[r-t] Fwd: "double" cambridge?

[Richard Smith]

Philip Earis replied, quoting Edward Martin:

> "Could someone please give me details of what was used in 
> 1752? and how do we know? I cannot find reference in any 
> of the 18th century books to which I have access"
>
> From www.methods.org.uk (at the end of the plain major collection):
>
> Eastern Bob -14-38-18-18-18-18-18-12 b 27.12.1747 Shoreditch  59/67
> Double Eastern Bob -14-38-18-78-58-16-18-12 d 12.1.1752 Westminster, St Margaret  59/67

Or with two (marginally) more familiar methods:

   Union         3.1.7.1.7.1.7.1.7.1.7.1.5.1 1256734
                 1728-02-17   Lawrence Jewry   RW 58/767

   Double Union  3.1.7.1.7.3.7.5.7.1.7.1.5.1 1273456
                 1771-03-01   Leeds, Yorks     RW 58/767

Edward Martin wrote:

> RAS's response has me very puzzled...  I respect his 
> opinions but why is it that when he asks: "Can you think 
> of any methods that were called 'Double' but that did not 
> have glide symmetry, then?  I'm not aware of any."

I think perhaps I wasn't very clear.  I meant that all of 
the examples I knew included glide symmetry amongst the 
symmetries possessed by the method.  Most methods named 
'Double', Double Norwich to take a concrete example, have 
three symmetries: palindromic, glide and rotational.

Modulo a few subtleties regarding mirror symmetry, it is 
possible to prove that if a method possesses any two of 
these three symmetries, then the third must also be present. 
However, as Phil's website shows, it is possible to have any 
a method one of the symmetries individually.

Lots of pre-20th century methods have just palindromic 
symmetry -- Plain Bob, Grandsire and Stedman, to pick three 
of the commonest.  So far as I know, none of these are 
called 'Double'.  A small number have just glide symmetry, 
and so far as I know they are all called 'Double'.  I know 
of no pre-20th century rotationally symmetric methods.

However, we should be careful relying on the methods 
collections as reliable sources as to the names of 
historical methods.  Historically, the Methods Committee 
hasn't been beyond a bit of revisionism when it comes to 
methods names.  So I would be interested in knowing how the 
contemporary sources actually referred to these methods.

> Actually I can find no examples of glide symmetry in 18th 
> cent books at all, but I have found both palindromic & 
> non-palindromic methods each with 'double' in their title

I would be interested in some examples of non-palindromic 
methods with 'Double' in their title.  The only two pre-20th 
century examples that I'm aware of are Double Eastern and 
Double Union.  (Double Newark and Double Wollaton Doubles 
could count, but I've not seen any evidence of these being 
pre-20th century.)  All of these have glide symmetry.

RAS