# [r-t] Infinite Extension

Thu Mar 23 12:02:39 UTC 2017

```|There is a compliant extension of CS6 which goes at every fourth stage -
10, 14, 18,... but the first of these stages (10) has a three-lead course
(as does n=22). It consists of repeating the |last section twice each time
- x4x5x4x5, etc, with pivot bells increasing by four: 3, 7, 11, 15,...
although this may not be what Alan had in mind.

I guess that pattern is explained by the fact that it just misses every
other stage when the bells on the front are out of step. So really it's
still 3,5,7,9... just with the stages corresponding to 5,9,13... missing.
I was thinking more of an example where the pivot bell jumped by more than
2 places in just one stage increase, or more than 4 places in two stage
increases etc.
Ultimately though whether they exist or not doesn't really get us any
closer to what Mark is interested in as I think he's postulating that there
are no examples where the lead head group can't be determined by a simple
formula involving stage.

On 23 March 2017 at 11:50, Robin Woolley <robin at robinw.org.uk> wrote:

> Hi All
>
>
> Alan said:
>
>> It seems possible that one might be able to construct examples where the
>> pivot bell follows a pattern like 2,5,9,..
>>
> Yes, there are some (many maybe). Here's one.
>
> There is a compliant extension of CS6 which goes at every fourth stage -
> 10, 14, 18,... but the first of these stages (10) has a three-lead course
> (as does n=22). It consists of repeating the last section twice each time -
> x4x5x4x5, etc, with pivot bells increasing by four: 3, 7, 11, 15,...
> although this may not be what Alan had in mind.
>
> The Major is a 2-2-3 differential.
>
> Best wishes
> Robin
>
>
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