To follow up on Stephen Burr's talk, here's a bit more on place notation and blue lines, and some examples for you to have a go at too.
Let's start by drawing out the Minor method with place notation X 16 X 14 X 14 X 12.
Minor means six working bells and the first change is X, so, from rounds, all three pairs will swap over:
Next is 16, so the bells in 1sts and 6ths place (i.e. leading and lying behind) stay in the same places:
And the other two pairs swap over:
Then we get another X, so everyone swaps:
The next change has place notation 14, so places are made in 1sts (the lead) and 4ths places:
Then the other two pairs swap:
Another X and we start to see some dodging happening in 5-6:
Then another 14 means the bells in lead and 4ths stay where they are:
And the remaining pairs swap:
X next, so everyone swaps; they're still dodging in 5-6!
Finally, place notation 12, so the bells in the first two places stay in the same position:
And everyone else swaps:
And so this gives us what is called one lead of the method. Note that we haven't worried about any numbers yet; whatever row we start from, the lines on what is called the grid tell us where each bell ends up. Following along the line for the treble, we can see that it comes back to where it started at the end of the lead. It only went up to 4ths place, so this is classified as a Little method. But we find that the other bells haven't got back to their starting places.
Following the lines through the grid for the 2nd, for instance (in orange below), we find that it ends up in 4ths place. We can do the same for each bell to give this grid:
But we're not back in rounds yet; the bells have reached the row 164235. What happens when we carry on? We could draw out the changes using the place notation again, just as we did above, but we'd get exactly the same pattern of lines, just starting from 164235, so in fact we already have all the information we need in the diagram above.
We said that the 2nd had reached 4ths place at the end of the first lead. So for the next lead, the 2nd must follow whatever the 4th did in the first lead, as the pattern of lines in each lead is the same. We say the 2nd has become "4ths place bell". So if we add the 4ths's line (blue) onto the end of the work that the 2nd did in the first lead (orange), we get the following. The numbers in circles at the right of the diagram show where each place bell starts.
By the end of the second lead, the 2nd still hasn't got back to rounds; it's currently in 3rds place. So how does it know what work to do next? It looks at 3rds place bell, i.e. what the 3rd does in the grid, shown in green:
So, 5ths place bell next (in purple), which brings the 2nd to 6ths place at the end of the fourth lead. Then we follow the path of 6ths place bell (in black) and this brings the 2nd back to 2nds place.
But is it rounds? Are all the other bells back in their starting places too? Let's look at the sequence of place bells that the 2nd followed; 2nds, 4ths, 3rds, 5ths, 6ths:
Meanwhile, which place bells has, for instance, the 3rd been? It started as 3rds place bell, then became 5ths place bell, then 6ths place bell, and so on. Again, after five leads, it will be back where it started, having rung the work of each other place bell once. And the same is true for each bell on the circle. So after five leads, every bell is back where it started and we get rounds.
The blue line is usually shrunk a bit vertically, to fit in more easily. Here's how it's often shown, with a dot marking the start for each bell. The method is named Christ Church Little Bob Minor.
So it's easy to see that, for example, the 5ths starts by lying behind, then doing a triple-dodge in 5-6 down and becomes 6ths place bell.
Now, here's one for you to have a go at. It's a Doubles method, with place notation 184.108.40.206.220.127.116.11.345.1. Note that, being Doubles, you can never have a place notation of X, as not everyone can swap over, being on an odd number of bells. The dots in the place notation are just to separate each change; the first change has place notation 3, the next is 1, then 5, and so on. The 345 place notation is all at one change, though, meaning the bells in 3rds, 4ths and 5ths places all stay still, so just the front two bells swap.
Draw out the grid - it's easiest on squared or dotty paper. Then, from that, produce a blue line. The method should have four leads before getting back to rounds.
The answer is here.
Next we will look at a differential method.