Quote:
Originally Posted by dlavery
The original measurement was given as "364.4 Smoots, plus or minus an ear." With this, we knew both the precision and the tolerance of the measurement. The original measurement was accurate, within the tolerance specified (noting that tolerance was determined by the equipment used for the original measurement - a unit of precisely one Smoot). The citation of "364.4 Smoots, minus an ear" would be incorrect, in that it implies a precision that does not actually exist. Furthermore, it fails to provide any indication of an acceptable tolerance (it is noted that it could be argued that the "minus an ear" phrase could be an indication of tolerance, but in that case it over-constrains the measurement by doubling the tolerance requirement - which I would find to be intolerable  ).
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I see your point and must acknowledge, in fact, my equation was in error.
I had made an assumption, for which I must apologize, that the weather conditions on that October day in 1961 (class of 1962) would have been quite warm. You see, where I live on the west coast, October afternoons can easily be in the mid 80's to upper 90's. I chose to use the "Smoot = (1/(364.4-ear))*(Harvard Bridge length)" equation assuming there would have been quite a bit of expansion of the bridge due to the temperature. Not knowing along which axis the ear was measured, I assumed,(there I go again), it's length. Approximating a 5' 7" tall man's ear to be 2.25", I figured this would be close enough to account for the assumed expansion. I then subtracted this amount, incorrectly I might add, to account for the assumed expansion. When in fact, instead of subtracting it from the divisor, it should have been subtracted from the product to yield a length that had been corrected for temperature. In other words, if my assumption was correct, the equation should have been Smoot = ((1/364.4)*(Harvard Bridge length)) - ear.
Now, based on your need for accuracy and tolerance, the equation would be:
Smoot = (1/(364.4 +/- ear))*(Harvard Bridge length), correct?
There, have I smeared enough mud on this to cover my error???