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By accident the whole issue of dimensions has taken on a new meaning for
me based on some work my spouse is doing regarding early use of
wind-tunnels in this country and England. One problem was how to scale
up (pardon me Bob) the wind tunnel measurements to be useful on full
scale aeroplanes, since flight tests in those days were frequently
tragic.
The scaling committee of the National Physical Laboratory at Teddington
included the best minds in England, including as I recall Lord Rayleigh,
the director of the Cavendish Laboratory. Rayleigh wrote articles about
Dimensional Analysis, in which one could construct groups of variables
where were dimensionless, and so could be scaled.
I had not realized that this, apparently side-line in my physics course
which was used mostly for checking the accuracy of students
mathematical manipulations, and the physical legitimacy of statements,
had such a noble history.