# Where did the notation for dimensions of a quantity come from?

The current SI Brochure defines the dimension of a certain physical quantity as something separate from its units, and treated in detail in its §2.3.3:

This is, by now, pretty bread-and-butter stuff in the handling of dimensional analysis, and the usage is extremely widespread (cf. e.g. this thread).

However, when looking things up for this question, which asks why the letter $$\mathsf J$$ was chosen as the dimension symbol for luminous intensity, I was extremely surprised to learn that this usage is extremely recent as far as the SI brochure is concerned: Over its almost fifty-year history, and nine editions, any talk of quantity dimension as something separate from the units is absent, all the way up to the 7th edition (1998), and it is only present in the 8th edition (2006) and the present 9th edition (2019).

Which then leads me to my question: how did this happen? Which is to say, what basis in the literature, both formal (say, CGPM resolutions?) and informal, was used to bring this in? What was the status of this distinction prior to 2006? How well-codified were these conventions at the time, and where were they documented? How and why did they make the leap to the standardized SI Brochure, and where is that process documented?

• I think it might be worth contacting the people who published the SI brochure. The use of M, L, T is very old. I searched Google Scholar and Google books, nothing comes up related to candela and the choice of letter J. – M. Farooq Aug 5 '19 at 16:36
• Also post this question is MathOverFlow. There is a gentleman by the name of Francois Zeigler who has amazing skills in finding the history of notations. – M. Farooq Aug 5 '19 at 16:37
• I suppose it evolved gradually, and one cannot pinpoint the date and the author. Maxwell in the first chapter of his Treatise on Electricity and magnetism discusses it at some length (as something which is not in common knowledge) and gives no references, but he makes no impression that he invented this himself. In 20th century a whole branch of science called "dimensional analysis" or "scaling" was developed, but the idea is very old. – Alexandre Eremenko Aug 5 '19 at 21:06