Body Mapping

Reading a very good book "What every pianist needs to know about the body" by Thomas Mark, which I'd recommend warmly to every pianist and teacher. But there is one thing not right, I think: "The concept of the body map and the power of Body Mapping in improving movement and curing injury among musicians were the joint discovery of Barbara and William Conable" (Preface, p X).
I believe many people discovered the concept of body mapping before then.
Moshe Feldenkrais, to name but one, in his 1964 article Aspects d'une technique:l'expression corporelle, translated into English in 1988 as Bodily Expressions by Thomas Hanna, editor of Somatics magazine [and quoted in full in the book: Embodied Wisdom: Collected Papers of Moshe Feldenkrais, publ. North Atlantic Books, Berkeley, CA, 2010].

"The behaviour of human beings is firmly based on the self-image they have made for themselves. Accordingly, if one wishes to change one's behaviour, it will be necessary to change this image. What is a self-image? It is a body image; namely, it is the shape and relationship of the bodily parts, which means the spatial and temporal relationships, as well as the kinesthetic feelings..."

Yehudi Menuhin was an enthusiastic advocate of Feldenkrais, but admittedly the teachings are not specifically for musicians, who will need to apply them to their individual instrument.
An earlier book (1903), specifically for musicians is Artistic Piano Playing as taught by Ludwig Deppe, by Elisabeth Caland. Page 29 of the 1903 edition refers to "a mental map of the entire route from brain to finger tips". 

The edition I bought is printed by amazon.co.uk - yes, printed by amazon. You can decide for yourself whether the presentation is competent, or not. There is no vol. 2, btw.

Who was the greatest piano teacher of the 19th century?

The candidates for this prize must include Chopin, Liszt, Leschetizky, the lesser known Ludwig Deppe, and Rubinstein (Anton).
Form a teacher does one seek a cogent method, or the passing on of a bright flame, burning and hard to contain?
About Chopin we have many comments from pupils, collected in a wonderful book by Eigeldinger, which I came across quite by chance in the town where it was published when I was giving a recital in Neuchatel in 1989. Chopin book. Chopin's teaching methods were geared toward refined, musical, singing, supple playing. With his high prices and aristocratic manner, Chopin was the teacher of choice for the female Parisian aristocrat, as witness the dedicatees of the majority of his piano music (eg Madame la Baronne de Rothschild for Waltz Op 64). But he did not leave a strong team of publically performing disciples to carry the flame.
Liszt did attract many ambitious male pupils, including Sauer, Siloti, Rosenthal, da Motta; and with Liszt one has a stronger sense of a lineage of playing (via for example Siloti to Rachmaninoff, or d'Albert to Dohnanyi to Ervin Nyiregyházi) but descriptions of his classes, while inspiring, are not the sort of thing you can put in a bottle and replicate.
Likewise Leschetizky  and Anton Rubinstein - fine pianists both, but in an inspirational rather than a methodical style. Rubsinstein's star pupil Josef Hofmann asked him how he should play a certain note and got the reply 'play it with your nose for all I care - so long as it sounds right!" According to Artur Schnabel there was no such thing as  a Leschetizky method, but this did not stop some of Leschetizky's pupils attempted to cash in on his cachet! eg Leschetizky Method (?!)

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As of today I am awarding first prize to Ludwig Deppe, whose Deppe Method is EXCELLENT. It makes sense, and unifies disparate elements of the playing process, such as the needs for elegant movement, effortlessness, concentration on musical tone. Granted it was written over a hundred years ago; but the instrument of the piano has not changed, and his advice can be taken with a pinch of salt here and there. Having read probably 150 books on piano playing, I think his is the best.