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The in-game help states that:

Connecting Cities to your capital by Railroad will give them a 25% Production bonus.

If the city in question is on a different continent, this would seem impossible. Does the link formed by a Harbor count for purposes of this bonus?

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If your harbor is connected via railroad to your capital, the harbor connection counts as a railroad. You'll have then to lay railroads from your harbor on the other continent to any inland cities.

In the following example B,C and D would receive the bonus, E would not.

                   ~ ~ ~ ~ ~ ~ ~ 
|A|============|B|~ ~ ~ ~ ~ ~ ~ ~|C|===========|D|
                   ~ ~ ~ ~ ~ ~ ~  |
                                  `------------|E|

In the next example no city would receive the railroad bonus.

                   ~ ~ ~ ~ ~ ~ ~
|A|------------|B|~ ~ ~ ~ ~ ~ ~ ~|C|===========|D|
                   ~ ~ ~ ~ ~ ~ ~  |
                                  `------------|E|

As DMA57361 pointed out, if the capital has a harbor, any other city with a harbor automatically receives the railroad bonus. In the next example, C and D receive the bonus, E does not.

                   ~ ~ ~ ~ ~ ~ ~
               |A|~ ~ ~ ~ ~ ~ ~ ~|C|===========|D|
                   ~ ~ ~ ~ ~ ~ ~  |
                                  `------------|E|

Legend:

 A : capital
 = : railroad
 - : road
 ~ : ocean
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  • 8
    This also works if your capital is on a coast and has a harbour, every other harbour city is "connected by railroad" and receives the bonus - even if you don't build a single hex of railroad.
    – DMA57361
    Nov 13, 2010 at 21:12

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