The other day I was reading the data plate on an electric motor:
HP : 1 1/3 Type : C
RPM : 1725 SF : 1.0
A : 12.3 PH : 1
V : 115 Hz : 60
This seems backwards relative to the way we would write things in the
physics lab:
1.333 HP
1725 RPM
12.3 A
115 V
60 Hz
A Philadelphia lawyer might argue that the A and V on the data plate
stand for amperage and voltage ... but that only goes so far. I'm
not going to buy horsepowerage or Hertzage or RPMage.
I'm not a historian, but I conjecture that the idea of "unit analysis"
(where the units are algebraic quantities, with their modern meaning)
is relatively new. I've seen the "backwards style" in old engineering
books. There's no doubt that the colons on the data plate are the
equivalent of equals signs. In old books I've seen formulas of the form
RPM = 28.75 * Hz
which is utterly backwards from a modern unit-analysis point of view.
We would write the conversion factor as 28.75 RPM per Hz.
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So, why mention this? Three reasons:
a) The weakest reason is that I'm mildly curious about the history.
Does anybody know when/where/how units came to be considered algebraic
quantities, in the modern fashion? There's probably a paper on this
somewhere in the history-of-science literature.
b) We should add this to the endless list of possible student misconceptions.
Life is hard enough when they show up with no idea how to use units, but
it is so very much harder when they show up with entrenched diametrically
backwards notions.
c) Even if the students have never encountered this before, at some point
in the game (not too early) we should warn them that they might encounter
backwards usage here and there.