example, a rapid with simple moves to avoid sieves that will kill you might be expressed as a 3.6.a, while a rapid with great difficulty but a clean washout might rate a 5.2.a.  Probably the chief benefits of this scale is that it provides a mechanism for avoiding 'inflated' ratings for rapids that feature disproportionate challenge or danger, and it provides a means of describing the remoteness of a run more clearly.

The International Scale:  For reference, here is a copy of the international scale of difficulty:

THE SIX DIFFICULTY CLASSES:

Class I: Easy. Fast moving water with riffles and small waves. Few obstructions, all obvious and easily missed with little training. Risk to swimmers is slight; self-rescue is easy.

Class II: Novice. Straightforward rapids with wide, clear channels which are evident without scouting. Occasional maneuvering may be required, but rocks and medium sized waves are easily missed by trained paddlers. Swimmers are seldom injured and group assistance, while helpful, is seldom needed. Rapids that are at the upper end of this difficulty range are designated "Class II+".

Class III: Intermediate. Rapids with moderate, irregular waves which may be difficult to avoid and which can swamp an open canoe. Complex maneuvers in fast current and good boat control in tight passages or around ledges are often required; large waves or strainers may be present but are easily avoided. Strong eddies and powerful current effects can be found, particularly on large-volume rivers. Scouting is advisable for inexperienced parties. Injuries while swimming are rare; self-rescue is usually easy but group assistance may be required to avoid long swims. Rapids that are at the lower or upper end of this difficulty range are designated "Class III-" or "Class III+" respectively.

Class IV: Advanced. Intense, powerful but predictable rapids requiring precise boat handling in turbulent water. Depending on the character of the river, it may feature large, unavoidable waves and holes or constricted passages demanding fast maneuvers under pressure. A fast, reliable eddy turn may be needed to initiate maneuvers, scout rapids, or rest. Rapids may require "must'' moves above dangerous hazards. Scouting may be necessary the first time down. Risk of injury to swimmers is moderate to high, and water conditions may make self-rescue difficult. Group assistance for rescue is often essential but requires practiced skills. A strong Eskimo roll is highly recommended. Rapids that are at the upper end of this difficulty range are designated "Class IV-" or "Class IV+" respectively.

Class 5: Expert. Extremely long, obstructed, or very violent rapids which expose a paddler to added risk. Drops may contain large, unavoidable waves and holes or steep, congested chutes with complex, demanding routes. Rapids may continue for long distances between pools, demanding a high level of fitness. What eddies exist may be small, turbulent, or difficult to reach. At the high end of the scale, several of these factors may be combined. Scouting is Recommended but may be difficult. Swims are dangerous, and rescue is often difficult even for experts. A very reliable Eskimo roll, proper equipment, extensive experience, and practiced rescue skills are essential. Because of the large range of difficulty that exists beyond class IV, Class 5 is an open ended, multiple level scale designated by Class 5.0, 5.1, 5.2, etc... Each of these levels is an order of magnitude more difficult than the last. Example: Increasing difficulty from class 5.0 to class 5.1 is a similar order of magnitude as increasing from class IV to Class 5.0.

Class VI: Extreme and Exploratory. These runs have almost never been attempted and often exemplify the extremes of difficulty, unpredictability and danger. The consequences of errors are very severe and rescue may be impossible. For teams of experts only, at favorable water levels, after close personal inspection and taking all precautions. After a Class VI rapids has been run many times, It's rating may be changed to an appropriate Class 5.x rating.