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The two rows where the treble leads hand and back are commonly referred to collectively as the lead end. (In older books, the lead head is sometimes called the lead end.) What is important is the positions (places) of the bells at the lead head, as we now attempt to explain.
We explain the idea by example. Consider the start of Plain Bob Major. You will find it helpful to have your diary out to look at the method. Look at bell 3, and the first lead. Bell 3 hunts out to the back, hunts down to lead and then makes seconds place. The second lead head is 13527486. Now, notice that bell 3 is in 2nd position for this row (it is making 2nds). This means that bell 3 now "takes the place" of bell 2 for the next lead. What happens is that bell 3 now rings for the second lead the very same thing that bell 2 rang in the first lead. We say that bell 3 is now second's place bell. Bell 3 assumes the work of the "two" for the next lead. Compare the paths (blue lines) of bell 3 for the second lead, and bell 2 for the first lead, and you will see that they are the same.
This is the essence of the place bells concept. At each lead end, you "become" a certain place bell. Which bell you become is simply determined by the position you are in at the treble's backstroke lead (the lead head). You then ring for the following lead what that bell would have rung in the first lead. Therefore, all you need to know is the work of each bell during the first lead.
Instead of learning seven leads for one bell, you learn one lead for seven bells.
As another example, bell 2 goes in to lead, then hunts to the back, then hunts towards the front and dodges 3-4 down, moving into fourth's place at the lead head and so assumes the work of the "four" i.e., bell 2 becomes fourth's place bell. Similarly, bell 8 becomes seventh's place bell.
The very same applies to Cambridge. It is also made up of leads. One needs to learn what each bell does for the first lead. At each lead end, every bell becomes a certain place bell. Which place bell you become is determined by your position during the lead head. Say you are in N-th place during the leadhead, so you become N-th place bell. You then ring the work of that bell (bell N) for the next lead. You ring the blue line that bell N would ring in the first lead. Think of the method as being made up of leads, and at the end of each lead everybody switches around what place bell they are.
In Cambridge Major, the second lead head is 15738264. This tells you that bell 3 (which is of course 3rd's place bell for the first lead) becomes 4th's place bell for the second lead. Similarly, bell 2 becomes 6th's place bell for the second lead. Everything can be deduced just by looking at the positions at the lead head.
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