Those mysterious digits on M lenses

There is a lot of discussion about the meaning of the double digit figures on mounts of Leica M lenses. But before explaining the facts and ideas behind them, I have to make an observation that may upset some of you. The sources of info about Leica are large and varied and comprise published books, articles and a vast amount of discussions, from presumedly knowledgeable, but anonymous sources and an even larger amount of free floating texts on the internet (newsgroups, websites) that are very uneven in quality and authority.
In scientific research the situation is quite simple. Facts and theories are original if the writer/author is the first to present facts (experimental research) or create a theory: a new interpretation of known facts. Frauds excluded (and there are many in the scientific field) any serious researcher will acknowledge his sources by referring to previous texts or to his original published research data. So anyone can trace the history of the facts or verify its origin and authority.
In Leica lore this is not the case: in most cases you will find a report or a discussion or an explanation without any reference at all.
And without being able to verify what is being stated, anything goes. A recent example is the analysis of the distance from the bayonet flange to the film plane, which may be 27.8 mm or 27.95mm, depending on resources and interpretations or translations.
The topic of the double digit figures on the M mount is in the same vein. Explanations and figures are numerous, but is there any one who will acknowledge his source and so allows fore identfication of the original data or individuals who wrote about this?
In fact most discussions and explanations are based on a very few sources, Rogliatti, being the foremost one.
It would really help if the sources would be mentioned, as it is clear that most discussions are a mix of previous reports and articles. By not mentioning the sources, one simply perpetuates the myth and evades the possibility of being wrong.
Focal lengths groups: the dimensions.
It is well known and this info can be found among many writers, for example Rogliatti: Leica and Leicaflex lenses (2nd edition), that the tolerances in the manufacturing process of lens elements (distances between elements, some difference in curvature of surfaces, different refractive indices per charge of glass melting etc) will generate some differences in the actual focal length of the lens.
But we have first to establish the calculated the true calculated optical focal length of a lens. For the Summicron 2/50 (second generation) this is 52.02 and for the Summarit 1.5/50 it ois 52.16mm.
In the past the production process was not as accurate as it is today and a wider range of measured focal length could be found.
The older Elmar 3.5/50 as example has been recorded as ranging from 48.6 to 51.9mm in steps of about 0.3mm (not exactly. (Info from the book " 25 years Leica Historica" and the magazine of the Leica Historical Society UK). The newer Elmar 2.8/50 had only three groups: 51.6 and 51.9 and 52.2mm.
The older Summicron has the same groups: 51.6 and 51.9 and 52.2: a difference in distance of 0.3mm.
The Summilux has these groups: 51.0 (indicated as (10),; 51.14 (11); 51.3 (13); 51.45 (14); 51,6 (16); 51.75 (17); 51.9 (19); 52,05 (20) and 52,2 (22).
The Noctilux (current) has only 50.00 (00); the 1,2 version has : 51.75 (17); 51.9 (19) .
The 75 and 90 and 135 have even more different designations.
Sources: 25 Years Leica Historica and My book:Leica Lens Compendium. .
So one should be careful to differentiate between lenses and the same figures do not indicate the same differences or focal lengths.
Focal lengths groups: why.
It seems to have escaped most observers that Leica R lenses do not have these numbers on the lens. Still we may assume that the same tolerances and manufacturing processes are being used. So why M and not R?
The explanation is quite simple. The true focal length of a lens is a characteristic of the optical cell of the lens: every lens element has its own focal length (negative or positive) and the sum of every focal length of these individual lens elements determines the system focal length or the focal length of the lens. The variations between the focal length is different per lens type. When assembling a lens, one can try to compensate these tolerances and use lens elements with plus and minus figures to stay within specified ranges of focal length.
Having established an actual focal length per lens, one has to mount the lens, first in its proper focusing arrangement and secondly match the rangefinder curve that is calculated and machined for a specific focal length.
This is the essential point. A change in actual focal length has no influence on the length of the mount itself, but only on the steepness of the RF curve of the lens. That is why the R lenses do not have these numbers: here you focus on the ground glass.
But with M-lenses you focus by matching the alignment of the rangefinder patch with the extension of the lens governed by the cam of the lens.
The focal length groups then indicate the true focal length and the fact that the correct cam has been fitted to the mount to ensure correct focussing. The RF roller movement "assumes" a true focal length of 50mm.
The engineering complexities of the M body and its lenses are as fascinating as are the solutions.