What is the formula for city connection income?

UPDATE The formula has changed as of the March 2011 patch, it is now

(city population * 1.1) + (capital population * .15) - 1 for each city connected to the capital, not including the capital.

• The Machu Pichu wonder increases the modifier by 20%, to (city population * 1.3) + (capital population * .15) - 1.
• Arabia increases the constant by 1, to (city population * 1.1) + (capital population * .15) (thanks WillfulWizard).

The economic overview also gives a far better explanation of how it is calculated - in other words, this question is now trivially solved by simply looking at that economic overview :)

Original answer below.

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Okay, I did a bit more testing, and bwarner's answer is almost accurate:

Each city, excluding the capital, provides (city's population * 1.25) + 0.01 gold per turn. Owning the Machu Pichu wonder increases the modifier by 20%, to (population * 1.5) + 0.01, for all the cities.

The capital does not provide any gold.

The 1.25 and 0.01 can be seen in the AssetsGameplayXMLGlobalDefines.xml file:

<Row Name="TRADE_ROUTE_BASE_GOLD">
    <Value>1</Value>
</Row>
<Row Name="TRADE_ROUTE_CAPITAL_POP_GOLD_MULTIPLIER">
    <Value>0</Value>
</Row>
<Row Name="TRADE_ROUTE_CITY_POP_GOLD_MULTIPLIER">
    <Value>125</Value>
</Row>

The economic overview also demonstrates these values.

I couldn't find any other factor which affects these values, and I checked different difficulty levels, different distances between cities, different city route type (road vs railroad, road/railroad vs harbor), different city health and whether it is occupied. Looks like it's solely the population.