Proprietary bike chain?
 

Recently my chain broke (when it comes off, I usually hook it partially on, and then rotate the peddles to make it go all the way on - I'm guessing this sideways pressure was beyond what it's designed to handle and led to it breaking - I didn't get to inspect it 'cause I had to run to catch the bus (right after my knee had jammed into the handlebar) and it was taken later). I note that a new chain on my old sprockets, causes the new chain to sort of ride up on the teeth of the sprocket and then jerk forward/backward (I can't remember exactly what happens). When I lined the old chain up against the new chain, I noticed that 10 links on the old chain was a shorter distance than 10 links on the new chain so I suspect this is the cause, rather than the chain-rings simply being worn. Unfortunately, I no longer have the old chain in my possession (I left it hanging over the pannier on my bike after it broke, and it had been removed when I went to inspect it the next day). So it seems, contrary to what Wikipedia says, there is no single standard size of chain (even if one is more common). The new chain that I bought was of the size 1/2 x 1/8. What do these numbers relate to (using a ruler, I can't match the dimensions to any of the numbers given. Can anyone advise where I can find a list of chain sizes smaller than this? I figure I can calculate the circumference of the sprocket and divide by the number of teeth to find the required size.

I'm not sure if it makes a difference but the bike is a Batavus Cambridge with a SRAM Super-7 internal gear hub but I don't know the date of manufacture nor how to determine it.

I don't really want to replace the sprockets because the front one is welded to the crank and I don't even know what misery the rear one has in store for me.

Your rear sprocket and possibly your chainring are worn out because you didn't replace your previous chain at the proper wear limit. Measuring your old chain is likely to yield some confusing numbers because it is worn. With a couple of rare exceptions, chains are standardized - you're just comparing an old chain with a new one.

Yeah, but the new chain has bigger links than the old one had, not the other way around. According to Sheldon Brown's website, the size of the links shouldn't even change - rather it's the wear on the inside of the chain that makes old links have more room inside. At least, that was my interpretation.

I just measured that the front sprocket has about one tooth per .46 inches (1.18 cm) of circumference (measured from trough to trough).

You're probably replacing a 3/32" chain with your new 1/8" chain. Yes, the links look differently, but the tooth profile that they engage is the same. The 1/8" chain should work on your 3/32 sprocket and chainrings, but it may be a bit noisy.

Edit: If the chain is riding up on the rear cog, you really should replace the cog, or you'll wear that new chain out pretty quick.

You are completely right about the chain wear.

I have never heard of a 1.18 cm pitch chain. I heard of 1 cm pitch chains - they're pretty impossible to find nowadays, but never heard of the kind you have.

The OP's measurement, 1.18cm = .465", was only an approximation. It's really 1/2" pitch chain (1.27 cm) which is standard for all current bicycles.

A new chain is longer than your worn chain? That doesn't make any sense to me. Can anyone think of a reason/situation where this would be true?

Some one doesn't know how to count the links and make it the right length and merely took it out of the box and tried to use it?:D

lol :) Nice try, but the OP was measuring 10 links against 10 links.

the difference in length comes form the wear on the brass bushings in the links. To make it easy to judge when to replace, Park (and others) makes a great measuring tool. Using a worn/stretched chain makes your cogs and rings wear quicker due to increased and uneven pressure fom th chain. If your parts are too worn you will have to buy new cassettes/freewheels and chainrings to avoid "skipping". Some say it's cheaper not to worry about it and let everything wear out 'till it doesn't wrk right and replace it all then. I don't suscribe to this theory myself, but it may have merit, as it depends on what you use, how you use it and the cost